Uncovering Differential Symptom Courses with Multiple Repeated Outcome Measures:
Interplay between Negative and Positive Symptom Trajectories in the Treatment of Schizophrenia
A dissertation submitted to the
Division of Research and Advanced Studies
of the University of Cincinnati
In partial fulfillment of the
requirements for the degree of
DOCTORATE OF PHILOSOPHY (Ph.D.)
In the Division of Epidemiology and Biostatistics
of the Department of Environmental Health
of the College of Medicine
2012
by
Lei Chen
M.D. West China University of Medical Sciences
M.S. University of Cincinnati
Committee Members: Paul Succop, PhD (Chair)
Kim Dietrich, PhD
Melissa Delbello, MD, MS
Haya Ascher-Svanum, PhD
“Influential ideas are always simple. Since natural phenomena need not be simple, we master
them, if at all, by exploring the limitations of simple ideas”
-- AD Hershey (1969 Nobel Prize winner in medicine)
ABSTRACT
Background: Schizophrenia is a highly heterogeneous disorder with positive and negative symptoms construed as distinct characteristic manifestations of the disease. Current antipsychotics work
primarily by relieving positive symptoms; while negative symptoms are thought hard to treat. However,
little is known about the heterogeneity and pattern of negative symptom response with respect to its linkage with the change in positive symptoms. This research work examined the temporal interplay be-
tween positive- and negative-symptom trajectories over a 1-year period in schizophrenic patients
under antipsychotic treatment, and evaluated the potential utility of patient subgroups defined by
the combined symptom trajectories.
Methods: This post hoc analysis used data from an open-label, randomized, 1-year pragmatic
trial of patients with schizophrenia spectrum disorder who were treated with first and second
generation antipsychotics in the usual clinical settings. Data from all the medications were
pooled with 399 patients having complete data on both the positive- and negative- subscale
scores from the Positive and Negative Syndrome Scale (PANSS). Individual-based, growth mixture modeling combined with a interplay matrix was used to identify the latent trajectory subgroups in term of both the negative and positive symptoms. Baseline demographics, clinical and
functional characteristics were examined among the above identified trajectory subgroups.
Results: The negative- and positive-symptom trajectory interplay matrix suggests changes in
negative and positive symptoms occurred mostly in tandem in the individual patient. Three major clinical subgroups were identified: (1) dramatic and sustained early improvement in both
negative and positive symptoms (DSI); (2) mild and sustained improvement in negative and
positive symptoms (MSI), with greater early improvement in positive rather than in negative
i
symptoms, and (3) no improvement in negative and/or positive symptoms (NI). Comparison
among the three trajectory subgroups indicates that at baseline, the DSI subgroup were less
likely to have substance use disorder; the MSI subgroup were psychopathogically less severe at
baseline; and the NI subgroup was associated with worse functioning .
Conclusions: The study demonstrated that 1) positive and negative symptoms are not necessarily independent, 2) there are identifiable subgroups of patients with similar symptom courses as
defined by the combined negative- and positive-symptom trajectories, and there exist clinical
differences at baseline that may permit identification of these subgroups a-priori. Further examination of the underlying biological determinants of these trajectory subgroups might be useful to
aid efforts of developing the targeted treatment for schizophrenia.
ii
iii
ACKNOWLEDGEMENTS
This work would not have been possible without the guidance, support, and patience of
many people, who in one way or another contributed and extended their valuable assistance in
the preparation and completion of this study.
First, I want to thank my advisor, my dissertation committee chair, Dr. Paul Succop, who
has been patiently provided opportunities and encouragement over the past ten years, who has
meticulously guided my training aimed to bridge medical research with advanced statistical
methodology, who has been a staunch supporter and sounding board throughout my time pursuing the PhD degree. I want to express gratitude to Dr. Haya Ascher-svanum who has been a
strong advocate of this project, who has inspired me with her wisdom, enthusiasm and dedication
in the schizophrenia outcome research, who has shaped, molded and gently prodded me, who has
been a constant source of positive energy for me and has provided a wonderful female role model. Her mentorship is greatly appreciated. I want to express gratitude to other Committee members, Drs. Kim Dietrich and Mellisa Delbello, who have provided kind consideration, new ideas,
fresh advice, encouragement, and especially the spirit of scientific excellence. Thank you for
your confidence in my abilities.
I want to express my sincere appreciation to Drs. Marepalli Rao, Amit Bhattacharya, Jareen Meinzen-Derr, and Stephen Ruberg who sat in my Qualify Exam Committee, who provided
thoughtful, critical comments that shaped the later development of the dissertation.
iv
My Special thanks go to Profs. James Deddens and Paul Horn from the University of
Cincinnati Math Department. Thank you to my teachers, my fellow graduate teaching assistants,
and my fellow classmates who not just helped build the sound mathematical and computer programming backbone, but also instilled the spirit of “Love what you do and feel it really matters”.
Also, I offer heartfelt thanks to my mentors and colleagues at Eli Lilly & Company who
have gone above and beyond to help me with career advice and study concepts: Drs. Joseph
Johnston and Douglas Faries. I would like to acknowledge the Lilly Schizophrenia Negative
Symptom Initiative Working Group, especially, Drs. Bruce Kinon, Virginia Stauffer, and Haya
Ascher-Svanum, for their advocacy of this project and for permitting me to work with data generated from the HGGD clinical trial. I would not have been able to proceed without this cohort
and offer gratitude to the statisticians, data management, scientific communication, patients,
nurses, physicians, and trial coordinators as well.
I wish to express my highest appreciation for my co-authors’ contribution to this work.
Haya Ascher-Svanum, Joseph A. Johnston, Bruce J. Kinon, Virginia Stauffer, Paul Succop, Tiago R. Marques, Shitij Kapur, and Haya Ascher-Svanum. Besides the writing of the articles, I
have enjoyed the conversations and the new perspectives you have taught to me.
I wish to thank the quality reviewers of my dissertation, Bruce Kinon, Sara KollackWalker, Douglas-Faries and Xiaomei Peng.
I would like to make a special reference to Mr. Peter Watson, who was my mentor and is
now my supervisor at Eli Lilly & Company, who has been a continuous support and role-model
for pursuing continuing education.
Last, but not least, I wish to avail myself of this opportunity, to express my thankfulness
to my husband, Shuolun Zhang, for his love, support, and understanding and complete faith in
v
my professional choices and personal growth. Thanks to my beautiful children, Kevin and Kate
Zhangchen who have always been my motivations for graduate study, who are always a source
of inspiration for new ideas. Thanks to my friends in Cincinnati and elsewhere who have always
been there no matter my up or down time. Thanks to my mom and dad who have been supportive
all the time. I’m grateful more than words can express.
vi
Table of Contents
CHAPTER ONE: INTRODUCTION AND OVERVIEW ............................................................. 1 1. 2. 3. Introduction and Specific Aims .......................................................................................... 1 Relevance to Public Health ................................................................................................. 4 Overview of the Dissertation .............................................................................................. 5 CHAPTER TWO: BACKGROUND ON SCHIZOPHRENIA ...................................................... 6 1. 2. 3. 4. 5. Epidemiology and Burden of Disease................................................................................. 6 Pathogenesis ........................................................................................................................ 7 Clinical Manifestation and Diagnosis ................................................................................. 8 Positive and Negative Symptoms of Schizophrenia ......................................................... 10 Instruments Assessing the Positive and Negative symptoms of Schizophrenia ............... 12 CHAPTER THREE: BACKGROUND ON GMM ...................................................................... 15 1. 2. 3. Latent Variable.................................................................................................................. 16 Structural Equation Modeling (SEM) ............................................................................... 16 Growth Mixture Modeling (GMM) .................................................................................. 18 3.1. The Expectation Maximization (EM) Algorithm ......................................................... 20 3.2. Diagnostic Criteria ......................................................................................................... 21 3.3. Modeling Diagram ......................................................................................................... 22 4. GMM and Latent Class Growth Analysis (LCGA) .......................................................... 25 5. Limitation of GMM and Related Coping Method ............................................................ 26 5.1. Local Maxima .............................................................................................................. 26 5.2. Distributional Assumption and Spurious Findings ........................................................ 27 5.3. Missing Data .................................................................................................................. 27 CHAPTER FOUR: THE LONGITUDINAL INTERPLAY BETWEEN NEGATIVE- AND
POSITIVE-SYMPTOM TRAJECTORIES .................................................................................. 30 1. 2. Introduction ....................................................................................................................... 31 Materials and Methods ...................................................................................................... 33 2.1. Patient Sample ............................................................................................................... 33 2.2. Measures ........................................................................................................................ 34 2.3. Statistical Analyses ........................................................................................................ 34 3. Results ............................................................................................................................... 35 3.1. Negative-symptom Trajectories ..................................................................................... 35 3.2. Positive-symptom Trajectories ...................................................................................... 38 3.3. Combined Positive- and Negative-symptom Trajectories ............................................. 40 3.4. Pearson Correlation Coefficient ..................................................................................... 43 3.5. Patient Characteristics and Patient-Perceived Medication Benefit ................................ 44 4. Discussion ......................................................................................................................... 45 4.1. Strength and Limitations ................................................................................................ 48 4.2 Future Direction .............................................................................................................. 49 4.3. Conclusions .................................................................................................................... 49 vii
CHAPTER FIVE: CONSTRUCT VALIDITY OF THE TRAJECTORY SUBGROUPS .......... 51 1. 2. Background ....................................................................................................................... 51 Methods............................................................................................................................. 51 2.1. Data source..................................................................................................................... 51 2.2. Measures ........................................................................................................................ 52 2.3. Statistical Analysis ......................................................................................................... 52 3. Results ............................................................................................................................... 53 3.1. Global Assessment of Functioning (GAF) at Baseline and 1-year Endpoint ................ 53 3.2. The 36-Item Short-Form Health Survey (SF- 36) at Baseline and 1-year Endpoint .... 54 3.3. Possible Predictors of the Trajectory Subgroups ........................................................... 55 4. Discussion ......................................................................................................................... 57 CHAPTER SIX: SIMULTANEOUS GMM ................................................................................. 59 1. 2. Methods............................................................................................................................. 59 Results ............................................................................................................................... 61 2.1 Trajectory Classes under Simultaneous GMM ............................................................... 61 2.2. Performance of the Simultaneous GMM ....................................................................... 64 3. Discussions ....................................................................................................................... 66 CHAPTER SEVEN: GMM WITH MISSING DATA ................................................................. 67 1. 2. Negative Symptom Trajectories ....................................................................................... 67 Positive Symptom Trajectories ......................................................................................... 70 APPENDICES .............................................................................................................................. 76 Appendix 1. Mplus Modeling Framework............................................................................... 76 Appendix 2. Positive and Negative symptoms of Schizophrenia ............................................. 77 Appendix 3. The Short Form (36) Health Survey ( SF-36) ...................................................... 78 Appendix 4. Global Assessment of Functioning (GAF) .......................................................... 80 Appendix 5. Frequently cited theories on the relationship between positive and negative
symptoms .................................................................................................................................. 82 Appendix 6. Data analyzing or suggesting the relationship between positive and negative
symptoms .................................................................................................................................. 83 Appendix 7. Definition of Deficit Syndrom and Primary/Secondary Negative Symptoms ..... 85 Appendix 8. Distribution of PANSS Negative and Positive Subscale Scores by Time ........... 86 Appendix 9. Trajectory Subgroups ........................................................................................... 89 Appendix 10. Negative-symptom Trajectories of 5-class Solution .......................................... 91 REFERENCES ............................................................................................................................. 93 viii
CHAPTER ONE: INTRODUCTION AND OVERVIEW
1.
Introduction and Specific Aims
Personalized therapy is becoming an ever-growing interest in the healthcare community
(Ruberg, Chen et al. 2010). With the ever-growing pressure from health care cost-containment,
and the potential of genomics to create more individualized treatments, the insurance and pharmaceutical industries have great interest to develop personalized medicine. This patient-centered
trend in healthcare poses a great demand for epidemiologists and biostatisticians to identify and
evaluate appropriate methodologies to address population heterogeneity in terms of disease manifestation and progression, and the predictors of the disease progression or outcome.
Growth Mixture modeling (GMM) is a promising new trajectory modeling technique that
permits investigators to understand the longitudinal features of disease progression or growth
trajectory(Muthen 2001). GMM allows unobserved heterogeneity among the subjects. Subgroups are not observed in the population but are inferred from the data. This approach has been
well accepted in the social sciences and was enthusiastically adopted by psychological researchers. This technique was recently employed in schizophrenia randomized clinical trials and has
provided a new insight about treatment response(Marques, Arenovich et al. 2011). Similar modeling (i.e., latent class growth analysis [LCGA]) has been used to reanalyze two negative alcoholism treatment clinical trials and the results revealed promising treatment effects for a subgroup of patients (Gueorguieva, Wu et al. 2007). Uher and colleagues (2009) demonstrated that
genetic markers had the ability to predict trajectories rather than a dichotomous outcomes class
membership. Thus trajectory analysis may allow for a more efficient treatment effect and pharmacogenetic analysis.
1
Chapter One: Introduction and Overview
Nevertheless, the empirical clinical implication of this promising statistical technique has
not been well understood and is under explored. GMM draws on finite mixture modeling
(Muthen 2002) and was developed in psychometrics under the framework of an extended structural equation modeling (SEM) latent variable framework. Since a latent variable is as much a
concept as an empirical fact, substantive expertise plays a crucial role in most stages of the modeling process (Bollen 1989). On the one hand, the statistical community has been debating the
robustness of this methodology; but on the other hand, the medical community is enthusiastically
deliberating the empirical applications of this novel approach.
The use of SEM in medicine can be traced back twenty-seven years when Dr. Succop and
colleagues from the University of Cincinnati first introduced SEM into medicine (Bornschein,
Succop et al. 1985; Buncher, Succop et al. 1991). Nowadays, more advanced computational
technology is emerging; programming software has become more sophisticated and easier to use
(Succop 2007; Succop 2009); and demand for individualized medicine is growing. We are on
the edge of extending the application of SEM latent variable analysis techniques, such as GMM,
to explore the clinical implication of this approach to personalized medicine.
In the arena of schizophrenia, it is well-known that this disease is highly heterogeneous.
(Tsuang, Lyons et al. 1990; McGrath 2008). Assessment of the disease is multi-axial (e.g. personality disorder, medical disorder, psychosocial problems, global functioning), symptoms are
multi-dimensional (e.g. positive symptoms and negative symptoms), and clinical outcomes are
heterogeneous.
Since the introduction of the first generation of antipsychotics in the 1950s and most of
the second generation of antipsychotics in the past two decades, management and treatment of
schizophrenia has progressed and improved tremendously, making it possible for patients with
2
Chapter One: Introduction and Overview
schizophrenia to leave institutionalized care, return to work, and lead normal lives. However,
relatively few patients are able to achieve symptom remission and recovery. Current antipsychotics work primarily in relieving positive symptoms of schizophrenia (e.g., hallucinatory behavior,
delusions) (Kapur 2003); but many patients continue to experience debilitating negative symptoms (e.g., emotional withdrawal, motor retardation) that limit their ability to function in the
community (Gourevitch, Abbadi et al. 2004; Lysaker and Davis 2004; Velligan, Alphs et al.
2009) . Controversies exist regarding the relationship between these two set of symptoms, as
well the underlying disease process (Addington and Addington 1991; Howes and Kapur 2009).
In our previous research, the individual-based growth modeling technique has been applied to schizophrenia clinical trial data to identify subgroups with a homogeneous treatment response pattern in terms of positive symptom score or total score (Case, Stauffer et al. 2010;
Marques, Arenovich et al. 2011; Stauffer, Case et al. 2011). However, the symptom trajectories
in terms of two concurrent repeated outcome measures (i.e., positive and negative symptoms)
have not yet been studied until now; nor has the temporal relationship between negative and positive symptoms been evaluated.
The hypotheses of this study are 1) in patients under antipsychotic treatment, the improvement of negative and positive symptoms is either inversely related or independent, and 2)
patients under antipsychotic treatment can be categorized into distinct subgroups in which the
longitudinal treatment response pattern is homogeneous in term of negative and positive symptoms. We also explored the application of GMM for detecting growth (e.g. symptom course or
disease prognosis) heterogeneity with two concurrent outcome measures. Specifically, we aimed
to:
3
Chapter One: Introduction and Overview

identify symptom trajectory heterogeneity in terms of negative and positive
symptoms in a cohort of patients with schizophrenia,

evaluate the temporal relation between the change in negative and positive symp-
toms,

assess the validity and potential utility of patient subgroups defined by the com-
bined symptom trajectories, and

2.
explore the empirical implications of the alternative GMM procedures.
Relevance to Public Health
Disease and treatment outcome heterogeneity is well-recognized in medicine. It has also
been recognized that statistical analyses conducted without attention to this heterogeneity may
fail to accurately depict the relationships that hold within any one of the groups, including important predictive relationships (Bauer and Curran 2003).
With the growing interest in personalized medicine, lines of development are emerging in
various scientific disciplines and fields of technology which could be combined to achieve a major reorientation of medicine (Ruberg, Chen et al. 2010). There is thus a strong need for analytical methods that are capable of discerning and testing hypotheses about the unobserved population subgroups or latent classes. This is especially true when the outcome assessments are multidimensional and longitudinal.
This dissertation reviewed the relevant trajectory methodologies, disease state of schizophrenia and innovatively applied GMM combined with the “matrix” method to a large cohort
of patients with schizophrenia(Tunis, Faries et al. 2006). We hope this research would inform
efforts to develop targeted treatment for schizophrenia; and at the same time, to contribute to
4
Chapter One: Introduction and Overview
bridging the gap between advanced mathematical methodology and general clinical research by
acknowledging strength of the methodology with the awareness of limitations when applied to
real-world data.
The novelty of this study includes 1) the combination of GMM with the clinician intuitive
“matrix” method; and 2) studying the temporal interplay of negative- and positive-symptom trajectories in patients with schizophrenia.
3. Overview of the Dissertation
This dissertation is presented in seven chapters. Chapter One, is an overview. Chapter
Two and Three are background introductions of the relevant disease state and mathematical methodology, respectively. Chapter Four is the application of GMM (combined with “matrix” method) in data from a 1-year clinical trial of patients with schizophrenia. Chapter Four is presented
in the format of a manuscript for a clinical journal publication. Chapter Five is an evaluation of
the validity and potential utility of symptom trajectory subgroups, and is presented in the format
of a poster presentation. Chapter Six explored the application of simultaneous GMM using the
same data as that in Chapter Four. Chapter Seven further explored the application of GMM with
missing data. Chapter Six and Chapter Seven are presented in the format of a methodological
study report.
5
CHAPTER TWO: BACKGROUND ON SCHIZOPHRENIA
1.
Epidemiology and Burden of Disease
Schizophrenia is a severe mental disorder involving chronic or recurrent psychosis and
long-term deterioration in functional capacity. It is among the most disabling and economically
catastrophic disorders, and is among the top ten of the World Health Organization’s Global Burden of Disease (Murray and Lopez 1996).
Schizophrenia affects about 7 per one thousand of the adult population (Kendler,
Gallagher et al. 1996). The annual incidence rate is 11 per 100,000 (Goldner, Hsu et al. 2002).
There are evidences that the prevalence of the disorder varies across populations, ethnic groups
and geographic regions(Torrey 1987). Schizophrenia is more common in men than in women
with a gender ratio of 1.4:1 (Picchioni and Murray 2007). Onset of schizophrenia generally occurs during the mid-20s for men, and late-20s for women, although earlier onset in childhood
and later onset in later adulthood do occur (Lindamer, Lohr et al. 1997).
The burden of schizophrenia is significant. The lifetime suicide risk among patients with
schizophrenia is 5 to 10 percent (Palmer, Pankratz et al. 2005) (Miles 1977). Schizophrenia is
associated with 20% reduction in life expectancy (Newman and Bland 1991). Mortality rates are
more than twice as high as the general population (age and gender standardized mortality ratio=
2.6) (Saha, Chant et al. 2007). Schizophrenia is highly comorbid with substance-use disorders. In
the US, patients with schizophrenia have a lifetime substance use disorder rate of 47 percent
(34% with alcohol use disorder and 28% with other drugs) (Regier, Farmer et al. 1990). A national survey study suggests that schizophrenia was significantly associated with low income,
unemployment, a marital status of single, divorced or separated; and urban residence (Kendler,
6
Chapter Two: Background on Schizophrenia
Gallagher et al. 1996). The trend toward higher prevalence in lower socioeconomic groups has
been attributed to the tendency of individuals with the disorders to become socially disadvantaged. The numerous variants of these factors might be responsible for the heterogeneity of this
disorder.
Schizophrenia is associated with significant social and financial burden. The impact of
schizophrenia on health care budgets is typically between 1.5 percent and 3 percent of total national health care expenditures (Knapp, Mangalore et al. 2004). Besides direct health care cost,
schizophrenia has wide-ranging indirect financial impact such as loss of work productivity,
family impact, criminal justice system, etc. It was estimated the overall cost of schizophrenia in
2002 in the US was $62.7 billion, of which, $22.7 billion is direct health care cost (Wu,
Birnbaum et al. 2005).
2. Pathogenesis
It is widely accepted that the pathogenesis of schizophrenia includes a combination of
genetic, developmental and environmental factors (Sawa and Snyder 2002) (Maynard, Sikich et
al. 2001). The concordance rate for schizophrenia between identical twins is 50%. (Tsuang 2000)
About 1500 genetic studies of schizophrenia have been conducted (van Os, Rutten et al. 2008),
but no consistent and reproducible genetic association has been found. It is hypothesized that
there is no single genetic determinant of schizophrenia risk, but that multiple genetic factors
work in combination to create varying degrees of vulnerability to the disorder(Allen, Bagade et
al. 2008).
A variety of environmental factors have been identified in the etiology of schizophrenia.
The environmental risk factors include prenatal exposure to viral infection (Munk-Jorgensen and
7
Chapter Two: Background on Schizophrenia
Ewald 2001), starvation (Susser, Neugebauer et al. 1996) (St Clair, Xu et al. 2005), and toxic exposure (Bresnahan, Schaefer et al. 2005). Exposure to psychoactive drugs in adolescence and
young adulthood is also associated with higher risk (Buhler, Hambrecht et al. 2002). From the
aspect of the molecular neurobiological mechanism, the dopamine hypothesis was one of the
most prevailing theories in psychiatry. The dopamine hypothesis conceived that hyperactivity of
dopaminergic projection from the midbrain to the anterior cortex is responsible for positive
symptoms, while negative symptoms are correlated with hypo-dopaminergia in the prefrontal
area (Kapur 2003; Howes and Kapur 2009). Currently available pharmaceutical treatments for
schizophrenia target the dopamine pathway. Another high profile hypothesis for the mechanism
of schizophrenia is the glutamate hypothesis which postulates the hypo-function of the NMDA
(N-methyl –D-Asparstate) receptor (Lewis and Gonzalez-Burgos 2006). There are currently several lines of drug development ongoing that target the glutamate neurotransmitter pathway.
3. Clinical Manifestation and Diagnosis
The clinical manifestation of schizophrenia includes positive symptoms such as delusions
and hallucinations, negative symptoms such as a flat affect or poverty of speech (First 2000), depression/anxiety symptoms and cognitive impairment; while positive and negative symptoms are
considered the core, characteristic symptom manifestation of this disorder.
A diagnosis of schizophrenia is based on the presence of symptoms, coupled with social
or occupational dysfunction for at least six months, in the absence of another diagnosis that
would better account for the presentation (First 2000). There are no pathognomonic features of
schizophrenia, nor are there confirmatory laboratory measures for the diagnosis and treatment
evaluation of schizophrenia.
8
Chapter Two: Background on Schizophrenia
The assessment is made on the basis of a pattern of psychotic symptoms and functional
deterioration established through clinical interview, observed and reported behavior and information obtained from family, friends and others in contact with the patient. Table 1 is the DSM-IVTR diagnosis criteria of Schizophrenia.
Table 1. DSM-IV-TR Diagnosis Criteria for Schizophrenia
A. Characteristic symptoms:
Two (or more) of the following, each present for a significant portion of time during a 1month period (or less if successfully treated):
(1) delusions
(2) hallucinations
(3) disorganized speech (e.g., frequent derailment or incoherence)
(4) grossly disorganized or catatonic behavior
(5) negative symptoms, i.e., affective flattening, alogia, or avolition
Note: Only one Criterion A symptom is required if delusions are bizarre or hallucinations
consist of a voice keeping up a running commentary on the person's behavior or thoughts,
or two or more voices conversing with each other.
B. Social/occupational dysfunction:
For a significant portion of the time since the onset of the disturbance, one or more
major areas of functioning such as work, interpersonal relations, or self-care are
markedly below the level achieved prior to the onset (or when the onset is in childhood or adolescence, failure to achieve expected level of interpersonal, academic, or
occupational achievement).
C. Duration:
Continuous signs of the disturbance persist for at least 6 months. This 6-month period must include at least 1 month of symptoms (or less if successfully treated) that
meet Criterion A (i.e., active-phase symptoms) and may include periods of prodromal or residual symptoms. During these prodromal or residual periods, the signs of the
disturbance may be manifested by only negative symptoms or two or more symptoms listed in Criterion A present in an attenuated form (e.g., odd beliefs, unusual
perceptual experiences).
D. Schizoaffective and Mood Disorder exclusion:
Schizoaffective Disorder and Mood Disorder With Psychotic Features have been ruled
out because either (1) no Major Depressive, Manic, or Mixed Episodes have occurred
concurrently with the active-phase symptoms; or (2) if mood episodes have occurred
during active-phase symptoms, their total duration has been brief relative to the duration of the active and residual periods.
9
Chapter Two: Background on Schizophrenia
E. Substance/general medical condition exclusion:
The disturbance is not due to the direct physiological effects of a substance (e.g., a
drug of abuse, a medication) or a general medical condition. F. Relationship to a Pervasive Developmental Disorder:
For a significant portion of the time since the onset of the disturbance, one or more
major areas of functioning such as work, interpersonal relations, or self-care are
markedly below the level achieved prior to the onset (or when the onset is in childhood or adolescence, failure to achieve expected level of interpersonal, academic, or
occupational achievement).
Adapted from DSM-IV-TR, 2000 (First 2000)
4. Positive and Negative Symptoms of Schizophrenia
One prominent concept of schizophrenia is the two-syndrome theory developed by Crow
(1980; 1980; 1985). In Crow’s theory, type I syndrome was characterized by delusions and hallucinations (positive symptoms), and an increase in the D2 dopamine receptor. Type II syndrome
was characterized by flattening of affect and poverty of speech (negative symptoms) and cell loss
in the temporal lobe structure. The two syndromes were regarded as relatively independent, but
could coexist in the same patients. More recently, Goghari and colleagues (2010) reviewed 25
task related functional magnetic resonance imaging studies, and found positive symptoms were
related to the functioning of the medial prefrontal cortex, while negative symptoms were related
to the functioning of the ventrolateral prefrontal cortex and ventral striatum (Figure 1). The linkage of the symptomatology domains with different underlying pathophysiology appears to hold
up the two-syndrome theory.
Figure 1. Relationship between Symptom Dimensions and Brain Activity
Positive symptoms, particularly persecutory ideation, were related to the functioning of the
medial prefrontal cortex. Negative symptoms were related to the functioning of the ventrolateral
prefrontal cortex and ventral striatum.
10
Chapter Two: Background on Schizophrenia
Note: PFC = prefrontal cortex; Medial temporal lobe = amygdala, hippocampus, and parahippocampus gyrus.
Adopted from Goghari, V. M., S. R. Sponheim, et al. (2010). "The functional neuroanatomy of
symptom dimensions in schizophrenia: a qualitative and quantitative review of a persistent
question." Neurosci Biobehav Rev 34(3): 468-486.
Currently available antipsychotics work primarily on blocking the dopamine D2 receptor
and relieving positive symptoms of schizophrenia (Seeman 2002). Negative symptoms are
thought to be more difficult to treat and may persist long after positive symptoms have been
significantly reduced (Velligan, Alphs et al. 2009). Negative symptoms have been previously
shown to be correlated with functional outcomes among schizophrenia patients (Arango,
Buchanan et al. 2004; Velligan, Alphs et al. 2009).
However, little is known about the longitudinal patterns of negative symptoms (i.e., timing and magnitude of change) or temporal linkage between negative and positive symptoms for
patient under antipsychotic treatment. Previous studies on the relationship between different
domains of symptoms have been mainly cross sectional in nature (Addington and Addington
1991).
11
Chapter Two: Background on Schizophrenia
5. Instruments Assessing the Positive and Negative symptoms of Schizophrenia
The Positive and Negative Syndrome Scale (PANSS) (Table 2) is a standard psychiatric
scale used for measuring symptoms of schizophrenia. It is widely used in clinical trials studying
psychosis. The scale has seven positive-symptom items, seven negative-symptom items, and16
general psychopathology symptom items. Each item is scored on an incremental seven-point severity scale (from 1=absent, 2=minimal, to up to 7=extreme) (The PANSS Institute). The positive-subscale score is calculated as the sum of seven positive items, and the negative-subscale
score is the sum of the seven negative items.
Table 2. Positive and Negative Syndrome Scale (PANSS)
12
Chapter Two: Background on Schizophrenia
Adapted from First Episode Network accessed @
http://www.fernonline.org/content/downloads/39/PANSS%20Scoring%20Criteria.pdf
The PANSS was developed in the 1980s as a well operationalized, drug-sensitive instrument that provides balanced representation of positive and negative symptoms (Kay, Fiszbein et
al. 1987; Kay, Opler et al. 1988). The psychometric property of PANSS had been studied and
proved reliable, valid and sensitive to change (Kay, Opler et al. 1988; Santor, Ascher-Svanum et
al. 2007). The PANSS have been widely used in the research of schizophrenia and is accepted
by the Food and Drug Administrative as the primary efficacy outcome for new drug applications
treating schizophrenic spectrum disorder (Cutler, Kalali et al. 2008; Kane, Assuncao-Talbott et
al. 2008; Nakamura, Ogasa et al. 2009).
Another widely used symptom assessment instrument is the Brief Psychiatric Rating
Scale (BPRS). There are two versions, an 18-item and a 24-item, and it is a clinician-based rating
scale. Ratings are made based on a 7-point Likert scale, from “Not Present” to “Extremely Se-
13
Chapter Two: Background on Schizophrenia
vere.” The scale was originally developed to measure changes in inpatients during clinical pharmacology trials, but is now used more broadly and can be accessed free of charge from the public domain (Ventura, Green et al. 1993).
14
CHAPTER THREE: BACKGROUND ON GMM
Growth mixture modeling (GMM) is a trajectory modeling technique, for which the patterns in the repeated measures reflect a finite number of trajectory types, each of which corresponds to an unobserved or latent class in the population (Bauer and Curran 2003). GMM could
be seen as a combination of mixed model repeated measures (MMRM) and cluster analysis
(Marques, Arenovich et al. 2011). From a psychometric point of view, GMM is a latent variable
model obtained via mean and covariance-structure structural equation modeling (SEM) (Muthen
2004).
The more general finite mixture model from which GMM was developed has a long history in the social science, and was further developed in psychology (Bauer and Curran 2003).
GMM was introduced in late 1990s and early 2000s under the extended SEM framework
(Muthen and Shedden 1999; Muthen 2001).
GMM is grounded on the assumption of growth (e.g. symptom or disease progression trajectory) heterogeneity. This modeling approach assumes that there exist a certain number of distinct pathways of growth, and therefore subjects can be grouped into a small number of distinct
clusters based on their growth profile (Bauer and Curran 2003). GMM employs both categorical
and random-effect continuous latent variables to capture population heterogeneity in the growth
(or disease progression). The categorical latent variables represent different curve shapes (i.e.
latent trajectory classes), while the class varying random-effect continuous latent variables capture heterogeneity among individuals within the class. Figure 2 is a visual representation of the
growth curves over time, and a GMM model diagram.
15
Chapter Four: The Background on GMM
Figure 1. Growth mixture modeling (GMM) paradigm
Adapted from Muthen, 2008
1. Latent Variable
Latent variables are unobserved variables. They are hypothetical variables and correspond to concepts. For example, intelligence, social class and industrialization are latent variables.
The antonym of a latent variable is an observed variable (or manifest variable, an indicator of a
latent variable). The observed variable contains random or systematic measurement error, but the
latent variable is assumed to be free of these(Bollen 1989).
In Muthen’s extended SEM framework, latent variables capture a variety of statistical
concepts, including random effects, missing data, sources of variation in hierarchical data, finite
mixtures, latent classes and clusters (Muthen 2002).
2. Structural Equation Modeling (SEM)
SEM is a statistical method for partitioning the variance in a set of interrelated multivariate outcomes into that which is due to direct, indirect and covariate (exogenous) effects
16
Chapter Four: The Background on GMM
(Buncher, Succop et al. 1991). Analogous to the traditional regression analyses which derive
estimates through minimizing the sum of squared differences of the predicted and observed dependent variable for each case, the SEM procedure minimizes the difference between the sample
covariance and the covariance predicted by the model. The fundamental hypothesis for the
structural equation procedures is that the covariance matrix of the observed variables is a function of a set of parameters (Bollen 1989).
The traditional SEM in psychometrics is focused on measurement error and hypothetical
constructs measured by multiple indicators (Muthen, 2002). Consider η=(η1, η2, … , ηm)` is the
latent endogenous variable vector, ξ=(ξ1, ξ2, …, ξn)` is the latent exogenous variable vector,
ζ=(ζ1, ζ2, …, ζm)` are the latent errors in the equation, B is a m by m coefficient matrix , and Г is a
m by n coefficient matrix. The SEM latent variable model could be written as
  B    
E ( )  0
E ( )  0
E ( )  0
Where
COV ( i ,  j )  0
where
i, j  (1,2,...m) i  j

is
uncorrelated with 
( I  B) is non sin gular
Consider x=(x1,x2,…,xq)` is the observed indicator of ξ , y=(y1,y2,…,yp)` is the observed
indicator of η, Λx is a q by n coefficient matrix, and Λy is a p by m coefficient matrix. The measurement model could be written as
Where
x   x  
y   y  
E ( )  E ( )  0


 , and 
uncorrelated with  ,  ,
and 
is uncorrelated
is
with  ,
17
Chapter Four: The Background on GMM
3. Growth Mixture Modeling (GMM)
Growth mixture modeling represents unobserved heterogeneity between the subjects in
their growth using both random effects (Laird and Ware 1982) and finite mixtures (McLachlan
and Peel 2000). This allows different sets of parameter values for mixture components corresponding to different unobserved subgroups of individuals, capturing latent trajectory classes with
different growth curve shapes (Muthen and Asparouhov 2008).
GMM is one of the applications of the extended SEM that integrates the psychometric
modeling idea with mainstream statistics. It is a longitudinal data analysis technique that combines the use of continuous (e.g. growth parameter) and categorical (e.g. subgroup membership)
latent variables.
Let yi denote a set of repeated outcome measures (e.g., PANSS positive- or negativesubscale scores) for individual i, xi denote a vector of time-invariant covariates, ci represent the
unobserved subpopulation membership for individual i (cik= 1 if i belong to class k [k=1, 2…k]).
Conditioning on the subpopulation membership k, a growth mixture model with quadratic
growth effect could be written as
yi   k i   i
Where
yi  ( yi1 , yi 2 , ....... yit )
[ yi | ci , xi ] is
(1)
represents the repeated outcome
N t ( i ,  i )
18
Chapter Four: The Background on GMM
i  (0i ,1i ,2i ) represents the continuous latent variables for the intercept, linear
slope and quadratic slope separately (the growth parameters)
 i is N (0, k ) , Θk is a t by t covariance matrix
1 0

1 a 2

 k  1 a3
. .
. .
1 a
t

0

a22 
a32 

. 
. 
at2 
represents the constant matrix of time scores
i   k  k xi   i
Where
(2)
 k  ( 0 k ,  1k ,  2 k ) represents the intercept of η for each c class
xi=( x1, x2,…, xq)` represents covariates
 i is N (0, k ) , Ψk is a 3x3 covariance matrix
 11k

k   21k
 31k

 11k . .  11k 

 22 k . .  2 qk 
 32 k . .  3qk 
For a given model solution, each individual’s probability of membership in each class can
be estimated through a multinomial logistic regression model
e  0 k  1 k xi
p (cik  1 | xi )  k
 c 1e  0 c  1c xi
(3)
The above model draws on that of Muthen and Shedden (1999), and Muthen (2002).
19
Chapter Four: The Background on GMM
3.1. The Expectation Maximization (EM) Algorithm
GMM employs the EM algorithm for parameter estimation. A bracket denotes the probability or density function of a vector, the observed-data log likelihood is
n

L 
log
y i
log
i1
| x
i

Where [yi|xi] is a mixture distribution defined as
K

[c
k 1
 1 | x i ][ y
ik
[ y
Where
i
| c
i
| c
 1, x i ]
ik
 1, x i ] 
ik

i


k
(

i


k

k
k
 
 k
N
k
( 
t
i
, 
i
)
x i )
 
k
Muthen and Muthen (2001) use an EM algorithm with c viewed as missing data, so that
the complete-data log likelihood is
n

i 1
(log[ c i | x i ]  log[ y i | c i , x i ] )
The EM algorithm maximizes the expected complete-data log likelihood given the data
on x and y. The E step computes the posterior probability for class membership,
p ik  p ( c ik  1 | y i , x i ) 
p ( c ik  1 | x i )[ y i | c ik , x i ]
[ yi | xi ]
20
Chapter Four: The Background on GMM
Maximizing the expected complete-data log likelihood leads to a separate M step for each
of the two model parts: c related to x, and y related to c and x. The maximization for c related to
x leads to
n

log[
c
i1
i
| xi] 
n
k
i1
k 1
 
p
ik
log
P (c
 1 | xi)
ik
The maximization for y related to c and x leads to
n

log[
i1
yi | ci, xi] 
n
k
i1
k 1
 
c ik log[
y i | xi ]k
So that the maximization considers
E (
n

i1
log
y i
| ci, x
i
|
yi, xi) 
n
k
i1
k 1
 
p
ik
log[
y
i
| xi ]k
3.2. Diagnostic Criteria
To compare models with different number of trajectory classes, the Bayesian information
criterion (BIC) (Schwarz 1978) is calculated as
BIC = –2logL + h × ln n
Where h is the number of parameters and n is the sample size. The lower the BIC, the better the
model and differences of 10 or more are usually considered as evidence favoring one model over
another (Raftery 1995).
A sample size adjusted BIC (Sclove 1987) is calculated as
21
Chapter Four: The Background on GMM
n2
24
It has been well accepted in the latent mixture model, BIC is better than Akaike informaaBIC  2 log L  h ln
tion criteria (AIC). However, there is an inconsistent finding comparing BIC vs. aBIC. In a simulation study (Yang 1999), it is suggested that sample size adjusted BIC gave superior performance for latent class analysis models. However, in another simulation study (Nylund, Bellmore
et al. 2007), it has been demonstrated the aBIC outperforms BIC.
Likelihood-based tests was used to quantify the likelihood that the data can be described
by a model with one less class and a small p-value (eg smaller than 0.05) indicates that the additional class significantly improves fit over a model with fewer classes. A likelihood ratio test
(LRT) is formulated as below
LRT = 2*[logL(model 1) – logL(model2)]
where model 2 is nested within model 1
Lo-Mendell-Rubin likelihood-ratio test (Lo, Mendel et al. 2001) was usually used. Due
to the boundary conditions, the LRT does not have a chi-square distribution when testing k-1
class model against k-class model. A bootstrapped likelihood ration test (BLRT) was recommended as accurate, robust test (Nylund, Bellmore et al. 2007).
3.3. Modeling Diagram
3.3.1 GMM combined with the ‘matrix’ method.
This dissertation conducted GMM analyses on the two outcome measures separately, and
generated an interaction matrix of the two outcome trajectories (referred to ‘matrix” method in
this dissertation). This approach incorporates the data-driven method of GMM and a qualitative
evaluation of the trajectories matrix, and may enhance data interpretation.
22
Chapter Four: The Background on GMM
The model diagram is illustrated in Figure 2 using the PANSS positive and negative
symptoms of schizophrenia as an example.
Figure 2. GMM model diagrams for positive and negative symptoms
a. Model on positive-subscale scores
y11
y12
i1
s1
……
y1t
q1
c1
b. Model on negative-subscale scores
y21
……
y22
i2
s2
y2t
q2
c2
y1t indicates the PANSS positive-symptom
subscale score at time t
y2t indicates the negative-symptom subscale
score at time t
c1 indicates the latent categorical variable of
subgroup membership in terms of the positive-symptom trajectory.
c2 indicates the latent categorical variable of
subgroup membership in terms of the negative-symptom trajectory.
i1, s1 and q1 indicate the latent intercept,
slope and quadratic coefficients, respectively,
for the positive-symptom trajectory
i2, s2 and q2 indicate the latent intercept,
slope and quadratic coefficients, respectively,
for the negative-symptom trajectory
After classifying each individual into his/her most likely class, we employed the innovative “matrix: method, with each entry of the matrix representing the mean trajectory of individuals classified in the corresponding trajectory classes of y1 and y2 (details will be presented in
Chapter Four).
23
Chapter Four: The Background on GMM
Hypothetically, this method is logically straightforward, and visually interpretable; thus,
is intuitive to a researcher’s judgment process. Results from this method could serve as the substantive basis for the more sophisticated modeling methods.
3.3.2. Simultaneous GMM
The goal of implementing simultaneous GMM is to identify the trajectory classes with
two outcome measures in one modeling procedure. The modeling diagram is represented in Figure 2 using positive- and negative-symptoms of schizophrenia as an example.
Figure 3. Bivariate simultaneous GMM model diagram
y11
y12
……
i1
s1
i2
s2
y1t
q1
c
q2
y21
y22
……
y2t
y1t indicates the positive-symptom subscale score at time t
y2t indicates the negative-symptom subscale score at time t
c indicates the latent categorical variable of subgroup membership in terms of both the positive- and negative-symptom trajectories.
i1, s1 and q1 indicate the latent intercept, linear slope and quadratic slopes, respectively, for the
positive-symptom trajectory.
i2, s2 and q2 indicate the latent intercept, slope and quadratic slopes, respectively, for the negative-symptom trajectory.
24
Chapter Four: The Background on GMM
The advantage of this simultaneous modeling method is obtaining subgroup membership
in one step of modeling procedure incorporating two outcome measures. However, literature on
the performance of this model is limited. In Chapter Six, we compare the results from this simultaneous model with that from the original GMM+MATRIX method.
4. GMM and Latent Class Growth Analysis (LCGA)
Latent class growth analysis (LCGA) is another trajectory analysis technique developed
by Nagin and colleagues (Nagin and Land 1993; Nagin 1999; Nagin and Tremblay 2001). Opposed to GMM, LCGA assumes fixed growth factor for each trajectory class. In another words,
individuals within a class are assumed to be homogeneous.
LCGA could be viewed as a special case of GMM in which the growth factor effects are
fixed. Table 1 provides a brief comparison between GMM and LCGA
Table 1. Comparison between GMM and LCGA
Original Developer Growth Mixture Modeling (GMM) Muthén Latent Class Growth analysis (LCGA), a special case of GMM Nagin Software M‐plus Assumption Parametric model: multivariate normal distribution Allow with‐in class variation SAS procedure Proc Traj (free download) Non‐parametric model of the growth factor Individuals within a class are assumed to be homogeneous BIC Modeling on trajecto‐
ry class Test for latent class Missing data BIC, BLRT(bootstrapped para‐
metric likelihood ratio test) Allows missing data under the premise MAR Does not allow missing data 25
Chapter Four: The Background on GMM
In brief, compare to LCGA, GMM has the advantage of a broader coverage of growth
mixture modeling. In addition, LCGA typically requires many more classes to fit the same data
and often several of the classes represent only minor variations in trajectories and not fundamentally different growth forms (Muthen 2006).
5.
Limitation of GMM and Related Coping Method
5.1. Local Maxima
GMM employs the EM algorithm for parameter estimation. One difficult with the EM
algorithm is local maxima. As a perfect scenario, log likelihood should increase smoothly and
reach a stable maximum (Case 1 in Figure 4). However, local maxima arise as in case 2, 3 and
4; thus multiple solutions are often found. In this dissertation, I adopted Muthen’s recommendation of checking local maxima through running the model with more than one set of starting values to see if convergence can be obtained at another set of parameter estimates, and to select the
solution with the largest log-likelihood value.
Figure 4. Local maxima of log likelihood
26
Chapter Four: The Background on GMM
Adopted from Mplus training handout, Muthen and Muthen(2008).
5.2. Distributional Assumption and Spurious Findings
As mentioned at the beginning of this chapter, GMM is a finite mixture modeling technique. Finite mixture modeling was developed for two purposes: 1) to identify qualitatively distinct classes of individuals in a population, and 2) to approximate a complex but homogeneous
distribution with a small number of simple component distributions. These two purposes are distinct but difficult to distinguish mathematically (Bauer and Curran 2003). The latter case could
lead to spurious findings. Muthen (2002) recommended that GMM should be carried out by
comparing the empirical trajectories with those from existing empirical data or theory.
5.3. Missing Data
Missing data is a common problem in clinical trials (Shih 2002). This is especially true
in long-term schizophrenia trials, when patients drop out without further measurement
(Lieberman, Stroup et al. 2005). In the previous section, we pointed out that one of the advantages of GMM is that it allows missing data under the assumption that the data are missing at random (MAR). What does MAR mean?
27
Chapter Four: The Background on GMM
Below is a description of the various missing data mechanism and the related mathematical representations.
Consider y is the outcome variable, and m is the missing data indicator.
Missing completely at random (MCAR) refers to the situation in which the events that lead to any
particular data-item being missing are independent of both observable variables and of unobservable parameters of interest.
P(mi | yiobs, yimis) = P (mi)
None of the variables yiobs, yimis have an effect on the missing data patterns. The set of
complete cases is a random sub-sample of the intended sample (Little and Rubin 2002).
Missing at random (MAR) refers to that the missing quantity depends on the other observed
quantities, but does not depend on the unobserved quantity itself.
P(mi | yiobs, yimis) = P (mi| yiobs)
Not missing at random (NMAR) refers to non-ignorable missing or informative missing. The
missing quantity depends on the missing data itself. Both the observed and unobserved quantity
could have an effect on the missing data.
P(mi | yiobs, yimis) = P (mi| yiobs, yimis)
As for the standard use of the mixed-model for repeated measures, GMM brought the
great advantage that the full sample could be used in the analysis under the assumption that the
data are missing at random (MAR). However, some researchers call this assumption into question. Studies have shown that dropouts are not random but represent real information
(Rabinowitz and Davidov 2008). In schizophrenia trials, patients that dropped out before the end
of the trial showed a worsening at the visit prior to the end of their participation (Kinon, Ascher28
Chapter Four: The Background on GMM
Svanum et al. 2008). Thus, cautions are warranted in interpreting the advantage of GMM in term
of handling missing data under the MAR assumption.
29
CHAPTER FOUR: THE LONGITUDINAL INTERPLAY BETWEEN NEGATIVE- AND
POSITIVE-SYMPTOM TRAJECTORIES
Abstract
Objectives: Positive and negative symptoms are often construed as distinct and orthogonal factors. We examined the longitudinal interplay of positive- and negative-symptom trajectories in a
large cohort, and we evaluated whether the improvements in these symptoms were orthogonal or
whether the improvements combined to form distinct response subgroups.
Methods: Using data from a large trial of first and second generation antipsychotics in the usual
clinical setting, we examined the change in the positive and negative subscales from the Positive
and Negative Syndrome Scale. Individual-based, growth mixture modeling was used to identify
the latent trajectories over a 1-year study period in negative and positive symptoms, separately.
An interplay matrix was generated to identify homogeneous patient subgroups in terms of both
negative- and positive-symptom trajectories.
Results: Changes in negative and positive symptoms occurred mostly in tandem in the individual patient. The negative- and positive-symptom trajectory interplay matrix suggests three major
clinical subgroups that exhibit (1) dramatic and sustained early improvement in both negative
and positive symptoms (18%), (2) mild and sustained improvement in negative and positive
symptoms (59%), and (3) no improvement in either negative or positive symptoms (21%).
Conclusions: Positive and negative symptom trajectories tend to move in tandem over time, in
the individual patient, indicating these two symptom domains are not necessary orthogonal with
each other,. Further examination of the underlying biological determinants of these subgroups
may inform effort to develop a targeted treatment for schizophrenia.
30
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
Keywords: positive symptoms, negative symptoms, trajectory interplay, schizophrenia
1. Introduction
One prominent concept of schizophrenia is the two-syndrome theory developed by Timothy Crow (1985). In Crow’s theory, type I syndrome was characterized by delusions and hallucination (positive symptom), an increase in D2 dopamine receptor, and a good response to neuroleptics. Type II syndrome was characterized by flattening of affect and poverty of speech (negative symptoms), cell loss in temporal lobe structure, and a poor response to neuroleptics. The two
syndromes were regarded as relatively independent, but could coexist in the same patients (Goghari et. al. 2010). It has been hypothesized that each one of these different domains of psychopathology could correspond to different etiopathogenic and pathophysiological mechanisms
(Cuesta and Peralta 2008), and several studies have explored the link between psychopathology
and its underlying neurobiology. Goghari and colleagues (2010) reviewed 25 task-related functional magnetic resonance imaging studies and found positive symptoms were related to the
functioning of the medial prefrontal cortex, while negative symptoms were related to the functioning of the ventrolateral prefrontal cortex and ventral striatum. The linkage of the symptomatology domains with different underlying pathophysiology appears to support the hypothesis that
different symptom dimensions have independent underlying neural substrates.
Accordingly, in schizophrenia clinical research, changes in the level of symptomatology
have typically been measured by examining the change in total negative- and positive- symptom
scores that are aggregated together or the change in scores for each of these symptom domains,
separately. Effective treatment regimens have demonstrated significant improvement in the
PANSS total score, and in both positive- and negative-symptom subscale scores, at the overall
study population level (Beasley, Sanger et al. 1996; Beasley, Tollefson et al. 1996; Patil, Zhang
31
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
et al. 2007; Cutler, Kalali et al. 2008; Kane, Assuncao-Talbott et al. 2008; Nakamura, Ogasa et
al. 2009).
However, it is unknown whether the above phenomenon holds for individual patients.
Assuming that positive and negative symptoms are independent, one could speculate that some
treated patients might have improvement in positive symptoms only, while others might have
improvement in negative symptoms only. When aggregated, the overall population effect (ie,
group means) would show improvement in both positive and negative symptoms, as observed in
previous studies (Beasley, Sanger et al. 1996; Beasley, Tollefson et al. 1996; Patil, Zhang et al.
2007; Cutler, Kalali et al. 2008; Kane, Assuncao-Talbott et al. 2008; Nakamura, Ogasa et al.
2009). In other words, while population level evidence does not reject the two-syndrome theory,
it fails to reveal how change in negative symptoms is linked to change in positive symptoms at
the individual patient level.
In our previous research, we applied trajectory analysis, an individual-based growth
modeling technique, to schizophrenia clinical trial data to identify subgroups of patients with
homogeneous treatment-response patterns in terms of positive symptom score or total score
(Case, Stauffer et al. 2010; Marques, Arenovich et al. 2011; Stauffer, Case et al. 2011). However, this technique has not been applied to positive and negative symptoms simultaneously to examine the relationship between these two symptom domains over time. In this study, we assessed the temporal interplay between negative- and positive-symptom trajectories over a 1-year
period by using data from a pragmatic trial of antipsychotics in schizophrenia. We also examined whether baseline differences exist that might permit a priori identification of patients
likely to exhibit a particular symptom course.
32
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
2.
Materials and Methods
2.1. Patient Sample
This analysis was based on data from a 1-year study, in the United States, of patients with
schizophrenia who were randomized to open-label treatment with olanzapine, risperidone, or
first-generation antipsychotics (Tunis, Faries et al. 2006). Study participants met criteria for
psychotic-symptom exacerbation, or they had recently experienced an adverse event that was
attributable to current antipsychotic treatment. Patients were assessed at seven visits, which corresponded to weeks 0, 1, 3, 9, 21, 33, and 49. Visit 1 was a screening visit. Visit 2 was the randomization visit. Initial dosing, titration, and dosing adjustments were determined by the treating physicians. Switching antipsychotic agents was allowed and was at the discretion of the
treating physician.
Patients with complete 1-year data on PANSS negative- and/or positive-subtotal scores
were included in this post-hoc analysis (N=401 for positive symptoms and N=400 for negative
symptoms). We choose to include only complete data in this study is due to that 1) the primary
objective of this study aimed to examine the long-term 1-year interplay between negative and
positive symptoms; using complete data would give us an unbiased estimation of the 1-year trajectory without impute (estimate) the missing data before we fully understand the missing data
mechanism; 2) it has increasing awareness that that missing data in schizophrenia studies are
very unlikely to be missing at random (MAR) (Kinon et al., 2008; Rabinowitz and Davidov,
2008).
33
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
2.2. Measures
Positive and negative symptoms were assessed using the PANSS positive- and negativesubscale scores, as defined by Kay et al (1987). Baseline characteristics assessed in this study
include demographics, primary psychiatric diagnosis, comorbid psychiatric diagnoses, etc. Subjective satisfaction with social life was assessed using the Lehman Quality of Life Interview
(LQLI) (Lehman 1988). Patient-perceived medication benefit, 2 weeks following randomization
to treatment, was determined using the Rating of Medication Influence (ROMI) scale, modified
version (Liu-Seifert, Adams et al. 2007).
2.3. Statistical Analyses
We used growth mixture modeling (GMM) (Muthen and Muthen 2007) to model
PANSS positive- and negative-subscale scores separately by using combined data from all antipsychotic treatment groups. Growth mixture modeling is an individual-based modeling technique that permits investigators to explore the longitudinal features of patients’ treatment response (ie, symptom trajectories) and to cluster patients accordingly (Muthen 2001). As subgroups formed in this way are inferred from the data, rather than defined in advance, these subgroups are also referred to as latent classes. Growth mixture modeling produces estimates of
each individual’s probability of membership in each latent class, and assignment is made to the
latent class for which membership probability is highest.
For our study, GMM using a quadratic growth function was applied separately to PANSS
positive- and negative-subscale scores. The model included random effects for intercept, linear
slope and quadratic slope. Multiple statistical criteria (i.e., Bayesian Information Criterion
[BIC], sample-size-adjusted BIC [aBIC] and the Bootstrap Likelihood Ratio Test [BLRT]), in
34
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
combination with qualitative judgment, were used to determine the optimal number of latent trajectory classes.
We first determined each individual’s latent class membership for positive- and negativesymptom trajectories, separately. Secondarily, we generated a matrix of PANSS negativesymptom trajectories versus positive-symptom trajectories to create patient subgroups based on
the combined symptom trajectories. To examine the extent to which negative and positive symptoms move in tandem, Pearson correlation coefficients (Pearson 1966) were calculated between
the changes in the two subscale scores within each matrix cell by visit interval after randomization.
We subsequently performed extensive qualitative evaluation of the trajectory-interplay
matrix and incorporated opinions of schizophrenia subject matter experts to identify clinically
meaningful subgroups for further study. We compared these subgroups on baseline characteristics and patient-perceived medication benefit by using analysis of variance for continuous variables and Chi-square or Fisher’s exact tests for categorical variables.
3. Results
Out of 664 patients from the original study, 400 patients had complete 1-year PANSS
negative-subscale scores, 401 patients had complete 1-year PANSS positive-subscale scores, and
399 patients had complete data on both PANSS positive- and negative-subscale scores.
3.1. Negative-symptom Trajectories
To identify the different trajectory subtypes observed for PANSS negative-subscale
scores, data were fit to a sequential series of quadratic growth models that reflected one to five
different trajectory latent classes. The statistical indices associated with the series of models
(i.e., one to five latent classes) are shown in Table 1. Per the sample-size-adjusted BIC (the low35
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
er the better) and BLRT, the four-trajectory model outperformed the others. Figure 1a shows the
observed and estimated mean negative-symptom subscale scores by latent classes. There were
44, 284, 9, and 63 patients in each latent class, which represented 11%, 71%, 2%, and 16% of the
entire cohort, respectively. Although the smallest group only accounts for 2% of the patients, its
symptom profile was exclusive (i.e., a continuous and robust response in PANSS negativesubscale score throughout the course of the study). Thus, we choose to keep this group as a distinct one and, as such, the four-trajectory solution. Figure 1b shows the trajectory of the negative-symptom subscale for each individual patient in each latent class and the observed mean trajectory of the corresponding latent class. Each class mean trajectory demonstrates a reasonable
level of concordance with individual patient trajectories and provides straightforward evidence
supporting the four-trajectory solution.
Table 1. The fit statistics for the different sequential models explored of the growth mixture
models for negative symptoms
Number of
Classes
BIC
1
2
3
4
5
16518
16517
16522
16526
16548
aBIC
16467
16453
16445
16437
16446
<0.001
<0.001
<0.001
0.167
BLRT
Number of pa400
378/22
22/374/4 44/284/9/63 16/3/56/319/6
tients in each
class
Abbreviations: aBIC = sample-size-adjusted Bayesian Information Criterion; BIC = Bayesian
Information Criterion; BLRT = Bootstrap Likelihood Ratio Test.
36
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
Figure 1a. Negative-symptom trajectory
Note: Triangles indicate estimated means, and circles indicate observed means.
Figure 1b. Individual profiles by negative-symptom trajectories
Group 1 Group 2 37
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
Group 3 Group 4 Black lines show the trajectory of the negative symptom subscale score for each individual patient in each
latent class. Colored lines show estimated mean trajectory of the corresponding latent class.
3.2. Positive-symptom Trajectories
Likewise, we modeled a sequential series of quadratic growth models for the PANSS
positive-subscale score. The statistical indices associated with the series of models (ie, one to
four latent trajectories) are shown in Table 2. Per BIC, the three-trajectory model outperformed
the others. Although the BLRT showed a significant difference of 4-class model versus 3-class
model (p<0.001), the fourth class only accounted for 1.5% (n=6) of the patients; thus, the 3-class
model was chosen. With this 3-class model, the class sizes were of reasonable magnitude for
interpretation with 41 (10%), 317 (79%), and 43 (11%) of patients in each latent class. In addition, the 3-class solution demonstrated a reasonable level of concordance with individual patient
trajectories (Figure 2b).
38
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
Table 2. The fit statistics for the different sequential models explored of the growth mixture
models for positive symptoms
Number of Classes
1
2
3
4
BIC
16091
16066
16064
16070
aBIC
16040
16002
15988
15981
<0.001
<0.001
<0.001
42/359
41/317/43
39/94/262/6
BLRT
Number of patients in
each class
401
Abbreviations: aBIC = sample-size-adjusted Bayesian Information Criterion; BIC = Bayesian Information Criterion; BLRT = Bootstrap Likelihood Ratio Test.
Figure 2a. Positive-symptom trajectories
Note: Triangles indicate estimated means, and circles indicate observed means.
39
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
Figure 2b. Individual profiles by positive-symptom trajectories
Group 1
Group 2
Group 3
Black lines show trajectory of negative symptom subscale for each individual patient in each latent class.
Colored lines show estimated mean trajectory of the corresponding latent class.
3.3. Combined Positive- and Negative-symptom Trajectories
Figure 3 is the combined negative- and positive-symptom trajectory matrix. The four
(negative-symptom trajectory classes) by three (positive-symptom trajectory classes) matrix
forms 12 cells with one empty cell (cell 1-1, no patient fell into this category), three cells (cells
3-1, 3-3, and 4-3) with only one patient each, one cell (cell 3-2) with seven patients, and the remaining seven cells with at least 14 patients each.
40
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
The combined trajectory matrix indicates that positive- and negative-symptom trajectories tend to move in tandem, over time, except in two idiosyncratic individual cases (cells 3-1
and 4-3), while the negative-symptom subscale scores tend to be consistently higher than positive-symptom subscale scores, over the 1-year study period, except in cell 2-1, which has a sample size of 20 patients (5%).
Qualitative assessment of the combined positive- and negative-symptom trajectories suggests that patients generally experience one of three distinct patterns: (1) dramatic and sustained
early improvement (DSI) in both negative and positive symptoms (cells 1-2, 1-3, and 2-3; N=70,
18%); (2) mild and sustained improvement (MSI) in negative and positive symptoms, with greater early improvement in positive, rather than in negative, symptoms (cell 2-2; N=237, 59%); or
(3) no improvement (NI) in either negative or positive symptoms (cells 2-1, 4-1, and 4-2; N=82,
21%). Ten patients (2.5%) from cells 3-1, 3-2, 3-3, and 4-3 followed idiosyncratic courses for
which the sample sizes were too few for a reliable evaluation; therefore, we did not include those
10 patients in the subsequent analyses.
41
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
Figure 3. Interplay matrix of negative- and positive-symptom trajectories
Note: Uncolored cells reflect trajectories with too few patients to reliably assess.
42
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
3.4. Pearson Correlation Coefficient
Significant and large correlations were observed between change of positive- and negative-subscale scores at some visit intervals for both DSI (cells 1-2, 1-3, and 2-3) and NI (cells 21, 4-1, and 4-2) subgroups, while moderate and significant correlations were observed in MSI
subgroups at most of the visit intervals (Table 3).
Table 3. Pearson correlation coefficient between change in PANSS negative and positive symptoms by visit interval and patient groups patient groups
DSI
Visit Interval
MSI
NI
Cell 1-2
(N=29)
Cell 1-3
(N=14)
Cell 2-3
(N=27)
Cell 2-2
(N=237)
Cell 2-1
(N=20)
Cell 4-1
(N=19)
Cell 4-2
(N=43)
Week 1-Week 3
0.65a
0.59a
0.02
0.30a
0.60a
0.41
0.58a
Week 3-Week 9
0.36
0.61a
0.39a
0.39a
0.20
0.58a
0.35a
Week 9-Week 21
0.69a
0.63a
0.11
0.22a
0.32
0.62a
-0.08
Week 21-Week 33
0.56a
0.47
0.54a
0.31a
0.42
0.59a
-0.19
Week 33-Week 49
0.23
0.61a
0.34
0.36a
0.42
0.35
0.05
Abbreviations: DSI = dramatic and sustained early improvement; MSI = mild and sustained improvement; NI = no improvement.
a
P-value<0.05
43
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
3.5. Patient Characteristics and Patient-Perceived Medication Benefit
Table 4. Patient characteristics and patient-perceived medication benefits
DSI
(N=70)
Age (years), mean (SD)
Male, %
44.9
(14.8)
54.3%
MSI
(N=237)
43.4
(11.5)
61.2%
NI
(N=82)
44.9
(10.4)
65.9%
Race/Ethnicity, %
Caucasian
61.4%
59.9%
57.3%
African American
28.6%
29.5%
30.5%
Other
10.0%
10.5%
12.2%
Primary Psychiatric Diagnosis, %
P-value
DSI vs.
MSI
0.368
MSI vs.
NI
0.320
DSI vs.
NI
0.976
0.302
0.452
0.146
0.974
0.888
0.853
0.948a
0.245a
0.377a
Schizophrenia
65.7%
63.3%
73.2%
Schizophreniform
0%
1.3%
0%
Schizoaffective Disorder
34.3%
35.4%
26.8%
Age at First Psychiatric Hospitalization
(years), mean (SD)
28.9
(10.3)
25.6 (8.7)
26.5
(10.1)
0.012
0.473
0.124
Number of previous episodes of
schizophrenia, mean (SD)
4.9 (4.9)
7.1 (9.9)
6.0 (7.4)
0.073
0.341
0.456
Co-morbid Mood disorder, %
21.4%
21.2%
22.0%
0.9653
a
0.8843
a
0.9379
0.1245a
Co-morbid Anxiety disorder, %
1.4%
5.1%
7.3%
0.3111
0.4193
Co-morbid Psychoactive substance
use disorder, %
18.6%
41.5%
40.2%
0.0005
0.839
0.0037
PANSS Total Score, mean (SD)
96.4
(23.1)
37.1
(13.6)
15.4
(3.0)
78.4
(15.3)
27.6 (9.1)
<0.001
<0.001
0.799
<0.001
<0.001
0.671
14.1 (3.5)
97.1
(16.4)
36.4
(10.9)
13.6 (4.1)
0.015
0.233
0.003
2.5 (0.5)
2.4 (0.5)
2.1 (0.6)
0.0893
0.0006
<.0001
BPRS Total Score, mean (SD)
Subjective Satisfaction with Social
Relation, mean (SD)
Perceived medication benefit at 2
weeks of treatment, mean (SD)
Abbreviations: BPRS = Brief Psychiatric Rating Scale; DSI = dramatic and sustained early improvement; MSI = mild and sustained improvement; NI = no improvement; PANSS = Positive
and Negative Syndrome Scale; SD = standard deviation.
a
P-value obtained from Fisher’s exact test.
44
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
Comparison among DSI, MSI, and NI subgroups revealed that the three subgroups were
comparable on demographics and primary psychiatric diagnosis (Table 4); however, MSI was
significantly less severe in symptomatology, as measured by PANSS total score and BPRS total
score at baseline (p<0.001), while DSI and NI were comparable (p>0.1). The DSI patients were
less likely to have psychoactive substance-use disorder (DSI 18.6%, MSI 41.5%, NI 40.2%; both
p<0.01, DSI vs. MSI and DSI vs. NI), while no significant difference was observed among subgroups on the comorbid diagnosis of mood disorder or anxiety disorder (all p>0.1). The DSI
subgroup was older at the mean age of first psychiatric hospitalization than the MSI subgroup,
but it was statistically comparable with the NI subgroup (DSI 28.9 yrs, MSI 25.6 yrs, NI 26.5
yrs; p<0.05 for DSI vs. MSI; p>0.1 for DSI vs. NI). The DSI subgroup was significantly better
in subjective satisfaction with social relation (DSI 15.4, MSI 14.1, NI 13.6; both p<0.05 for DSI
vs. MSI and DSI vs. NI). By 2 weeks of treatment, the NI subgroup was significantly worse in
patient-perceived medication benefit (DSI 2.5, MSI 2.4, NI 2.1; both p<0.001 for NI vs. DSI and
NI vs. MSI).
4.
Discussion
In this study, we observed that positive and negative symptom trajectories tended to
move in tandem over the 12-month study for the majority of 11 patterns of combined latent trajectory classes, and the correlation between the change of PANSS positive and negative symptoms was significant as demonstrated by Pearson correlation coefficients. These findings suggest that changes in negative and positive symptoms are neither independent nor reversely related, at least in chronically ill patients who represent the study population.
The congruence observed for longitudinal change in these two sets of symptoms was not
anticipated. Indeed, our observations suggest that negative and positive symptoms may be sys45
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
tematical manifestations of the “downstream” of the neurotransmitter abnormality (i.e. the dopamine dysregulation), and these two-symptom domains may depend on each other through an
unified “upstream” pathological disease process (Howes and Kapur 2009).
Our finding could be a result of pseudospecificity, a persistent issue in the development
of drug treatment for schizophrenia that specifically targets the negative symptoms and cognitive
deficit. Pseudospecificity refers to a treatment effect that is secondary to changes in other symptoms (Breier 2005). Our observation that negative and positive symptoms move in tandem at the
individual patient level could suggest that changes in negative symptoms may be a pseudospecific effect of change in positive symptoms or, conversely, that change in positive symptoms is the
pseudospecific effect of change in negative symptoms.
One possible resolution for the discrepancy, between our observation and the twosyndrome theory, may lay in the deficit syndrome or primary vs. secondary negative symptoms
theory(Carpenter, Heinrichs et al. 1988). A significant aspect of the deficit syndrome theory is
the separation of primary and secondary negative symptoms (i.e., the negative symptoms are not
fully accounted for by Depression or anxiety, drug effect or environmental deprivation (Arango,
Buchanan et al. 2004) (Carpenter, Heinrichs et al. 1988) (Kirkpatrick, Fenton et al. 2006), and
the enduring trait( i.e. two or more of the negative symptoms have been present for the preceding
12 months). According to Carpenter and colleagues(1988). This approach to deficit /non-deficit
syndromes and primary/secondary negative symptoms requires clinical judgment and long-term
observation. In the real life study design, defining the enduring nature of the disease is challenging(Tandon and Greden 1991). Stauffer et al (2012) studied primary negative symptoms using
the proxy of predominant negative symptom precluding the effect of positive symptoms, depres-
46
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
sive symptoms, and Parkinsonism, but the study showed that such a segregation of patients does
not suggest prognostic implications.
We observed negative and positive symptom move in tandem, it could be argued that
drugs used to treat one may have (e.g. antipsychotics and EPS) a side-effect that confounds the
measurement of the other dimension. This seems unlikely, because if anything, one would have
expected that the treatment of positive symptoms would be associated with EPS, which would
increase (not decrease) the severity of negative symptoms. Toffeson (1997) conducted a path
analysis to tease out the secondary effect of positive symptom, mood or adverse event, and found
the negative symptoms of schizophrenia are directly responsive to treatment. Thus the observed
improvement in negative symptoms is not necessary improvement in secondary negative symptoms only. For clinical purpose, regardless of whether they are primary or secondary in nature,
negative symptoms as a whole are a indication of disease severity (Kinon, Kane et al. 1993), are
significantly related with the quality of life and level of function of patient with schizophrenia
(Velligan, Alphs et al. 2009; Chen, Ascher-Svanum et al. 2011). Our finding that positive and
negative symptoms move in tandem implies that improving improvement in both positive and
negative symptoms is possible. In addition, we observed that negative-symptom subscale scores
tend to be consistently higher than positive-symptom subscale scores. Although the clinical
meaning of a certain score on the PANSS negative or positive subscale are not clear, this observation is consistent with the observation that chronic populations have higher negative symptoms
(Arango, Buchanan et al. 2004; Velligan, Alphs et al. 2009) (Velligan, Alphs et al. 2009) and if
they improve in concert, it is understandable that their severity will continue to be higher. It is
worth noting the exception of one small subgroup of 20 patients (5% of the overall studied popu-
47
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
lation) who showed a higher positive- than negative-symptom subscale score. It would be interesting to understand the characteristics of such a group of patients in a larger database.
Lastly, we observed three distinct patterns of symptom trajectories and potential predictors for treatment-response course. The three subgroups are as follows: (1) dramatic and sustained early improvement in both negative and positive symptoms (DSI), (2) mild and sustained
improvement in negative and positive symptoms (MSI), and (3) no improvement in either negative or positive symptoms (NI). These three subgroups were comparable in term of demographics and primary psychiatric diagnosis, but they represent a different baseline symptomatology
level, lifetime substance use disorder, subjective satisfaction with social life, and patientperceived medication benefit by 2 weeks of treatment. This kind of distinction amongst trajectories now seems a replicable fact: Dramatic responders tend to have greater severity of psychopathology (Case, Stauffer et al. 2010; Marques, Arenovich et al. 2011; Stauffer, Case et al. 2011)
and are older at disease onset age (Case, Stauffer et al. 2010). In addition, our interplay matrix
captured the clusters of patients with dramatic response demonstrated by only one of the two
symptom domains (e.g., cell 1-2), which may be missed if using a single symptom domain or
total score to define the treatment-response trajectory. Our findings support the potential utility
of defining patient subgroups that are based on negative and positive symptom trajectories interplay. Further research is warranted to study the association between these treatment-response
trajectory subgroups and the underlying biological determinants (i.e., pathophysiology and etiology indicators).
4.1. Strength and Limitations
There are various strengths and limitations to this study. First of all, this study is utilizing an in-
dividual-based methodology to categorize the relationship between positive and negative symp48
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
toms over a 12-month period under usual care setting. This hasn’t been done before. Most studies studying the relationship of these two symptom domains are mainly cross-sectional in nature
(Addington and Addington 1991), or not be able to count for the heterogeneous nature of the
symptom manifestation(Tollefson and Sanger 1997). This methodology (i.e. GMM + matrix method) allows us to maximize the value of longitudinal data, acknowledge the symptom manifestation heterogeneity in multiple dimensions (domain, time span, and severity). Secondary, this is a
large cohort with 1 year long data. This kind of data is rare in clinical trial. Thirdly, the original
trial was a pragmatic trial, which was designed to reflect usual care setting. Thus the findings
would apply in real-world practice settings.
On the other hand, the pragmatic trial design inevitably posed limitation to our findings.
There is no placebo arm, the treatment is open-label, thus make it challenge to implement analyses and inference on the treatment-effect. In addition, patients are mainly chronically ill, and
findings may not generalize to patients who are on the early stage of the disease. This is a posthoc analysis, and replication of the finding using independent data is necessary.
4.2 Future Direction
This link between positive and negative symptoms deserves further study, including replication of the findings in patients during their early stage of disease, and the effect of different
antipsychotic drugs in mediating or moderating the relationship. Further examination of the underlying biological determinants of the trajectory subgroups may advance efforts to develop the
personalized treatment for schizophrenia.
4.3. Conclusions
In this 12-month study, positive and negative symptom trajectories appeared to move in
tandem over time in the antipsychotic treatment of the individual schizophrenia patient. Thus, the
49
Chapter Four: The Longitudinal Interplay between Negative and Positive Symptoms
negative and positive symptoms are not necessarily independent of each other. There were identifiable subgroups of patients with similar symptom profiles. Further examination of the underlying biological determinants of these subgroups may inform efforts to develop targeted treatments for schizophrenia.
50
CHAPTER FIVE: CONSTRUCT VALIDITY OF THE TRAJECTORY SUBGROUPS
1. Background
In schizophrenia research, changes in the level of symptomatology have been typically
measured by examining the change in negative and positive symptom aggregated in total scores
or the change in symptom domains separately. In a previous retrospective study analyzing the
interplay between negative and positive symptom trajectories in the naturalistic treatment of patients with schizophrenia, we observed three distinct patterns of symptom trajectories: (1) dramatic and sustained early improvement in both negative and positive symptoms (DSI); (2) mild
and sustained improvement in negative and positive symptoms (MSI); and (3) no improvement
in either negative or positive symptoms (NI). In the present analysis, we explored baseline differences among these subgroups as a means of assessing the construct validity and potential utility of patient groups defined in this way. Specifically, we aimed to examine:
•
if changes occur in one-year functional and health-related quality of life outcomes, and if
so, are these changes are consistent with patterns of symptom change,
•
whether baseline differences exist that might predict those patients likely to exhibit a particular symptom course.
2. Methods
2.1. Data source
This post hoc analysis used data from a randomized, open-label, 1-year study of patients
with schizophrenia who were treated with typical or atypical antipsychotics in usual clinical care
settings (See detail on Chapter 4).
51
Chapter Five: Validity of the Trajectory Subgroups
2.2. Measures
2.2.1 Functioning outcomes
•
Global Assessment of Functioning (GAF) (Edicott, Spitzer et al. 1976).
•
GAF rates the overall functioning of the patients on a scale from 1 to 100.
Both symptomatology and social/occupational functioning are taken into
account.
•
•
Lower GAF scores represent a lower level of functioning
The 36-Item Short-Form Health Survey (SF-36) (Ware and Sherbourne 1992).
•
The physical component summary (PCS) and mental component summary
(MCS) were constructed based on eight SF-36 subscales.
•
PCS and MCS represent independent indices of perceived physical and
emotional functioning and well-being.
•
PCS and MCS were standardized based on US population norms (Ware,
Kosinski et al. 1995).
2.2.2
Baseline Characteristics
Baseline characteristics include demographics, diagnosis, psychiatric treatment history,
scores on symptomatology scale, subjective satisfaction with life, and perceive medication benefit at 2-week of treatment.
•
Subjective satisfaction with social life was extracted from the Lehman Quality of
Life Interview (LQLI) (Lehman 1988).
•
Perceived medication benefit was constructed based on the Rating of Medication
Influence (ROMI) scale, modified version (Liu-Seifert, Adams et al. 2007).
2.3. Statistical Analysis
Three subgroups established from previous research -- DSI (N=70), MSI (N=237) and NI
(N=82) (Chapter Four)-- were compared on baseline to one-year change in global functioning via
GAF, and physical and mental component scores via SF-36. Within group changes from base52
Chapter Five: Validity of the Trajectory Subgroups
line to endpoint were analyzed using the t-test. Between group differences in change from baseline were analyzed using analyses of co-variance [ANCOVA] adjusting the baseline value of the
analyzed outcome variable. Baseline characteristics and perceived medication benefit at 2-week
were analyzed using analysis of variance [ANOVA] and Fisher’s exact test.
3. Results
3.1. Global Assessment of Functioning (GAF) at Baseline and 1-year Endpoint
As shown in Figure 1, the NI group showed significantly worse functioning than the DSI
and MSI groups as indicated by lowest GAF scores at baseline and highest level in the past year
(P<0.01). The NI group also failed to show meaningful improvement by the 1-year endpoint
(P>0.05). DSI group demonstrated the greatest improvement (P<0.01) from “Serious” at baseline
to “Mild” at 1-year endpoint
Figure 1. Subgroup Comparison on Global Assessment of Functioning (GAF) at baseline and the
1-year
endpoint
Note: Higher GAF score represents a lower level of symptoms or impairment in social, occupational or
school functioning
MSI=Mild and Sustained Improvement, DSI=Dramatic and Sustained Improvement, NI=No Improvement.
53
Chapter Five: Validity of the Trajectory Subgroups
3.2. The 36-Item Short-Form Health Survey (SF- 36) at Baseline and 1-year Endpoint
As shown in Figure 2, no significant difference was observed on the Physical Component
Score among the three groups at baseline and at the 1-year endpoint (P>0.05), neither was there
a significant change from baseline to the 1-year endpoint for any of the three groups
(P>0.05)(data not shown). On the other hand, the DSI and MSI groups exhibited improvements
on the Mental Component Score (p<0.001) while the NI group demonstrated no significant
change (P>0.05) (data not shown). Of interest, the DSI group and MI group are parallel in terms
of the 1-year improvement on the Mental Component Score, with the MSI group starting with a
lower baseline level.
Figure 2. Group Comparison on SF- 36 at Baseline and 1-year Endpoint
Note: Higher SF-36 scores indicate higher levels of perceived functioning and well being.
MSI=Mild and Sustained Improvement, DSI=Dramatic and Sustained Improvement,
NI=No Improvement
54
Chapter Five: Validity of the Trajectory Subgroups
3.3. Possible Predictors of the Trajectory Subgroups
Table 1. Baseline information on demographics and diagnosis
DSI (N=70) MSI (N=237) NI (N=82) P‐value DSI vs. MSI MSI vs. NI DSI vs. NI Age (years), mean (SD) Male, % Race/Ethnicity, % Caucasian African American Other Primary Psychiatric Diagnosis, % Schizophrenia Schizophreniform Schizoaffective Disorder 44.9 (14.8) 54.3% 61.4% 28.6% 10.0% 65.7% 0% 34.3% 43.4 (11.5) 61.2% 59.9% 29.5% 10.5% 63.3% 1.3% 35.4% 44.9 (10.4) 65.9% 57.3% 30.5% 12.2% 73.2% 0% 26.8% 0.368 0.302 0.974 0.948a 0.320 0.452 0.888 0.245a 0.976 0.146 0.853 0.377a Abbreviations: DSI = dramatic and sustained early improvement; MSI = mild and sustained improvement; NI = no improvement; SD = standard deviation.
a
P-value obtained from Fisher’s exact test.
Table 2. Baseline information on psychiatry treatment history, current evaluation on clinical and
social relation measures,
DSI
(N=70)
MSI
(N=237)
NI
(N=82)
P-value
Age at First Psychiatric Hospitalization (years), mean (SD)
28.9 (10.3)
25.6 (8.7)
26.5 (10.1)
DSI vs.
MSI
0.012
Number of previous episodes of
schizophrenia, mean (SD)
4.9 (4.9)
7.1 (9.9)
6.0 (7.4)
0.073
0.341
0.456
81.4%
53.2%
68.3%
<0.001
0.017
0.065
Atypical (s) only
2.9%
12.7%
8.5%
0.015a
0.424a
0.179a
Both
7.1%
24.5%
19.5%
0.002
0.359
0.028
18.6%
41.5%
40.2%
<0.001
0.839
0.004
Antipsychotic Treatment in the
Past year
Conventional(s) only
Comorbid Psychiatric Diagnoses,
%
Psychoactive substance
use disorder
MSI vs.
NI
0.473
DSI vs.
NI
0.124
55
Chapter Five: Validity of the Trajectory Subgroups
DSI
(N=70)
MSI
(N=237)
NI
(N=82)
P-value
Mood disorder
21.4%
21.2%
22.0%
DSI vs.
MSI
0.9653
MSI vs.
NI
0.8843
DSI vs.
NI
0.9379
Anxiety disorder
1.4%
5.1%
7.3%
0.3111a
0.4193a
0.1245a
PANSS Total Score, mean (SD)
96.4 (23.1)
78.4 (15.3)
97.1 (16.4)
<0.001
<0.001
0.799
BPRS Total Score, mean (SD)
37.1 (13.6)
27.6 (9.1)
36.4 (10.9)
<0.001
<0.001
0.671
Subjective Satisfaction with Social
Relation, mean (SD)
15.4 (3.0)
14.1 (3.5)
13.6 (4.1)
0.015
0.233
0.003
Abbreviations: DSI = dramatic and sustained early improvement; MSI = mild and sustained improvement; NI = no improvement; SD = standard deviation.
a
P-value obtained from Fisher’s exact test.
Note: Psychoactive substance including alcohol, sedative/hypnotic/anxiolytic, cannabis, stimulants, opioid, cocaine and hallucinogen/PCP
Table 3. Initial treatment assignment and 2-week perceived medication benefit
DSI
(N=70)
MSI
(N=237)
NI
(N=82)
Initial Treatment Assignment, %
Olanzapine
16(13.1)
80 (65.6)
26(21.3)
Risperidone
26(19.3)
78(57.8)
31(23.0)
Conventional Antipsychotics
28 (21.2)
79(59.9)
25(18.9)
2.5 (0.5)
2.4 (0.5)
2.1 (0.6)
Perceived medication benefit at 2
weeks of treatment, mean (SD)
P-value
DSI vs.
MSI
0.220
MSI vs.
NI
0.721
DSI vs.
NI
0.358
0.089
<0.001
<0.001
Abbreviations: DSI = dramatic and sustained early improvement; MSI = mild and sustained improvement; NI = no improvement; SD = standard deviation.
Data in Table 1-3 suggest the following:
 While there is no significant difference observed on the comorbid diagnosis of mood disorder or anxiety disorder, DSI patients were less likely to have psychoactive substance
use disorder (p<0.01),
56
Chapter Five: Validity of the Trajectory Subgroups
 The DSI group was significantly better in subjective satisfaction with social relation
(both p<0.05 for NI vs. DSI, and NI vs. MSI),
 DSI patients are more likely to have used conventional antipsychotics only (DSI vs. MSI:
p<0.001 ; DSI vs. NI: p=0.06),
 The initial treatment assignment appears not to be related with the symptom trajectories
(p>0.2)
 The NI group was significantly worse in perceived medication benefit (both p<0.001 for
NI vs. DSI, and NI vs. MSI) at 2 weeks of treatment.
4. Discussion
Findings from this study suggest the three subgroups-Dramatically and Sustained Improvement (DSI), Mildly and Sustained Improvement (MSI), and No Improvement (NI)- were
comparable in term of demographics and primary psychiatric diagnosis, while there are differences exist in 1) the functional outcome over the 1-year study period, and 2) certain baseline characteristics that may be potential predictors of the symptom course.
We found differences that 1-year functional outcomes were directionally consistent with
differences in subgroup symptom courses. These findings support the construct validity of the
subgroups defined using both negative and positive symptom trajectories. It is noteworthy that
DSI and MSI clusters are comparable in the magnitude of improvement observed in the SF-36
mental component score.
Potential predictors for symptom course were observed including baseline severity on
symptomatology scores, comorbid substance use disorder and antipsychotic use pattern in the
57
Chapter Five: Validity of the Trajectory Subgroups
past year, baseline movement disorder status, baseline subjective satisfaction with social life and
perceived medication benefit by two weeks of treatment. These findings support the potential
utility of using patient subgroups defined by both negative and positive symptom trajectories.
Notably, the initial treatment assignment was not related with the symptom trajectory membership. It should be emphasized that the inference on drug efficacy from the study is limited by the
nature of the open-label pragmatic design in which medication switching was allowed per physician discretion.
The inferences drawn from the analyses are limited by the fact that the analyses were exploratory in nature, and as such, this study was not powered to detect differences in the selected
measures. On the other hand, no adjustments were made for multiple comparisons, and the finding that were statistically significant findings require further validation using independent data
sources. Moreover, the original study did not collect genetic data. Uher et al (2009) studied the
genetic predictors of response to antidepressants and found that genetic markers predict trajectories better than the responder/non-responder dichotomy and conceived that trajectory subgroups
may allow for a more efficient pharmacogenetic analysis. The association between baseline characteristics, pharmacologic treatment and symptom course deserve further study, as well as that
of the underlying biologic determinants.
Different from previous trajectory studies which used only one outcome measure to define the trajectory subgroup (Case, Stauffer et al. 2010) (Muthen, Brown et al. 2002;
Gueorguieva, Wu et al. 2007; Marques, Arenovich et al. 2011; Stauffer, Case et al. 2011), we
used trajectory subgroups defined by two concurrent outcome measures. The findings suggest
this method might be a valid and useful strategy to study the heterogeneity of symptom progress
and its underlying determinants.
58
CHAPTER SIX: SIMULTANEOUS GMM
In Chapter four, I employed the GMM+ “matrix” method to analyze the interplay between negative and positive symptom trajectories in the naturalistic treatment of patients with
schizophrenia. We observed distinct patterns of symptom trajectories (subgroups). Individual
trajectory profiles are relatively homogeneous in each subgroup and align well with the subgroup
mean trajectory. In Chapter Five, it is demonstrated that the trajectory subgroups identified were
valid based on the observed consistency between the functional outcomes and the symptom
course. Methodologically, GMM+”matrix” method involves two major steps of analyses, and
requires qualitative judgment to group the matrix cells into clinically meaningful groups.
The current chapter aims to explore the application of the advanced simultaneous GMM
to detect the trajectories in one step. We used the same database as that in Chapter Four and Five,
and compared the results from the simultaneous GMM with the established findings from the
previous Chapters.
1.
Methods
We used simultaneous GMM to model PANSS positive- and negative-subscale scores
simultaneously. A quadratic growth function was applied with distinct intercept, linear slope and
quadratic slope for the positive- and negative- subscale scores. We fitted a sequential series of
models reflecting increasing number of trajectory latent classes until BLRT >0.05. The model
diagram is shown below.
59
Chapter Six: Simultaneous GMM
y11
y12
……
i1
s1
i2
s2
y1t
q1
c
q2
y21
y22
……
y2t
y1t indicates the positive-symptom subscale score at time t
y2t indicates the negative-symptom subscale score at time t
c indicates the latent categorical variable of subgroup membership in terms of both the positive- and negative-symptom trajectories.
i1, s1 and q1 indicate the latent intercept, linear slope and quadratic slopes, respectively, for the
positive-symptom trajectory.
i2, s2 and q2 indicate the latent intercept, slope and quadratic slopes, respectively, for the negative-symptom trajectory.
To ensure that the best solution corresponds to a global optimum rather than a local maximum likelihood solution, we repeated the fitting procedure with different sets of random starting
values until solutions were replicated with different starting values. Multiple statistical criteria,
including BIC, aBIC and BLRT were used to determine the optimal number of the latent trajectory class.
To evaluate the performance of simultaneous GMM, we constructed a classification table
with rows representing the estimated latent classes based on “simultaneous GMM” and columns
60
Chapter Six: Simultaneous GMM
representing the classes based on “GMM+matrix”. Using results from “GMM+matrix” as references (true classes), we calculated a summary measure, the proportion of patients who were classified correctly under “simultaneous GMM”.
2. Results
2.1 Trajectory Classes under Simultaneous GMM
Per the statistical indices associated with the series of models (one to six latent classes),
the five-trajectory model is optimal with the lowest aBIC, while the six-trajectory model is not
significantly different from five-trajectory model (Table 1). Thus the 5-class model was chosen.
Table 1. The fit statistics for the different sequential models of the simultaneous GMM for both
negative- and positive-symptoms
Number of Classes 1 2 3 4 5 6 BIC 32346 32357 32349 323354 32370 32397 aBIC 32216 32205 32174 32158 32151 32155 BLRT <0.001 <0.001 <0.001 <0.001 0.097 Number of pa‐
tients in each class 399 28/371 300/52/47 51/49/ 285/14 239/39/ 55/19/47 275/12/ 41/18/23/30 Abbreviations: aBIC = sample-size-adjusted Bayesian Information Criterion; BIC = Bayesian
Information Criterion; BLRT = Bootstrap Likelihood Ratio Test.
Figures 1-2 illustrate the class mean trajectories, and the individual trajectory under the 5class model.
61
Chapter Six: Simultaneous GMM
Figure 1a. Negative-symptom trajectories
Note: Triangles indicate estimated means, and circles indicate observed means.
Figure 1b. Positive- symptom trajectories
Note: Triangles indicate estimated means, and circles indicate observed means.
Under the 5-class model, the class trajectory means suggest that Classes 2 and 5 have
dramatic improvement in positive and/or negative symptoms, thus should correspond to the DSI
62
Chapter Six: Simultaneous GMM
subgroup (Figure 3, Chapter Three); Class 1 has mild improvement in positive and negative
symptoms, thus should correspond to the MSI subgroup; Class 3 shows no improvement in both
negative and positive symptoms, and thus should correspond to the NI subgroup. Class shows
dramatic improvement in negative symptoms, but with a relative low mean severity in positive
symptoms and no change in positive symptoms, thus Class 4 may correspond to the DSI group.
Figure 2. Estimated mean and observed individual trajectories
Class Neagtive‐symptom trajectories Positive‐symptom trajectories 1 2 63
Chapter Six: Simultaneous GMM
3 4 5 2.2. Performance of the Simultaneous GMM
To evaluate the performance of the simultaneous GMM, we generated a classification table for “Simultaneous GMM” vs. “GMM + matrix” (Table 2).
64
Chapter Six: Simultaneous GMM
Table 2. Classification table: “Simultaneous GMM” vs. “GMM + matrix”
Classes from “Simultaneous GMM” Total Classes from “GMM + matrix” 1 2 3 4 5 Total DSI 5 MSI 201 NI 32 ITC 1 239 28 1 1 35 70 9 12 6 9 237 2 41 6 1 82 0 1 6 2 10 39 55 19 47 399 Abbreviations: DSI = dramatic and sustained early improvement; MSI = mild and sustained improvement; NI = no improvement; ITC=idiosyncratic trajectory classes
The concordance between “Simultaneous GMM” and “GMM + matrix” was shaded in pink for DSI,
green for MSI and blue for NI
Using the individual’s class membership obtained from “GMM + matrix” (Chapter
Three and Four) as the true classes, the sensitivity of “Simultaneous GMM” in detecting DSI is
90% (63/70), of detecting MSI is 85% (201/237), and of detecting NI is 50% (41/82).
Table 3 shows the descriptive statistics of a discordant classification: the NI patients who
were classified in class 1 (minimal improvement) per the simultaneous GMM.
Table 3. Mean score of negative symptom for NI patients who were classified in class 1 (minimal improvement) per the simultaneous GMM
Week
N
Mean
Std Dev
Minimum
Maximum
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
0
32
27.9062500
3.5501874
23.0000000
37.0000000
1
32
27.1250000
3.4054037
22.0000000
33.0000000
3
32
25.9062500
4.3800087
19.0000000
38.0000000
9
32
25.7812500
4.0059180
19.0000000
34.0000000
21
32
26.3750000
3.7481178
17.0000000
37.0000000
33
32
25.6562500
2.4044230
21.0000000
31.0000000
49
32
26.2187500
2.5366269
20.0000000
32.0000000
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
65
Chapter Six: Simultaneous GMM
3. Discussions
We found the sensitivity of the simultaneous GMM in detecting the true individual membership ranged from 50% -90%. Figure 2 suggests that the class memberships from simultaneous
GMM tend to be driven by one dominant outcome measure (e.g. class 4). It is unclear what the
root cause of the above phenomena is.
In Chapter Three, we discussed the distribution assumption of GMM, and the current mathematical analysis would not be able to distinguish if the extracted classes represent population
heterogeneity or just spurious heterogeneity by approximating a complex non-normal distribution (which actually is a homogeneous population) by multiple normal distributions (Bauer and
Curran 2003). It has been strongly suggested that substantive knowledge should provide guidance on this matter (Bollen 1989; Bauer and Curran 2003; Muthen 2004). When multiple outcomes and /or covariate(s) are included, data distribution complexity increases, and would subsequently complicate the judgment, or even make it impossible to differentiate true vs. spurious
heterogeneity based on substantive knowledge.
Before we have a full understanding of the above phenomena, we believe simultaneous
GMM may serve as a good start for inspecting the trajectory pattern with multiple outcome
measures. It also warrants qualitative inspection of the individual trajectory patterns, along with
analysis using clinician-intuitive methods such as “GMM+matrix” method.
66
CHAPTER SEVEN: GMM WITH MISSING DATA
As for the commonly used mixed model with repeated measures (MMRM), one advantage of
GMM is that it allows missing data under the assumption that data are missing at random
(MAR). Most applied trajectory analyses in schizophrenia and depression have been carried out
including the missing data under the assumption of MAR. In addition, we believe that including
missing data with appropriate method would be critical when assessing treatment effect. Therefore, using the same data source as described in the previous chapters, we conducted GMM on
the PANSS negative- and positive-subscale scores including the missing data (MD). We assumed that the mechanism of missing data is MAR. We also compared the findings from this
analysis with the results based on the complete data (CD) as carried out in Chapter Four.
1. Negative Symptom Trajectories
Table 1 shows the fit statistics associated with the series of models (i.e. one to six latent
classes). The 6-class model outperforms others per the aBIC and the Bootstrap Likelihood Ratio
test.
Table1. The fit statistics for the different sequential models with missing data -- GMM for negative symptom
Number of Classes BIC 1 2 3 4 5 6 7 23647 23640 23628 23622 23631 23637 23654 aBIC 23596 23579 23551 23533 23530 23523 23527 BLRT <0.001 <0.001 <0.001 <0.001 0.013 0.5 Number of patients in each class 664 566/98 49/3/612 87/45/ 3/529 46/3/8/ 85/522 3/468/11/ 88/12/11/ 7/103/72 3/106/437/7 Abbreviations: aBIC = sample-size-adjusted Bayesian Information Criterion; BIC = Bayesian Information Criterion; BLRT = Bootstrap Likelihood Ratio Test.
67
Chapter Seven: GMM with Missing Data
Figure 1a and Figure 1b are the mean trajectories and individual trajectory profiles from
of the 4-class solution.
Figure 1a. Negative-symptom trajectories
Note: Triangles indicate estimated means, and circles indicate observed means.
Figure 1b. Individual profiles by negative-symptom trajectories
(Black lines show trajectory of negative symptom subscale for each individual patient in each
latent class. Colored lines show estimated mean trajectory of the corresponding latent class.)
Class 1 (n=67) Class 2 (n=46) 68
Chapter Seven: GMM with Missing Data
Class 3 (n=3) Class 4 (n=529) Table 2. Comparison between “GMM with MD” vs.”GMM with CD”
“Estimated” Class per GMM with MD Total “True” Group per GMM with CD ) 1 2 3 4 Total 1 0 2 1 3 4 4 50 NC 32 67 31 0 13 44 0 0 283 284 0 0 5 9 0 0 13 63 14 3 215 264 46 3 529 664 Abbreviation: MD=missing data, CD=complete data, NC= non-classified
Note: the concordance between “GMM with CD” and “GMM with MD” was indicated in color shading
Using GMM with MD, the sensitivity for detecting the “true” negative symptom trajectory classes was 70% (31/44), 100% (283/284), 79% (50/63) for the “True” Groups 1, 2, and 4 (per
“GMM with CD”), respectively. And the individuals belonging to the “True” Group 3 (per
“GMM with CD”) were buried in the other Classes. Except for 3 individuals who had incomplete data, the majority of the patients with missing data were assigned to the corresponding
classed as defined by the cases with complete data. The results suggested that when including
missing data under the assumption of missing at random, the model becomes less sensitive to
69
Chapter Seven: GMM with Missing Data
detect patients who show a dramatic improvement (class 1 and class 3 in Figure 1, Chapter Four)
in negative symptoms. Table 3 shows the PANSS negative-subscale scores for the two patients
who have missing data but were classified into the dramatic and continuous improvement class
(class 3 per the “GMM with MD” model). Individual data suggest that the classification does not
fit.
Table 3. Descriptive statistics of negative symptom of patients classified in the ”true” Group 1
(the dramatic-improvement group) per the “GMM with MD” model, but “estimated” Class 4
(non- improvement class) per the “GMM with CD” model
Week
N
Mean
Std Dev
Minimum
Maximum
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
0
13
30.4615385
3.5966509
25.0000000
36.0000000
1
13
24.8461538
7.7658027
10.0000000
35.0000000
3
13
25.0000000
7.5277265
11.0000000
37.0000000
9
13
19.6153846
4.8740548
11.0000000
28.0000000
21
13
16.6923077
6.2367809
7.0000000
27.0000000
33
13
14.4615385
4.7542154
7.0000000
20.0000000
49
13
15.1538462
4.7931575
9.0000000
23.0000000
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Table 3 suggests that dramatic-improvement (‘true” group per the “GMM with CD”) rather than non-improvement (“estimated” class per “GMM with MD”) is a better classification
scheme for those patients. Thus, “GMM with CD” is more sensitive in detecting patients who
demonstrate dramatic improvement.
To assure the above finding, we tested the 5-class solution per GMM with MD model.
We got similar findings. The results are displayed in Appendix 8.
2. Positive Symptom Trajectories
Table 4 shows the fit statistics associated with the series of models (i.e., one to four latent
classes). The 3-class model outperformed others per BIC, as well as number of patients in each
class.
70
Chapter Seven: GMM with Missing Data
Table 4. The fit statistics for the different sequential models exploring the GMM with missing data for
positive symptoms
Number of Classes
1
2
3
4
BIC
23039
23004
22982
22984
aBIC
22988
22940
22905
22895
<0.001
<0.001
<0.001
BLRT
Number of patients 664
86/578
87/559/18
87/21/1/555
in each class
Abbreviations: aBIC = sample-size-adjusted Bayesian Information Criterion; BIC = Bayesian
Information Criterion; BLRT = Bootstrap Likelihood Ratio Test.
Figure 2a and 2b are the mean trajectories and individual trajectory profiles from of the
5-class solution.
Figure 2a. Positive-symptom trajectory
Note: Triangles indicate estimated means, and circles indicate observed means.
71
Chapter Seven: GMM with Missing Data
Figure 2b. Individual profiles for positive-symptom trajectories
(Black lines show trajectory of negative symptom subscale for each individual patient in each
latent class. Colored lines show estimated mean trajectory of the corresponding latent class.)
Class 1 Class 2 Class 3 Table 5. Comparison between GMM with missing and GMM without missing
Classes from GMM with MD Total Classes from GMM with CD 1 2 3 Total 1 39 2 1 3 1 NC 46 87 2 0 41 316 0 317 31 11 43 210 7 263 559 18 664 Abbreviation: MD=missing data, CD=complete data, NC= non-classified
Note: the concordance between “GMM with CD” and “GMM with MD” was indicated in color
72
Chapter Seven: GMM with Missing Data
Table 5 is the classification table comparing results between GMM with and without
missing data. Using the “GMM with MD”, the sensitivity for detecting the true positivesymptom trajectory are 95% (39/41), 98% (316/317), and 28% (11/43) for class 1, 2 and 3, per
the “GMM with CD” model, respectively. The findings suggest when including missing data
under the assumption of missing at random, the model becomes less sensitive for detecting patients who show a dramatic improvement (class 3, Figure 2 of Chapter Four) in positive symptoms.
Table 6 shows the means score of PANSS positive-subscale scores for those patients who
were classified in the minimal-improvement class (class 2) from the “GMM with MD” model,
but in the dramatic-improvement class (class 3) from the “GMM with CD” model. It is obvious
that the dramatic-improvement classification (per the “GMM with CD” model) better describes
the symptom course for these individual patients.
Table 6. Mean scores of the PANSS positive-subscale score for patients fall in the minimalimprovement class of the “GMM with MD” model, but and dramatic-improvement class in the
“GMM with CD” model .
Week
N
Mean
Std Dev
Minimum
Maximum
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
0
31
27.3225806
3.3998735
21.0000000
33.0000000
1
31
24.7096774
6.0838231
10.0000000
33.0000000
3
31
18.2580645
6.2979771
9.0000000
30.0000000
9
31
13.2903226
4.5767059
7.0000000
26.0000000
21
31
12.3870968
3.8181795
7.0000000
24.0000000
33
31
11.1935484
3.3208368
7.0000000
19.0000000
49
31
12.7096774
3.8139529
7.0000000
22.0000000
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
Thus, Compared with GMM with missing data under MAR assumption, GMM using
complete data is more sensitive in detecting patients who demonstrates a dramatic improvement.
This phenomenon of non sensitivity for detecting the dramatic improvement in positive symptoms is consistent with that observed in negative symptoms. To our knowledge, this phenomenon
73
Chapter Seven: GMM with Missing Data
has not been reported in previous schizophrenia research using trajectory analyses. A high proportion of incomplete data (40% in this case), and long study duration (1-year in this case) may
be two of the reasons for this. It is possible that the missing data due to non-ignorable missing
played a substantial role in this case.
In the previous chapter, we discussed that missing data in schizophrenia studies are very
unlikely to be MAR, and treatment discontinuation itself contains meaningful information of the
treatment effect (Lieberman, Stroup et al. 2005). From a statistics perspective of view, though there
have been many different non-ignorable missing data models proposed in recent years(Roy 2003;
Dantan, Proust-Lima et al. 2008; Gomeni, Lavergne et al. 2009), critiques on the underlying assumption of those models are substantial (Little 1994; Roy 2003). As a matter of fact, any statistical
modeling of non-ignorable missingness (NMAR) is built on un-testable assumptions (Muthen,
Asparouhov et al. 2011). Simulation studies has shown that minor model misspecification can in-
troduce significant bias (Demirtas and Schafer 2003) and subsequently impact the assessment
of the treatment effectiveness. Further studies integrating missing data methodology and substantive knowledge in schizophrenia study are warranted, especially within the context of pragmatic
long-term study design. Upon a solid methodology developed for NMAR with single outcome
measure, we would envision to further develop the NMAR model with multiple concurrent outcome measures.
While not including patients with incomplete data may have confounded the interpretation of the treatment effect, our original intent was not to determine the effect of treatment. Rather we were interested in evaluating the temporal interplay between negative and positivetrajectories over a 1-year period. In this regard, using GMM with complete data appears to provide a more reliable and transparent picture of the symptom courses.
74
Chapter Seven: GMM with Missing Data
In summary, GMM offers the attractive advantage of including missing data under the assumption of MAR, it is requires: 1) informative inspection of the missing data mechanism, and
2)sensitivity analyses with varied NMAR assumptions.
75
APPENDICES
Appendix 1. Mplus Modeling Framework
The following information is from Mplus Users Guide, Version 5 by Muthen and Muthen
The rectangles represent observed variables. Observed variables can be outcome variables or
background variables. Background variables are referred to as x; continuous and censored outcome variables are referred to as y; and binary, ordered categorical (ordinal), unordered categorical (nominal), and count outcome variables are referred to as u. The circles represent latent variables. Both continuous and categorical latent variables are allowed. Continuous latent variables
are referred to as f. Categorical latent variables are referred to as c. The arrows in the figure
represent regression relationships between variables.
76
Appendices
Appendix 2. Positive and Negative symptoms of Schizophrenia
Adopted from WHO Surgeon General’s Report on Mental Health, accessed @
http://www.surgeongeneral.gov/library/mentalhealth/chapter4/sec4.html#table4_7
Positive Symptoms of Schizophrenia
Delusions are firmly held erroneous beliefs due to distortions or exaggerations of reasoning
and/or misinterpretations of perceptions or experiences. Delusions of being followed or watched
are common, as are beliefs that comments, radio or TV programs, etc., are directing special messages directly to him/her.
Hallucinations are distortions or exaggerations of perception in any of the senses, although auditory hallucinations (“hearing voices” within, distinct from one’s own thoughts) are the most
common, followed by visual hallucinations.
Disorganized speech/thinking, also described as “thought disorder” or “loosening of associations,” is a key aspect of schizophrenia. Disorganized thinking is usually assessed primarily
based on the person’s speech. Therefore, tangential, loosely associated, or incoherent speech severe enough to substantially impair effective communication is used as an indicator of thought
disorder by the DSM-IV.
Grossly disorganized behavior includes difficulty in goal-directed behavior (leading to difficulties in activities in daily living), unpredictable agitation or silliness, social disinhibition, or behaviors that are bizarre to onlookers. Their purposelessness distinguishes them from unusual behavior prompted by delusional beliefs.
Catatonic behaviors are characterized by a marked decrease in reaction to the immediate surrounding environment, sometimes taking the form of motionless and apparent unawareness, rigid
or bizarre postures, or aimless excess motor activity.
Other symptoms sometimes present in schizophrenia but not often enough to be definitional
alone include affect inappropriate to the situation or stimuli, unusual motor behavior (pacing,
rocking), depersonalization, derealization, and somatic preoccupations.
Negative Symptoms of Schizophrenia
Affective flattening is the reduction in the range and intensity of emotional expression, including
facial expression, voice tone, eye contact, and body language.
Alogia, or poverty of speech, is the lessening of speech fluency and productivity, thought to reflect slowing or blocked thoughts, and often manifested as laconic, empty replies to questions.
Avolition is the reduction, difficulty, or inability to initiate and persist in goal-directed behavior;
it is often mistaken for apparent disinterest.
77
Appendices
Appendix 3. The Short Form (36) Health Survey (SF-36)
The SF-36 is a multi-purpose health survey with 36 questions. It yields an 8-scale profile
of functional health and well-being scores as well as psychometrically-based physical and mental
health summary measures and a preference-based health utility index. It is a generic measure, as
opposed to one that targets a specific age, disease, or treatment group. Accordingly, the SF-36
has proven useful in surveys of general and specific populations, comparing the relative burden
of diseases, and in differentiating the health benefits produced by a wide range of different
treatments.
Adapted from Ware, J.E., Kosinski M. SF-36 Physical and Mental Health Summary Scales: A
78
Appendices
Manual for Users of Version 1, Second Edition. Lincoln, RI: QualityMetric, Incorporated,
2001.
The SF-36 summary components are computed following a standardized three-step procedure. First, all eight subscale scores are standardized using a linear z-score transformation. Zscore are calculated by subtracting subscale means for the general US population sample from
each individual’s subscale score and dividing the difference by the standard deviation of the US
sample. Second, z-score are multiplied by the subscale factor score coefficients for PCS and
MCS and summed over all eight subscales. Finally, t-scores are calculated by multiplying the
obtained PCS and MCS sums by 10 and adding 50 to the product, to yield a mean of 50 and a
standard deviation of 10 per the US norm population.
79
Appendices
Appendix 4. Global Assessment of Functioning (GAF)
The Global Assessment of Functioning (GAF) is a numeric scale used by mental health clinicians and physicians to subjectively rate the social, occupational, and psychological functioning
of adults. The instructions specify, "Do not include impairment in functioning due to physical (or
environmental) limitations. The scale is presented and described in the DSM-IV multiaxial classification as axis V assessment.
The following GAF is adapted from MICHAEL B. FIRST, M.D., ed. 2000. Diagnostic and Statistical Manual of Mental Disorders – 4th Ed. (DSM-IV-TR™, 2000). Washington, DC. American Psychiatric Association.
80
Appendices
81
Appendix 5. Frequently cited theories on the relationship between positive and negative symptoms
Citation Method (Carpenter, Bartko Based on sign and symptom data et al. 1976) from the International Pilot Study of Schizophrenia (Andreasen and Olsen 1982) (Crow 1985) (Carpenter, Heinrichs et al. 1988) The authors explored the clinical correlates of ventricular enlarge‐
ment in schizophrenia by comparing 16 patients with "large" ventricles (ventricles more than I SD above the control mean) with 16 patients with the smallest ventricles from a sam‐
ple of 52 schizophrenic patients. Review article Per experience in using clinical judgment based on longitudinal ob‐
servations to identify deficit and nondeficit subtypes of schizophrenic patients Relationship between positive and negative symptoms Profile analysis of variance results indicate that each subtype appears similar, regardless of center of ori‐
gin. Patients with ventricular enlarge‐
ment showed some impairment in the sensorium and had a prepon‐
derance of "negative" symptoms (e.g., alogia, affective flattening, avolition, anhedonia), while those with small ventricles were characte‐
rized by "positive" symptoms Type I vs. type II syndrome They presumably have the same eti‐
ology. Proposed distinguishing the primary negative symptoms of schizophrenia (termed "deficit symptoms") from the more negative symptoms sec‐
ondary to other factors. Concept cited by others “Independent domain of pa‐
thology” “Positive and negative symptom are inversely related” “Positive and negative symp‐
toms might be inversely re‐
lated” “The two syndromes are re‐
garded as relatively in‐
depend process” “Deficit vs. non‐deficit schizoph‐
renia” 82
Appendices
Appendix 6. Data analyzing or suggesting the relationship between positive and negative symptoms
Citation Study Population Methodology Results Conclusion Young patients with Prospectively examined Negative symptoms were signifi‐
(Breier, The negative and positive Wolkowitz chronic schizophre‐ the effects of double‐blind, cantly reduced by neuroleptic symptom profiles of indi‐
et al. 1987) nia (N=19) placebo‐controlled neuro‐ treatment, and negative and posi‐
vidual patients were signif‐
leptic withdrawal and ad‐
tive symptoms demonstrated simi‐ icantly altered by neuro‐
ministration on ratings of lar patterns of reduction and ex‐
leptic treatment, indicating negative and positive acerbation during neuroleptic limitations to the cross‐
symptoms in treatment and withdrawal, respec‐ sectional classification of tively. The changes in negative and patients on the basis of positive symptoms induced by neu‐ predominance of one or roleptic treatment and withdrawal the other symptom group. were not significantly correlated. Sought relationships be‐
No correlations were found be‐
Methodologies that form (Guelfi, Medication‐free tween positive and nega‐
tween positive and negative symp‐ restrictive subgroups of Faustman et inpatient popula‐
al. 1989) tion of schizophre‐ tive schizophrenic symp‐
toms patients with exclusively nia (N = 61) toms positive or negative symp‐
toms may have little gene‐
ralizability to schizophrenic populations. (Addington DSM III diagnosed in the acute phase of the Positive and negative symptoms There may be a single dis‐
schizophrenics illness and then, 6 months were not inversely related at either ease entity and Addington (N=41) later, in a period of relative acute or remission phase 1991) remission. (Tollefson Hospitalized pa‐
Study was conducted for Olanzapine demonstrated a signifi‐ The negative symptoms of and Sanger tients with schi‐
up to 52 weeks. Path anal‐ cantly greater direct effect than schizophrenia are directly 1997) zophrenia(N=335) ysis was used to determine haloperidol on negative symptoms responsive to treatment. to what extent the total treatment effect on nega‐
tive symptoms was direct 83
Appendices
(Buchanan, Breier et al. 1998) (Danion, Rein et al. 1999) (Kane, Marder et al. 2001) (Stauffer, Song et al. 2012) or indirect Outpatients with A 10‐week double‐blind, schizophrenia, who parallel‐groups compari‐
met criteria for re‐
son of clozapine and halo‐
sidual positive or peridol. negative symptoms (n=75) Schizophrenic pa‐
A 12‐week, multicenter tients with primary double‐blind trial of place‐
negative symptoms bo, amisulpride, 50 mg/day, or amisulpride, (N=242) 100 mg/day. Subjects with schi‐
zophrenia who were being treated in community (N=71) Adult patients with schizophrenia (n=227) or schizoaffective dis‐
order (n=116) Clozapine was superior to halope‐
ridol in treating positive symptoms There was no evidence of any su‐
perior efficacy or long‐term effect of clozapine on primary or second‐
ary negative symptoms Both amisulpride treatment groups showed significantly greater im‐
provement in negative symptoms than the placebo group. Positive symptom scores were low at baseline and changed minimally during the study Randomized, double‐blind, Significantly greater improvement 29‐week trial comparing was seen in symptoms of psycho‐
clozapine with haloperidol sis…. No differences were detected in negative symptoms Patients with either predominant Randomized, doubled or prominent negative symptoms blind 24‐ week study. appear to respond similarly to Predominant negative symptoms atypical antipsychotic treatment were defined by the fore‐
going plus a PANSS posi‐
tive score of <19, a Barnes Akathisia score of <2, a Simpson– Angus score of <4, and a Calgary Depressive Scale score of <9. clozapine has superior effi‐
cacy for positive symptoms but not negative symptoms The improvement in nega‐
tive symptoms was inde‐
pendent of improvement in positive symptoms. Advantages of clozapine are seen in a broad range of symptoms but do not extend to negative symp‐
toms. The distinction, incorporat‐
ing an evaluation of the presence of positive, affec‐
tive, and extrapyramidal symptoms, may not have prognostic implications for the responsiveness of pa‐
tients' negative symptoms to treatment. 84
Appendices
Appendix 7. Definition of Deficit Syndrom and Primary/Secondary Negative Symptoms
The concept of Deficit negative symptom was first brought out by Carpenter (1988) and colleagues from Maryland Psychiatric Institute. Below is the operational criteria offered by Carpental et al _____________________________________________________________________________ 1. The patient meets DSM criteria for schizophrenia. 2. At least two of the following negative symptoms are present: a. Restricted affect b. Diminished emotional range c. Poverty of speech with curbing of interest and decrease in curiosity d. Diminished sense of purpose e. Diminished social drive 3. The negative symptoms are not fully accounted for by one or more of the following: a. Depression or anxiety b. Drug effect c. Environmental deprivation 4. Some combination of two or more of the negative symptoms listed above has been present for the preceding 12 months, and these symptoms were always present during periods of clinical stability (including chronic psychotic states) or during recovery from psychotic exacerbation. These symptoms may not be detectable during transient epi‐
sodes of acute psychotic disorganization or decompensation.  Patients meeting all four criteria can be designated as schizophrenic with deficit syndrome.  Patients meeting criteria 1 and 2 and possibly 4, but not meeting criterion 3, can be designated as schizophrenic with secondary negative symptoms.  Patients meeting criteria 1, 2, and 3, but not criterion 4, could either be schi‐
zophrenic with primary, nonenduning negative symptoms or with time will meet the full criteria for schizophrenia with deficit syndrome. _____________________________________________________________________________ Adopted from “Carpenter, W. T., Jr., D. W. Heinrichs, et al. (1988). "Deficit and nondeficit
forms of schizophrenia: the concept." Am J Psychiatry 145(5): 578-583”.
85
Appendices
Appendix 8. Distribution of PANSS Negative and Positive Subscale Scores by
Time
Week Negative subscale score Positive subscale score 0 1 3 86
Appendices
9 21 33 87
Appendices
49 88
Appendices
Appendix 9. Trajectory Subgroups
Dramatic and Sustained Early Improvement (DSI) in Both Negative and Positive
Symptoms (N=70, 18%)
35
35
35
Group 1‐2: N=29
Group 2‐3: N=27
30
30
30
25
25
25
20
20
20
15
15
15
10
10
0
50
10
0
50
Negative symptoms
Positive symptoms
Week
0
50
Week
13
Mild and Sustained Improvement (MSI) in Negative and Positive Symptoms, with
Greater Early Improvement in Positive than Negative Symptoms (N=237, 59%)
35
Observed Sub‐scale Means Observed Sub‐scale Means
Group 1‐3: N=14
Group 2‐2: N= 237
30
25
Negative symptoms
Positive symptoms
20
15
10
0
10
20
Week
30
40
50
89
Appendices
No Improvement (NI) in Negative and/or Positive Symptoms (N=82, 21%).
35
Observed Sub‐scale Means
Group 2‐1: N=20
35
35
Group 4‐1 : N=19
Group 4‐2: N=43
30
30
30
25
25
25
20
20
20
15
15
15
10
10
0 10 20 30 40 50
Week
10
0 10 20 30 40 50
Negative symptoms
0 10 20 30 40 50
Week
Positive symptoms
90
Appendices
Appendix 10. Negative-symptom Trajectories of 5-class Solution
Figure 1a. Mean negative-symptom trajectories
Note: Triangles indicate estimated means, and circles indicate observed means.
Figure 1b. Individual profiles by negative-symptom trajectories
(Black lines show trajectory of negative symptom subscale for each individual patient in each
latent class. Colored lines show estimated mean trajectory of the corresponding latent class.)
Class 1 Class 2 91
Appendices
Class 3 Class 4 Class 5 Table 2. Comparison between “GMM with MD” vs.”GMM with CD”
Classes from GMM with MD Total Classes from GMM with CD 1 2 3 4 5 Total 1 30 2 0 3 0 4 0 NC 16 46 0 0 0 14 44 0 0 0 284 284 0 6 0 3 9 0 0 54 9 63 3 2 31 212 264 3 8 85 522 664 Abbreviation: MD=missing data, CD=complete data, NC= non-classified
Note: the concordance between “GMM with CD” and “GMM with MD” was indicated in color shading
92
REFERENCES
Addington, J. and D. Addington (1991). "Positive and negative symptoms of schizophrenia.
Their course and relationship over time." Schizophr Res 5(1): 51-59.
Allen, N. C., S. Bagade, et al. (2008). "Systematic meta-analyses and field synopsis of genetic
association studies in schizophrenia: the SzGene database." Nat Genet 40(7): 827-834.
Andreasen, N. C. and S. Olsen (1982). "Negative v positive schizophrenia. Definition and
validation." Arch Gen Psychiatry 39(7): 789-794.
Arango, C., R. W. Buchanan, et al. (2004). "The deficit syndrome in schizophrenia: implications
for the treatment of negative symptoms." Eur Psychiatry 19(1): 21-26.
Bauer, D. J. and P. J. Curran (2003). "Distributional assumptions of growth mixture models:
implications for overextraction of latent trajectory classes." Psychol Methods 8(3): 338-363.
Beasley, C. M., Jr., T. Sanger, et al. (1996). "Olanzapine versus placebo: results of a doubleblind, fixed-dose olanzapine trial." Psychopharmacology (Berl) 124(1-2): 159-167.
Beasley, C. M., Jr., G. Tollefson, et al. (1996). "Olanzapine versus placebo and haloperidol:
acute phase results of the North American double-blind olanzapine trial."
Neuropsychopharmacology 14(2): 111-123.
Bollen, K. A. (1989). Structural Equations with Latent Variables New York, Wiley.
Bornschein, R. L., P. Succop, et al. (1985). "The influence of social and environmental factors on
dust lead, hand lead, and blood lead levels in young children." Environ Res 38(1): 108-118.
Breier, A. (2005). "Developing drugs for cognitive impairment in schizophrenia." Schizophr Bull
31(4): 816-822.
Breier, A., O. M. Wolkowitz, et al. (1987). "Neuroleptic responsivity of negative and positive
symptoms in schizophrenia." Am J Psychiatry 144(12): 1549-1555.
93
References
Bresnahan, M., C. A. Schaefer, et al. (2005). "Prenatal determinants of schizophrenia: what we
have learned thus far?" Epidemiol Psichiatr Soc 14(4): 194-197.
Buchanan, R. W., A. Breier, et al. (1998). "Positive and negative symptom response to clozapine
in schizophrenic patients with and without the deficit syndrome." Am J Psychiatry 155(6): 751760.
Buhler, B., M. Hambrecht, et al. (2002). "Precipitation and determination of the onset and course
of schizophrenia by substance abuse--a retrospective and prospective study of 232 populationbased first illness episodes." Schizophr Res 54(3): 243-251.
Buncher, C. R., P. A. Succop, et al. (1991). "Structural equation modeling in environmental risk
assessment." Environ Health Perspect 90: 209-213.
Carpenter, W. T., Jr., J. J. Bartko, et al. (1976). "Another view of schizophrenia subtypes. A
report from the international pilot study of schizophrenia." Arch Gen Psychiatry 33(4): 508-516.
Carpenter, W. T., Jr., D. W. Heinrichs, et al. (1988). "Deficit and nondeficit forms of
schizophrenia: the concept." Am J Psychiatry 145(5): 578-583.
Case, M., V. L. Stauffer, et al. (2010). "The heterogeneity of antipsychotic response in the
treatment of schizophrenia." Psychol Med: 1-10.
Chen, J., H. Ascher-Svanum, et al. (2011). "Reasons for continuing or discontinuing olanzapine
in the treatment of schizophrenia from the perspectives of patients and clinicians." Patient Prefer
Adherence 5: 547-554.
Crow, T. J. (1980). "Molecular pathology of schizophrenia: more than one disease process?" Br
Med J 280(6207): 66-68.
Crow, T. J. (1980). "Positive and negative schizophrenic symptoms and the role of dopamine."
Br J Psychiatry 137: 383-386.
Crow, T. J. (1985). "The two-syndrome concept: origins and current status." Schizophr Bull
11(3): 471-486.
94
References
Cuesta, M. J. and V. Peralta (2008). "Current psychopathological issues in psychosis: towards a
phenome-wide scanning approach." Schizophr Bull 34(4): 587-590.
Cutler, A. J., A. H. Kalali, et al. (2008). "Four-week, double-blind, placebo- and ziprasidonecontrolled trial of iloperidone in patients with acute exacerbations of schizophrenia." J Clin
Psychopharmacol 28(2 Suppl 1): S20-28.
Danion, J. M., W. Rein, et al. (1999). "Improvement of schizophrenic patients with primary
negative symptoms treated with amisulpride. Amisulpride Study Group." Am J Psychiatry
156(4): 610-616.
Dantan, E., C. Proust-Lima, et al. (2008). "Pattern mixture models and latent class models for the
analysis of multivariate longitudinal data with informative dropouts." Int J Biostat 4(1): Article
14.
Demirtas, H. and J. L. Schafer (2003). "On the performance of random-coefficient patternmixture models for non-ignorable drop-out." Stat Med 22(16): 2553-2575.
Edicott, J., R. Spitzer, et al. (1976). Global Assessment of Functioning (GAF) Scale. Outcomes
assessment in clinical practice. D. B. Sederer LI. Baltimore, MD:, Williams and Wilkins: 76-78.
First, M. B. (2000). Diagnostic and Statistical Manual of Mental Disorders 4th Ed. (DSM-IVTR™, 2000). . Washington, DC, American Psychiatric Association.
Goghari, V. M., S. R. Sponheim, et al. (2010). "The functional neuroanatomy of symptom
dimensions in schizophrenia: a qualitative and quantitative review of a persistent question."
Neurosci Biobehav Rev 34(3): 468-486.
Goldner, E. M., L. Hsu, et al. (2002). "Prevalence and incidence studies of schizophrenic
disorders: a systematic review of the literature." Can J Psychiatry 47(9): 833-843.
Gomeni, R., A. Lavergne, et al. (2009). "Modelling placebo response in depression trials using a
longitudinal model with informative dropout." Eur J Pharm Sci 36(1): 4-10.
95
References
Gourevitch, R., S. Abbadi, et al. (2004). "Quality of life in schizophrenics with and without the
deficit syndrome." Eur Psychiatry 19(3): 172-174.
Guelfi, G. P., W. O. Faustman, et al. (1989). "Independence of positive and negative symptoms
in a population of schizophrenic patients." J Nerv Ment Dis 177(5): 285-290.
Gueorguieva, R., R. Wu, et al. (2007). "New insights into the efficacy of naltrexone based on
trajectory-based reanalyses of two negative clinical trials." Biol Psychiatry 61(11): 1290-1295.
Howes, O. D. and S. Kapur (2009). "The dopamine hypothesis of schizophrenia: version III--the
final common pathway." Schizophr Bull 35(3): 549-562.
Kane, J. M., S. Assuncao-Talbott, et al. (2008). "The efficacy of aripiprazole in the treatment of
multiple symptom domains in patients with acute schizophrenia: a pooled analysis of data from
the pivotal trials." Schizophr Res 105(1-3): 208-215.
Kane, J. M., S. R. Marder, et al. (2001). "Clozapine and haloperidol in moderately refractory
schizophrenia: a 6-month randomized and double-blind comparison." Arch Gen Psychiatry
58(10): 965-972.
Kapur, S. (2003). "Psychosis as a state of aberrant salience: a framework linking biology,
phenomenology, and pharmacology in schizophrenia." Am J Psychiatry 160(1): 13-23.
Kay, S. R., A. Fiszbein, et al. (1987). "The positive and negative syndrome scale (PANSS) for
schizophrenia." Schizophr Bull 13(2): 261-276.
Kay, S. R., L. A. Opler, et al. (1988). "Reliability and validity of the positive and negative
syndrome scale for schizophrenics." Psychiatry Res 23(1): 99-110.
Kendler, K. S., T. J. Gallagher, et al. (1996). "Lifetime prevalence, demographic risk factors, and
diagnostic validity of nonaffective psychosis as assessed in a US community sample. The
National Comorbidity Survey." Arch Gen Psychiatry 53(11): 1022-1031.
96
References
Kinon, B. J., H. Ascher-Svanum, et al. (2008). "The temporal relationship between symptom
change and treatment discontinuation in a pooled analysis of 4 schizophrenia trials." J Clin
Psychopharmacol 28(5): 544-549.
Kinon, B. J., J. M. Kane, et al. (1993). "Possible predictors of neuroleptic-resistant schizophrenic
relapse: influence of negative symptoms and acute extrapyramidal side effects."
Psychopharmacol Bull 29(3): 365-369.
Kirkpatrick, B., W. S. Fenton, et al. (2006). "The NIMH-MATRICS consensus statement on
negative symptoms." Schizophr Bull 32(2): 214-219.
Knapp, M., R. Mangalore, et al. (2004). "The global costs of schizophrenia." Schizophr Bull
30(2): 279-293.
Laird, N. M. and J. H. Ware (1982). "Random-effects models for longitudinal data." Biometrics
38(4): 963-974.
Lehman, A. F. (1988). "A quality of life interview for the chronically mentally ill." Eval.
Program Plann 11: 51-62.
Lewis, D. A. and G. Gonzalez-Burgos (2006). "Pathophysiologically based treatment
interventions in schizophrenia." Nat Med 12(9): 1016-1022.
Lieberman, J. A., T. S. Stroup, et al. (2005). "Effectiveness of antipsychotic drugs in patients
with chronic schizophrenia." N Engl J Med 353(12): 1209-1223.
Lindamer, L. A., J. B. Lohr, et al. (1997). "Gender, estrogen, and schizophrenia."
Psychopharmacol Bull 33(2): 221-228.
Little, R. J. (1994). "Discussion of the paper by Diggle and Kenward." Applied Statistics 43(86).
Little, R. J. A. and D. B. Rubin (2002). Statistical analysis with missing data. New York, John
Wiley and Sons.
97
References
Liu-Seifert, H., D. H. Adams, et al. (2007). "Patient perception of medication benefit and early
treatment discontinuation in a 1-year study of patients with schizophrenia." Patient Prefer
Adherence 1: 9-17.
Lo, Y., N. R. Mendel, et al. (2001). "Testing the number of components in a normal mixture."
biometrika 88: 767–778.
Lysaker, P. H. and L. W. Davis (2004). "Social function in schizophrenia and schizoaffective
disorder: associations with personality, symptoms and neurocognition." Health Qual Life
Outcomes 2: 15.
Marques, T. R., T. Arenovich, et al. (2011). "The different trajectories of antipsychotic response:
antipsychotics versus placebo." Psychol Med 41(7): 1481-1488.
Maynard, T. M., L. Sikich, et al. (2001). "Neural development, cell-cell signaling, and the "twohit" hypothesis of schizophrenia." Schizophr Bull 27(3): 457-476.
McGrath, J. (2008). "Dissecting the heterogeneity of schizophrenia outcomes." Schizophr Bull
34(2): 247-248.
McLachlan, G. and D. Peel (2000). Finite Mixture Models. New York, Wiley.
Miles, C. P. (1977). "Conditions predisposing to suicide: a review." J Nerv Ment Dis 164(4):
231-246.
Munk-Jorgensen, P. and H. Ewald (2001). "Epidemiology in neurobiological research:
exemplified by the influenza-schizophrenia theory." Br J Psychiatry Suppl 40: s30-32.
Murray, C. J. L. and A. D. Lopez (1996). The Global Burden of Disease. Cambridge
Muthen, B. (2001). Latent variable mixture modeling. New developments and techniques in
structural equation modeling G. A. M. R. E. Schumacker, Lawrence Erlbaum Associates. : 1-33.
Muthen, B. (2002). "Beyond SEM: General Latent Variable Modeling." Behaviormetrika 29: 81117.
98
References
Muthen, B. (2004). Latent variable analysis: Growth mixture modeling and related techniques
for longitudinal data. Handbook of quantitative methodology for the social sciences. D. Kaplan.
Newbury Park, CA, Sage Publications: 345-368.
Muthen, B. (2006). "The potential of growth mixture modeling." Inf. Child Dev 15: 623–625.
Muthen, B. and T. Asparouhov (2008). Growth mixture modeling: Analysis with non-Gaussian
random effects. Longitudinal Data Analysis G. Fitzmaurice, M. Davidian, G. Verbeke and G.
Molenberghs. Boca Raton, Chapman & Hall/CRC Press: 143-165.
Muthen, B., T. Asparouhov, et al. (2011). "Growth modeling with nonignorable dropout:
alternative analyses of the STAR*D antidepressant trial." Psychol Methods 16(1): 17-33.
Muthen, B., C. H. Brown, et al. (2002). "General growth mixture modeling for randomized
preventive interventions." Biostatistics 3(4): 459-475.
Muthen, B. and L. Muthen (2007). Mplus - Statistical analysis with latent variables - user's
guide. Los Angeles, Muthen and Muthen.
Muthen, B. and K. Shedden (1999). "Finite mixture modeling with mixture outcomes using the
EM algorithm." Biometrics 55(2): 463-469.
Nagin, D. S. (1999). "Analyzing developmental trajectories: A semi-parametric, group based
approach." Psychological Methods 4: 139-157.
Nagin, D. S. and K. C. Land (1993). "Age, criminal careers, and population heterogeneity:
Specification and estimation of a nonparametric, mixed Poisson model." Criminology 31: 327–
362.
Nagin, D. S. and R. E. Tremblay (2001). "Analyzing developmental trajectories of distinct but
related behaviors: a group-based method." Psychol Methods 6(1): 18-34.
Nakamura, M., M. Ogasa, et al. (2009). "Lurasidone in the treatment of acute schizophrenia: a
double-blind, placebo-controlled trial." J Clin Psychiatry 70(6): 829-836.
99
References
Newman, S. C. and R. C. Bland (1991). "Mortality in a cohort of patients with schizophrenia: a
record linkage study." Can J Psychiatry 36(4): 239-245.
Nylund, K., A. Bellmore, et al. (2007). "Subtypes, severity, and structural stability of peer
victimization: what does latent class analysis say?" Child Dev 78(6): 1706-1722.
Palmer, B. A., V. S. Pankratz, et al. (2005). "The lifetime risk of suicide in schizophrenia: a
reexamination." Arch Gen Psychiatry 62(3): 247-253.
Patil, S. T., L. Zhang, et al. (2007). "Activation of mGlu2/3 receptors as a new approach to treat
schizophrenia: a randomized Phase 2 clinical trial." Nat Med 13(9): 1102-1107.
Pearson, W. H. (1966). "Estimation of a correlation coefficient from an uncertainty measure."
Psychometrika 31(3): 421-433.
Picchioni, M. M. and R. M. Murray (2007). "Schizophrenia." BMJ 335(7610): 91-95.
Rabinowitz, J. and O. Davidov (2008). "The association of dropout and outcome in trials of
antipsychotic medication and its implications for dealing with missing data." Schizophr Bull
34(2): 286-291.
Raftery, A. (1995). "Bayesian model selection in social research." Sociological Methodology
25: 111-163.
Regier, D. A., M. E. Farmer, et al. (1990). "Comorbidity of mental disorders with alcohol and
other drug abuse. Results from the Epidemiologic Catchment Area (ECA) Study." JAMA
264(19): 2511-2518.
Roy, J. (2003). "Modeling longitudinal data with nonignorable dropouts using a latent dropout
class model." Biometrics 59(4): 829-836.
Ruberg, S. J., L. Chen, et al. (2010). "The mean does not mean as much anymore: finding subgroups for tailored therapeutics." Clin Trials 7(5): 574-583.
Saha, S., D. Chant, et al. (2007). "A systematic review of mortality in schizophrenia: is the
differential mortality gap worsening over time?" Arch Gen Psychiatry 64(10): 1123-1131.
100
References
Santor, D. A., H. Ascher-Svanum, et al. (2007). "Item response analysis of the Positive and
Negative Syndrome Scale." BMC Psychiatry 7: 66.
Sawa, A. and S. H. Snyder (2002). "Schizophrenia: diverse approaches to a complex disease."
Science 296(5568): 692-695.
Schwarz, G. E. (1978). "Estimating the dimension of a model." Annals of Statistics 6(2): 461–
464.
Sclove, S. L. (1987). "Application of model-selection criteria to some problems in multivariate
analysis
" Psychometrika 52: 333-343.
Seeman, P. (2002). "Atypical antipsychotics: mechanism of action." Can J Psychiatry 47(1): 2738.
Shih, W. (2002). "Problems in dealing with missing data and informative censoring in clinical
trials." Curr Control Trials Cardiovasc Med 3(1): 4.
St Clair, D., M. Xu, et al. (2005). "Rates of adult schizophrenia following prenatal exposure to
the Chinese famine of 1959-1961." JAMA 294(5): 557-562.
Stauffer, V., M. Case, et al. (2011). "Trajectories of response to treatment with atypical
antipsychotic medication in patients with schizophrenia pooled from 6 double-blind, randomized
clinical trials." Schizophr Res 130(1-3): 11-19.
Stauffer, V. L., G. Song, et al. (2012). "Responses to antipsychotic therapy among patients with
schizophrenia or schizoaffective disorder and either predominant or prominent negative
symptoms." Schizophr Res 134(2-3): 195-201.
Succop, P. (2007). Does M+4.2 compute? Presentation at the Epidemiology and Biostatistics
Seminar, University of Cincinnati School of Medicine.
Succop, P. (2009). Dial M for Modeling. Presentation at the Epidemiology and Biostatistics
Seminar, University of Cincinnati School of Medicine.
101
References
Susser, E., R. Neugebauer, et al. (1996). "Schizophrenia after prenatal famine. Further evidence."
Arch Gen Psychiatry 53(1): 25-31.
Tandon, R. and J. F. Greden (1991). "Negative symptoms of schizophrenia: the need for
conceptual clarity." Biol Psychiatry 30(4): 321-325.
Tollefson, G. D. and T. M. Sanger (1997). "Negative symptoms: a path analytic approach to a
double-blind, placebo- and haloperidol-controlled clinical trial with olanzapine." Am J
Psychiatry 154(4): 466-474.
Torrey, E. F. (1987). "Prevalence studies in schizophrenia." Br J Psychiatry 150: 598-608.
Tsuang, M. (2000). "Schizophrenia: genes and environment." Biol Psychiatry 47(3): 210-220.
Tsuang, M. T., M. J. Lyons, et al. (1990). "Heterogeneity of schizophrenia. Conceptual models
and analytic strategies." Br J Psychiatry 156: 17-26.
Tunis, S. L., D. E. Faries, et al. (2006). "Cost-effectiveness of olanzapine as first-line treatment
for schizophrenia: results from a randomized, open-label, 1-year trial." Value Health 9(2): 77-89.
Uher, R., P. Huezo-Diaz, et al. (2009). "Genetic predictors of response to antidepressants in the
GENDEP project." Pharmacogenomics J 9(4): 225-233.
van Os, J., B. P. Rutten, et al. (2008). "Gene-environment interactions in schizophrenia: review
of epidemiological findings and future directions." Schizophr Bull 34(6): 1066-1082.
Velligan, D. I., L. Alphs, et al. (2009). "Association between changes on the Negative Symptom
Assessment scale (NSA-16) and measures of functional outcome in schizophrenia." Psychiatry
Res 169(2): 97-100.
Ventura, M., M. F. Green, et al. (1993). " Training and quality assurance with the brief
psychiatric rating scale: "The drift buster"." International Journal of Methods in Psychiatric
Research 3: 221-244.
102
References
Ware, J. E., Jr., M. Kosinski, et al. (1995). "Comparison of methods for the scoring and
statistical analysis of SF-36 health profile and summary measures: summary of results from the
Medical Outcomes Study." Med Care 33(4 Suppl): AS264-279.
Ware, J. E., Jr. and C. D. Sherbourne (1992). "The MOS 36-item short-form health survey (SF36). I. Conceptual framework and item selection." Med Care 30(6): 473-483.
Wu, E. Q., H. G. Birnbaum, et al. (2005). "The economic burden of schizophrenia in the United
States in 2002." J Clin Psychiatry 66(9): 1122-1129.
Yang, C.-C. (1999). Finite mixture model selection with psychometric applications.
103