University of Groningen
Translational PKPD modeling in schizophrenia
Pilla Reddy, Venkatesh
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Structural Models Describing Placebo
Treatment Effects in Schizophrenia
and Other Neuropsychiatric Disorders
Venkatesh Pilla Reddy, 1 Magdalena Kozielska,1
Martin Johnson,1 An Vermeulen,2 Rik de Greef,3
Jing Liu,4 Geny M.M. Groothuis,1 Meindert Danhof5 and
Johannes H. Proost.1
Division of Pharmacokinetics, Toxicology and Targeting,
University of Groningen, Groningen, the Netherlands,
2
Advanced PKPD Modelling and Simulation, Janssen
Research & Development, a Division of Janssen
Pharmaceutica NV, Beerse, Belgium,
3
Clinical PKPD, Merck Research Labs, Merck Sharp &
Dohme, Oss, the Netherlands,
4
Clinical Pharmacology, Pfizer Global Research and
Development, Groton, CT, USA,
5
Division of Pharmacology, Leiden/Amsterdam Center for
Drug Research, Leiden, the Netherlands
1
3
CHAPTER
Clinical Pharmacokinetics 2011; 50 (7): 429-450
34
Abstract
3
Large variation in placebo response within and among clinical trials can
substantially affect conclusions about the efficacy of new medications in
psychiatry. Developing a robust placebo model to describe the placebo response
is important to facilitate quantification of drug effects, and eventually to guide the
design of clinical trials for psychiatric treatment via a model-based simulation
approach. In addition, high dropout rates are very common in the placebo arm
of psychiatric clinical trials. While developing models to evaluate the effect of
placebo response, the data from patients who drop out of the trial should be
considered for accurate interpretation of the results.
The objective of this paper is to review the various empirical and semimechanistic models that have been used to quantify the placebo response
in schizophrenia trials. Pros and cons of each placebo model are discussed.
Additionally, placebo models used in other neuropsychiatric disorders like
depression, Alzheimer’s disease and Parkinson’s disease are also reviewed with
the objective of finding those placebo models that could be useful for clinical
studies of both acute and chronic schizophrenic disease conditions. Better
understanding of the patterns of dropout and the factors leading to dropouts are
crucial in identifying the true placebo response. We therefore also review dropout
models that are used in the development of models for treatment effects and in
the optimization of clinical trials by simulation approaches.
The use of an appropriate modelling strategy that is capable of identifying
the potential sources of variable placebo responses and dropout rates is
recommended for improving the sensitivity in discriminating between the effects
of active treatment and placebo.
Placebo-Response Modelling in Schizophrenia
35
Introduction
Modelling in Schizophrenia and Other Neuropsychiatric Disorders
A modelling and simulation-based approach is increasingly applied to enhance
the efficiency of clinical trials in multifaceted pathological conditions like
schizophrenia, depression, Alzheimer’s disease and Parkinson’s disease. These
disorders have in common that they lack objective measures (laboratory tests
or biomarkers) to evaluate the outcome of treatment effects.[1] As a result, the
evaluations of the severity of illness and the treatment effects are based on the
rating scales as assessed by a physician or by a trained rater. Rating scales in
psychiatric research have been designed primarily to measure psychopathological
symptoms. A rating scale usually consists of several questionnaires (items),
where each item is scored based on the severity of the symptom. For example, the
Positive and Negative Syndrome Scale (PANSS), developed by Kay et al.,[2] is one
of the symptom rating scales used to rate the symptom severity in schizophrenia.
It consists of 30 items, where each item is scored from 1 through 7 (1 indicating
the absence of the symptom and 7 indicating extremely suffering from the
symptom). These 30 items are grouped into 3 subscales; positive (7 items),
negative (7 items) and general psychopathology (16 items). These rating scales
are typically associated with significant placebo responses.[3]
Schizophrenia is often described in terms of positive symptoms (e.g. delusions,
hallucinations), negative symptoms (e.g. lack of motivation, social withdrawal)
and cognitive symptoms. The clinical response in schizophrenia is usually
measured by the Brief Psychiatric Rating Scale (BPRS)[4] and the PANSS.[5] The
BPRS has a limited scope because it focuses mainly on positive and general
psychopathology. The PANSS is an advancement on the BPRS as it also addresses
the negative symptoms. Recently, Leucht et al.[6] recommended the Clinical Global
Impression (CGI)[7] rating scale (score range: 1–7) because of lower cost and time
saving. A summary of commonly used rating scales for schizophrenia, depression,
Alzheimer’s disease and Parkinson’s disease is listed in table I.
In pharmacokinetic-pharmacodynamic modelling and simulation the outcomes
on the basis of rating scales are typically treated as categorical variables. Logistic
regression techniques are generally used to model categorical or ordinal variables
associated with a treatment and their relationship with drug exposure. When the
number of categories in a rating scale is sufficiently large, they can be considered
as continuous variables. Longitudinal time-course data on the scores on these
rating scales after placebo or drug treatment generally show a nonlinear trend,
with an initial drop from baseline followed by maximal improvement in disease
condition and, in some cases, worsening of the disease towards the baseline as
shown in figure 1a. Figure 1b illustrates the most commonly observed patterns
of the time course of the rating scores. These nonlinear trends (e.g. arising from
disease progression and from physiological, pharmacokinetic and feedback
processes) cause conventional statistics to underperform in the analysis of the
3
36
outcomes of clinical trials, or cause a difficulty in identifying the difference
between drug and placebo responses.[13] Recently it has been shown that obstacles
in conventional statistical analysis to detect drug-placebo differences can be
overcome using pharmacokinetic-pharmacodynamic modelling and simulationbased approaches.[14]
3
Table I. Summary of rating scales commonly used to assess the treatment effects in brain
disorders.
Rating scale (typical values)
Brain disorder
Schizophrenia
Depression
Alzheimer’s disease
Parkinson’s disease
Individual
mild severe
Rating scale items (n) range healthy disease disease Reference
PANSS
BPRS
CGI
HAMD-17
MADRS
ADASC
UPDRS
30
18
7
17
10
11
44
30–210
18–126
1–7
0–54
0–60
0–70
0–176
30
18
1
0
0
11a
0
58
31
3
11
13
18a
60
116
53
6
29
38
55a
140
5
4
7
8
9
10
11
Derived from the MMSE score, where ADASC = 70 − 2.33 × MMSE.[12]
ADASC = Alzheimer’s Disease Assessment Scale-Cognitive; BPRS = Brief Psychiatric Rating
Scale; CGI = Clinical Global Impression; HAMD-17 = 17-item Hamilton Depression Rating
Scale; MADRS = Montgomery-Åsberg Depression Rating Scale; MMSE = Mini-Mental State
Examination; PANSS = Positive and Negative Syndrome Scale; UPDRS = Unified Parkinson’s
Disease Rating Scale.
a
Fig. 1. (a) Sample plot showing the time course of Positive and Negative Syndrome Scale
(PANSS) scores following placebo administration. (b) Various typical trends of longitudinal
time-course data following placebo treatment.
Placebo-Response Modelling in Schizophrenia
37
Pharmacokinetic-Pharmacodynamic Modelling and Simulation
Pharmacokinetic-pharmacodynamic modelling and simulation-based approaches
are increasingly applied in the area of drug development.[15-18] Pharmacokineticpharmacodynamic modelling provides a link between the dose and concentration
of the drug (pharmacokinetics) to its effects in the body (pharmacodynamics).
Normally, population pharmacokinetic-pharmacodynamic modelling utilizes
a nonlinear mixed-effects approach (e.g. in the widely used software program
NONMEM), where both fixed effects (e.g. the clearance and volume of distribution
for pharmacokinetics, or the maximum effect [Emax] and the drug concentration
producing 50% of the Emax [EC50] for pharmacodynamics) and random effects
(interindividual variability [IIV] and residual unexplained variability [RUV) are
included in the model. A typical pharmacokinetic-pharmacodynamic model
consists of three submodels: a structural, a stochastic and a covariate model.
The structural submodel describes the overall trend in the data (e.g. a onecompartment pharmacokinetic model or an Emax pharmacodynamic model), using
fixed-effect parameters. The stochastic submodel accounts for IIV, interoccasion
variability (IOV), variability among trials and the RUV. Finally, the covariate
submodel is used to describe a relationship between the structural model
parameters and the covariates (e.g. patient characteristics or trial design details).
The variation in treatment response among the individuals is explained in part by
parameter-covariate relationships. In addition, covariate models help to design
the optimal (individualized) dosage regimen.[19]
Simulation is a process that helps in evaluating the robustness of a model and can
also be used for predicting the future outcome of a trial with different trial designs,
using parameters from the final modelling of observed data from a previously
executed trial. An important feature is that pharmacokinetic-pharmacodynamic
models are constantly updated, evaluated and subsequently validated at various
stages of drug development to be able to include new information. These
updated models and simulations support an efficient decision-making process by
facilitating the selection of the right compound, dose, dosage regimen and other
relevant factors needed to obtain regulatory authority approval. Figure 2 depicts
the process of typical modelling and simulation processes.
Pharmacokinetic-pharmacodynamic models can be divided into two groups:
empirical (i.e. ‘top-down’) models; and mechanistic models based on the concepts
of system biology. Empirical models describe the time course of clinical endpoints
(e.g. the rating scale and biomarkers) based on fitting a mathematical function
to the observed data, often without considering the underlying mechanisms of
action. They are simple and descriptive but may have less predictive power than
mechanism-based models.[20] Mechanism-based models describe the time course
of clinical effects based on parameters assessed in vitro and physiological values.
They make a clear distinction between drug-specific parameters and systemspecific parameters. Drug-specific parameters describe the interaction between
3
38
3
Fig. 2. Schematic representation of the process of pharmacokinetic-pharmacodynamic
modelling and simulation.
the drug and the biological system in terms of target binding and target activation.
System-specific parameters describe the inherent properties of the biological
system (e.g. receptor density, homeostatic feedback and disease progression).
An important factor is that system-related factors can be altered due to diseaserelated factors. This may affect the clinical outcome.[21] Figure 3 illustrates the
various factors that could affect the outcome of a pharmacological effect.
Fig. 3. Factors affecting the drug-response relationships.
Placebo Response in Neuropsychiatric Disorders
The term ‘placebo’ is derived from Latin: ‘I shall please’. A placebo is a substance
or procedure that is considered pharmacologically inactive for the condition
being treated. The use of a placebo treatment in clinical research allows better
conclusions relating to efficacy, adverse outcomes and scientific validity of
alternative trial designs of new drugs. In addition, it helps to detect the treatment
effect and discriminate it from nonspecific effects that may arise from trial
design, patient expectancies, demographic differences and medical intervention
factors. The current clinical approach of evidence-based drug discovery relies on
proving the superiority of a drug treatment compared with a placebo treatment,
Placebo-Response Modelling in Schizophrenia
implying a central role of placebo treatment in the drug development process. An
improvement of the clinical condition of patients in response to the administration
of the placebo constitutes a benefit to the patients, but it also obscures
quantification of drug effects. Placebo response could be due to psychological
effects owing to medical intervention or to non-psychological factors (e.g. trial
design and demographic differences). Over the last three decades, understanding
of underlying mechanisms of placebo response has improved as an increasing
number of researchers have become involved in identifying the possible causes of
placebo response.[22]
Approximately 50% of recent central nervous system (CNS) clinical trials
failed to show statistical superiority of the drug over placebo, due to the variable
placebo response (20–70%).[23,24] The trend of placebo responses in antipsychotic
trials over the last two decades is shown in figure 4. In addition to placebo
response, high dropout rates (40–70%)[3] from a trial tend to blunt the differences
in placebo-drug effect. Table II summarizes the important contributors for
variable placebo response and dropout rates in schizophrenia. The impact of
these contributors on the outcome of the trial results and possible remedies to
overcome these issues have been discussed in detail by many authors.[1,24,32,39-41]
For better quantification of drug effect a robust placebo model is needed.
It should account for dropouts and provide an insight into the parameters that
contribute to differences in treatment response among patients or studies. A good
model combining both placebo and drug effects could eventually guide the design
Fig. 4. Trend of the placebo response: data from short-term trials conducted between 1991
and 2006. The mean reduction in the total Positive and Negative Syndrome Scale (PANSS)
score from baseline for patients receiving placebo has increased. (Reproduced from Kemp et
al.,[3] by permission of Oxford University Press.)
39
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40
Table II. Summary of potential contributors for the reduced differences in placebo-drug effect
in schizophrenia
Contributors
Clinical relevance
References
Patient characteristics
3
Age
Sex
Race
Disease duration
and disease condition
BASL
The dopaminergic system and pharmacokinetics of
antipsychotics change with age
Men experience earlier onset of schizophrenia
compared to women, with a more debilitating course
and more suffering from negative symptoms. Women
tend to be treated with lower doses of antipsychotics,
as they suffer from antipsychotic drug-induced
hyperprolactinemia. These differences could be
attributed to hormonal reasons – more specifically, the
protective effect of estrogen
Ethnic or racial differences in response to placebo
or antipsychotic medications are reported due to
the difference in genetics, kinetic variations, dietary
factors and environmental factors
Many differences are evident between recentonset (acute) and chronic schizophrenia regarding
morphological changes in the brain, consecutive
cognitive impairment, level of compliance or
sensitivity to side effects, and these may result in
different outcomes in clinical trials for the respective
patient subgroup. A higher treatment effect in acute
patients compared to chronic patients was reported
Higher BASLs are associated with higher dropout rates
25-27
27-30
30,31
32
33
Methodological issues (trial design, site characteristics and clinical treatment settings)
Trial designs are usually different for phase II and
Clinical trial phase
phase III clinical trials. There are more stringent
criteria for phase II trials compared to phase III trials
Poor compliance with oral antipsychotic medications
Route of administration
was reported for patients with schizophrenia and can
34
and dosage regimen
correlate with treatment response and dropouts
Negative symptoms tend to respond slowly to
treatment and need longer time before they improve.
A longer duration of treatment is also helpful for
maintenance of the antipsychotic effect. A pronounced
35,36
placebo response in short-term trials was reported,
Study duration
which might reflect the immediate stabilizing effects
of hospitalization. Trials of long duration have shown
weakening of the placebo response as a function of
time
The duration of the washout period is crucial,
since relatively short washout periods can result
1
in the existence of carryover effects from previous
Washout period
treatments. Longer washout periods can result in
worsening of symptoms
continued next page
Placebo-Response Modelling in Schizophrenia
41
Table II. Summary of potential contributors for the reduced differences in placebo-drug effect
in schizophrenia
Contributors
Frequency of clinical
score measurement
Study site
Clinical endpoint
assessment tools
Hospitalization
(inpatient/outpatient)
Others
Clinical relevance
Significant effects of visit frequency on adherence
to antipsychotic therapy were noted. Frequent visits
may be assumed to have a positive impact on the
psychological feeling of the patient, which could
eventually contribute to higher placebo response and
lower dropout rates
Higher placebo response was reported in studies
conducted in the US. Possible reasons could be the
differences in ethnicity, kinetic variation, dietary
factors, genetics and environmental factors
Different rating scales (e.g. PANSS, BPRS or CGI) can
show different sensitivity for detection of treatment
effect
Compliance with the treatment regimen in
hospitalized patients, and consequently higher
placebo response and lower dropout rates may be
expected with hospitalized patients, owing to medical
attention
References
37
14
32,38
14
Site characteristics (e.g. academic or commercial,
experience and training of personnel, recruitment
pressures and procedures, ‘recycling’ of subjects) may
contribute to variable placebo response
BASL= baseline score; BPRS = Brief Psychiatric Rating Scale; CGI = Clinical Global Impression;
PANSS = Positive and Negative Syndrome Scale.
of a clinical trial via a simulation-based approach. Advanced pharmacokineticpharmacodynamic modelling and simulation are relatively less explored tools
in detecting the true drug effect. A pertinent advantage of a pharmacokineticpharmacodynamic modelling approach over traditional statistical approaches is
that components of disease progression and potential factors for high placebo
response, such as trial design and patient characteristics, are easily implementable.
Dropouts in Neuropsychiatric Disorders
Dropouts from longitudinal studies are very common in clinical trials of brain
diseases. For instance a dropout rate of 40–70%[33,42] has been observed in
placebo treatment groups of antipsychotic trials (figure 5). Ignoring these
missing response values due to dropouts may lead to biased results and affects
model building and evaluation. The common reasons for patients to withdraw
from the longitudinal clinical trials are: (i) recovery from disease; (ii) lack of
efficacy; (iii) adverse events; (iv) unpleasant study design; (v) co-morbidity; and
(vi) external factors unrelated to the trial.[43] Withdrawal due to external factors
unrelated to the trial is usually regarded as a completely random dropout (CRD)
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3
Fig. 5. Kaplan-Meier plot of
observed dropouts (a) in shortterm schizophrenia trials and
(b) in long-term schizophrenia
trials. A dropout rate of 40–70%
was observed with data from 15
placebo arms in trials conducted
between 1992 and 2006.
or ‘non-informative dropout’. If a patient drops out from a trial due to one of the
other factors (e.g. lack of efficacy as perceived by the patient [reflected in a higher
disease severity score]), such a dropout is regarded as an ‘informative dropout.
In New Drug Applications (NDAs) submitted to the US FDA, the lastobservation-carried-forward (LOCF) approach is still a widely used statistical
approach to account for dropouts. The use of LOCF may not be ideal, particularly
in chronic progressive disorders, as it assumes that there is no change in the score
(or other clinical endpoint) after the event of dropout, while in reality the patient
might have experienced worsening or improvement of the disease condition. If
the dropout mechanism is independent of any observed or non-observed variable
(where dropout can be ignored), the use of LOCF may give unbiased results.[44]
However, if the dropout mechanism is dependent on any observed or unobserved
variables, or in the case of unequal dropout rates between treatment arms, use
of LOCF is biased, with the bias being determined by the tendency of the data
and the ratio of the dropout rates. In regulatory settings, one of the reasons that
LOCF is commonly used is perhaps because it is straightforward and familiar to
researchers, clinicians and statisticians. In addition, potential bias arising from
LOCF could lead to a more conservative analysis outcome. In the context of drug
development, conservative can be thought of as providing protection against
falsely concluding that a drug is more effective than the placebo arm.[45,46]
Mixed modelling of repeated measurements (MMRM), an advanced statistical
approach, has been shown to be superior to LOCF for accounting for dropouts.
Placebo-Response Modelling in Schizophrenia
The MMRM approach is a member of likelihood-based mixed-effects analyses,
where this analysis takes account of nonlinear response to a set of parameters of
interest and takes account of the correlation between measurements. In addition,
IIV and IOV can also be handled appropriately.[46,47] The MMRM method uses the
generalized linear model approach to predict the time course of clinical response
and considers all the data collected from patients (those who drop out and those
who complete the study). In this approach, the observations from each patient
are assumed to originate from a multivariate normal distribution, with different
means for each time point and with a correlation between each measurement,
which is determined via a correlation matrix. MMRM leads to unbiased estimates
irrespective of dropout mechanisms, i.e. independent of or dependent on any
observed or unobserved variables.[48-51] The main objective of confirmatory clinical
trials is typically to delineate the differences between drug and placebo treatment
and not the effectiveness of treatment. Siddiqui et al.[49] have demonstrated the
superiority of the MMRM approach over LOCF in their analysis using 25 NDAs
datasets of neurological and psychiatric drug products. Due to the robustness
of MMRM against dropout it is recommended in the regulatory setting, as well
as in statistical analysis of longitudinal clinical trials.[45,52,53] However, MMRM
requires explicit modelling choices and implementation expertise, hindering its
use in regulatory drug approvals compared to LOCF. In addition, with MMRM it
is not easy to incorporate mechanistic components such as the disease system
(disease progression) and drug-specific characteristics (adverse events and
pharmacokinetic profile).
Integration of pharmacokinetic-pharmacodynamic concepts helps to account
for and identify predictors of dropout. In this respect, different dropout models
(see section 3) can be incorporated as an integral part of the pharmacokineticpharmacodynamic analysis to reduce the bias by accounting for underlying
missing data. Recently, Friberg et al.,[14] Frame et al.[54] and Gomeni et al.[55] have
shown the utility of an advanced pharmacokinetic-pharmacodynamic modelling
approach by combining the results of dropout rates and a pharmacokineticpharmacodynamic model (derived from rating scales) to describe the association
of drug and placebo treatment to dropout events.
Covariate Modelling
Identification of covariates that are important contributors of the placebo
response and dropout could help to design efficient prospective clinical trials and
thereby increase the success rate of clinical trials. Covariates are characteristics
describing the patient, the conditions of the drug treatment, the trial design or
other factors potentially influencing the clinical outcome. The covariates may be
constant within an individual (e.g. sex) or change over time (e.g. age). With regard
to covariates, typically a distinction is made between categorical and continuous
covariates. Categorical covariates are variables which can be binary (e.g. disease
condition: acute/chronic), ordered (e.g. severity of side effects: none, mild,
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3
moderate, and severe) or non-ordered (e.g. race). Continuous covariates have a
defined scale and can be quantified (e.g. bodyweight and age).
A covariate model describes the relations between covariates and
model parameters. Clinically relevant covariates are usually included in the
pharmacokinetic-pharmacodynamic model as factors which influence the values
of structural parameters and random effects.[56] In this regard they account for
a part of the observed IIV. There are several methods to build covariate models,
such as automated stepwise covariate modelling[57] and generalized-additive
modelling.[58] Covariate-parameter relationships can be modelled using different
functional forms like linear, piece-wise linear, power and exponential functions.
Table II summarizes the important contributors for variable placebo response
and dropout rates particularly in relation to schizophrenia, which necessitate the
use of a covariate model in conjunction with the placebo and dropout models.
Item-Response Analysis of Rating Scales
From a psychiatric drug-development perspective, the question is not only to
establish the relationship between the mechanism of action and the clinical
response but also to ensure that the clinical scales are sufficiently sensitive to
differentiate between the treatment effects. Rating scales may be suitable and
reliable but may lack sensitivity in discriminating between the effects of active
treatment and placebo.[59] Several authors[38,60,61] have explored the sensitivity of
the individual items of the rating scales and the consequences for the assessment
of clinical efficacy in diseases such as depression and schizophrenia. For example,
in depression trials, the 17-item Hamilton Depression Rating Scale (HAMD-17)
total score has been the gold-standard tool for establishing and comparing the
efficacy of treatments. However, the HAMD is a multidimensional measure and is
a weak index of depressive syndrome severity. This may reduce its ability to detect
differences between treatments – in particular, changes in the core symptoms of
depression. There have been a number of analyses to improve the rating scales,
such as by combining the scores of the individual items that are more sensitive,
and these studies often have included an empirical statistical analysis approach
(e.g. a linear mixed-effects modelling approach for repeated measures[61] or
principal component analysis[38]).
Recently, Santen et al.[60,61] explored the sensitivity of individual items of the
HAMD and Montgomery-Åsberg Depression Rating Scale (MADRS), using the
difference between responders and non-responders instead of the traditional
contrast between active treatment and placebo. The results showed that the HAMD
subscales were more sensitive to the treatment effect than the MADRS. Similarly,
in schizophrenia, Lader[62] and Santor et al.[38] have suggested that not all of the
PANSS items are sensitive to detect the true treatment effects. Such a difference in
the sensitivity between scales and the presence of items insensitive to response
may explain the high failure rate in detecting statistically significant separation
between active- and placebo-treated arms for most psychiatric drugs. It is clear
Placebo-Response Modelling in Schizophrenia
that new endpoints for clinical trials in psychiatric research should be developed
which do not only describe the symptoms but also accurately characterize the
disease severity on different levels. The pharmacokinetic-pharmacodynamic
modelling approaches are underutilized in this context and we envisage that
pharmacokinetic-pharmacodynamic model-based analysis could potentially be
used to identify the most sensitive items.
Placebo-Response Models
In pharmacokinetic-pharmacodynamic modelling, it is essential to first develop
a disease progression and a placebo model, before adding a model for the drug
effect. The status of the patient is a reflection of the state of the disease at any
given point in time. The disease status changes with time; therefore, modelling
of the disease status in the absence of treatment describes the expected changes
in the patient’s disease progression. The disease progression model can be
extended by including the treatment effects (placebo or drug) that refer to all
the underlying pharmacokinetic and pharmacodynamic processes involved in
producing a treatment effect on the time course (t) of disease progression, as
shown below (equation 1):[63]
(Eq. 1)
where t0 is the time at the start of the trial. The pharmacological effectiveness
of the drug is usually estimated on top of the placebo effect. A model for disease
progression and placebo response can be developed separately for diseases
such as Alzheimer’s and Parkinson’s disease, due to linear disease progression.
[64,65]
However, in other cases, it is difficult to separate disease progression from
placebo response due to the episodic nature of the disease (e.g. schizophrenia
and depression); in such cases, disease progression and placebo response can
be considered as a single entity. Figure 6 illustrates the natural time course
of disease severity in schizophrenia during ageing. A complicating factor is
that in most brain diseases, characterization of the natural time course of the
disease in an untreated condition is not possible due to ethical reasons. In such
circumstances, it is not possible to distinguish between placebo response and
disease progression. In some cases, clinical measurements obtained during the
washout period (i.e. at the beginning of trial initiation or during the screening
period) can provide a basis to describe disease progression.
In practice, typically, several placebo models are investigated, and the one that
describes the time course of the clinical endpoint best is taken further to integrate
with the drug-effect models.[63] While developing a drug-effect model, the placeboresponse model parameters are initially fixed (sequential analysis), and then
different drug-effect models are explored. Subsequently, all the parameters of the
final placebo and drug-effect models are simultaneously estimated. By utilizing
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3
Fig. 6. Natural history of schizophrenia. The disease progresses from a state of no symptoms
(presymptomatic) to the prodromal stage with cognitive and negative symptoms (but not
positive symptoms) and ultimately to first-episode psychotic symptoms (progressive stage).
The solid line indicates deterioration of normal functional abilities of a schizophrenic patient
over time. The dashed line shows the incidence of psychotic symptoms over time. Drug
treatment is more effective during the prodromal stage than in the later stages.
the population pharmacokinetic-pharmacodynamic approach with combined
placebo and drug-effect models, one can estimate the placebo parameters for the
drug treatment group.
In this review paper, we mainly focus on the placebo-response models, which
also account for dropouts and predictors of placebo response in psychiatric
research. A thorough search for placebo models was conducted in MEDLINE,
including published clinical trial results and exposure-response analyses
from 1980 to 2010. We also looked at the Drugs@FDA website (http://www.
accessdata.fda.gov/scripts/cder/drugsatfda/) for summary basis of approvals
(SBAs/NDAs) and the Population Approach Group in Europe website (http://
www.page-meeting.org/), the American Conference on Pharmacometrics website
(http://www.go-acop.org/) and the American Society for Clinical Pharmacology
and Therapeutics website (http://www.ascpt.org/) for abstracts or posters. We
searched for placebo- or drug-effect modelling results in neuropsychiatric disorders
irrespective of the rating scale used. In the area of antipsychotic pharmacokineticpharmacodynamic placebo-effect modelling, various empirical models such as the
linear model,[66] the power model,[67] the Weibull model,[14] the bi-linear model[68]
and the exponential model[69] have been used to describe the time course of the
PANSS score following a placebo treatment. A schematic representation of various
empirical model plots is shown in figure 7. More recently, semi-mechanistic
models like the indirect-response model (IRM)[70,71] have also been proposed to
describe the time course of the natural disease progression (table III). Alternative
Placebo-Response Modelling in Schizophrenia
47
3
Fig. 7. Schematic representation of various empirical models used in central nervous system
disorders. The numbers in parentheses indicate the disease for which the model was tested: 1 =
schizophrenia; 2 = depression; 3 = Alzheimer’s disease; 4 = Parkinson’s disease; BASL = baseline
score; kon = rate constant of score worsening; krec = rate constant of improvement after
placebo dosing; PE = magnitude of the placebo effect; PEmax = maximum placebo effect; SLOP =
slope; TD = time when 63.2% of maximum change from baseline is reached; tlag = delay in the
placebo response; TREM = time to reach 50% of remission.
placebo-response models (which have been explored in other brain disorders such
as depression, Alzheimer’s disease and Parkinson’s disease) such as polynomial
functions,[13] transit models[72] and inverse Bateman functions (IBFs)[72-74] are
presented in table IV. Sections 2.1 and 2.2 describe these models in detail. Table V
shows typical parameter values for each of the placebo models.
Empirical Models
Linear Model
The mathematical function describing linear model for placebo response is
represented in equation 2:
48
(Eq. 2)
3
The linear placebo model, using the BPRS score, was utilized to anticipate phase
III trial outcomes based on the phase II trial results in a placebo-controlled clinical
trial for quetiapine.[66] A slope parameter (SLOP) and baseline score (BASL) as the
intercept at time (t) zero describe the time course of the BPRS in the placebo
group treated for 6 weeks. The parameter values of this model were estimated by
mixed-effects linear regression analysis.
In this analysis the IIV in the BASL and SLOP parameters was evaluated
according to log-normal distribution and normal distribution, respectively. The
normal distribution of the IIV for the SLOP parameter allows the placebo effect
to be negative or positive. This is important as some patients show improvement
and others show deterioration in rating scores. Kimko et al.[66] reported that their
phase II modelling and phase III simulation results showed a significant favourable
placebo response, but the actual phase III trial placebo group results showed a
worsening of the disease condition (3% increase in BPRS score). Furthermore,
the linear model failed to describe their phase III placebo data by simulation.
There are at least three possible explanations for the poor performance of this
model. Firstly, the linear model may not have captured a nonlinear trend in the
BPRS score. The use of a different placebo model (a nonlinear model) to describe
Table III. Summary of placebo models tested in the area of schizophrenia.
Placebo
model
Placebo
model
parameters Estimation
Active
(n)
method
treatment Route
Linear
Quetiapine
Power
Bi-linear
Oral
2
Paliperidone Oral
5
Aripiprazole Oral
Exponential Olanzapine
Weibull
IRM
IRM
Asenapine
Oral
SL
Paliperidone Oral
Risperidone Oral/
IM
3
2
4
3
3
Dropout
model
Model
evaluation
criteria Ref.
ExponentialOFV, GOFP
TTE
FOCE/ODE
NT
OFV, GOFP
VPC,
FOCE/ODE
LRM
bootstrap
FOCE/
ExponentialVPC, PPC
Laplace
TTE
VPC,
FOCE/PRED
LRM
bootstrap
FOCE/ODE
Linear
VPC, PPC
FOCE/ODE
FO/ODE
Linear
GOFP
66
67
68
69
14
70
71
FO = first-order approximation; FOCE = first-order conditional estimation; GOFP = goodnessof-fit plots; IM = intramuscular; IRM = indirect-response model; LRM = logistic regression
model; NT = not tested; ODE = ordinary differential equations ; OFV = objective function value;
PPC = posterior predictive checks; PRED = prediction subroutine in NONMEM; SL = sublingual;
TTE = time-to-event dropout model; VPC = visual predictive checks.
Placebo-Response Modelling in Schizophrenia
the placebo response might have been more appropriate, but the authors justified
the use of a linear model based on its performance in the phase II BPRS data.
Secondly, the inclusion of a CRD model may not have been adequate, as this model
ignores the disease progression information. Use of informative dropout models
instead of a CRD model would have been more appropriate for the simulations.
Thirdly, no covariate analysis on the BASL structural parameter was tested that
might have explained part of the variability in placebo response.
In Parkinson’s disease[64] the linear model has been used successfully to
describe both the trajectory of disease progression and the change in the disease
status pertaining to the placebo response. In contrast, in Alzheimer’s disease
the linear model was employed to model disease progression while the IBF (for
details see section 2.1.7) was used to describe the placebo effect.[76-78]
The linear model is a simplistic model with two parameters and can be
a reasonable model for describing the time course of symptom scores when
measured for a short period of time (4–6 weeks). It has been suggested that placebo
response is usually more pronounced at the beginning of the placebo treatment
but decreases with time.[1,35] For this reason the linear model may be less useful for
trials of longer duration. In addition, the linear model is incapable of determining a
maximum placebo effect as it never reaches a steady state or plateau, whereas such
a steady state or plateau is often observed in clinical studies.
Power Model
The mathematical model describing a curvilinear change in disease severity is
shown in equation 3:
(Eq. 3)
Compared to the linear model, the power model utilizes an additional exponent
shape parameter (POW) to describe the time course of the disease score. This
model was used to describe the time course of PANSS in the placebo group of
a clinical trial of the antipsychotic drug aripiprazole.[67] In this analysis the
covariates influencing the placebo response were included in the model on the
SLOP parameter. The BASL of the patient was an important covariate for the
placebo response. Inclusion of POW helps to describe the shape of the PANSS
time-course curve. The estimated value of the shape parameter is influenced by
study duration or the PANSS measurement frequency. Like the linear model, the
power model is also incapable of determining a maximum placebo effect.
Bi-Linear Model
The mathematical function describing a bi-linear trajectory of change in disease
status is presented in equation 4:
(Eq. 4)
49
3
50
The bi-linear model describes the time course of a score as a combination of
two linear functions. The SHIFT describes the transition between the two slopes
(SLOP1 and SLOP2 in equation 4). The SHIFT is not discrete but is estimated by a
hyperbolic function (equation 5):
3
(Eq. 5)
where BREAK is the transition time and the exponent γ is the shape parameter.
SHIFT is required to obtain a smooth transition between the two slopes. This
model was successfully used to describe prolactin elevation as a predictor of
the clinical effect (PANSS) following the treatment with placebo or paliperidone
in schizophrenia trials.[68] In this analysis a normal distribution of the IIV was
included for the SLOP and BASL parameters. The bi-linear model is an interesting
model, as it can describe different time-course patterns – for example, patients
with only improvement or worsening in score, or patients with improvement and
then worsening or vice-versa.
Exponential Model
The mathematical model describing an exponential change in disease severity
with time is shown in equation 6:
(Eq. 6)
The basic exponential model (equation 6) was used to characterize the placebo
effect over time in schizophrenia, using the PANSS score of 51 subjects.[69] In this
model, k is a rate constant that characterizes the rate of change in disease severity
(placebo response) and PE is a parameter describing the magnitude of the placebo
effect, which is additive to BASL. The authors reported that this model adequately
described the time course of the PANSS score.
Holford[75] used a slight modification of this model for depression trials
(equation 7) to account for the delay in the placebo response (tlag):
(Eq. 7)
where TREM is the time to reach 50% of remission.
Both exponential models (equations 6 and 7) assume that placebo response
reaches a plateau at infinite time (∞). Compared to the linear and power models,
the exponential model can approximate nonlinear response curves better.
Paroxetine
Paroxetine
Paroxetine
Paroxetine
Levodopa
Paroxetine
2 antidepressant
drugs
Tacrine
Oral/IV
Oral/IV
Oral
Oral/IV
Oral
NM
NM
Oral
Oral
NM
Route
3
3
4
4
4
4
4
3
4
4
FOCE/ODE
FOCE/ODE
NA
FOCE/PRED
FOCE
FO
FOCE
NA
FOCE/Laplace
NM
Estimation
method
NT
NT
NT
NT
ExponentialTTE
NT
ExponentialTTE
NT
ExponentialTTE
NM
Dropout model
73
VPC, NPC, shrinkage
and bootstrap
VPC, NPC, shrinkage
and bootstrap
DIC, GOFP (Winbugs)
VPC, NPC, shrinkage
and bootstrap
OFV, GOFP and VPC
OFV
72
72
13
72
65
73
13
OFV, GOFP and VPC
DIC, GOFP (Winbugs)
13
75
OFV, GOFP and VPC
OFV, GOFP (NONMEM)
Reference
Model evaluation
criteria
DIC = deviance information criterion; FO = first-order approximation; FOCE = first-order conditional estimation; GOFP = goodness-of-fit plots;
IBF = inverse Bateman function; IRM = indirect-response model; IV = intravenous; LRM = logistic regression model; NA = not applicable; NM
= not mentioned; NPC = mumerical predictive checks; NT = not tested; ODE = ordinary differential equations ; OFV = objective function value;
PRED = prediction subroutine in NONMEM; tlag = delay in the placebo response; TTE = time-to-event dropout model; VPC = visual predictive checks.
Transit model
IRM
IBF
IBF
IBF
IBF
IBF
4 antidepressant
drugs
Exponential model
with tlag
Mixed Weibull and
linear function
Polynomial
Paroxetine
Active treatment
Placebo model
Placebo
model
parameters
(n)
Table IV. Summary of placebo models tested in the area of depression, Alzheimer’s and Parkinson’s diseases.
Placebo-Response Modelling in Schizophrenia
51
3
52
Weibull Model
The mathematical model describing complex nonlinear patterns of placeboresponse progression (the Weibull function) is shown in equation 8:
3
(Eq. 8)
The Weibull model describes the decrease of the score from baseline which
eventually reaches a plateau. PEmax is the maximum placebo effect, TD is the time
when 63.2% of maximum change from baseline is reached. The Weibull model is
an extension of the basic exponential model including POW, and it reduces to the
exponential model when POW = 1. Friberg et al.[14] successfully used the Weibull
model to describe the placebo response in a clinical trial of the antipsychotic drug
asenapine. In this analysis the placebo effect was included as being proportional to
the PANSS BASL, as illustrated in equation 8. This model also enabled demonstration
of the importance of covariates for the outcome of the modelling. Both disease
duration and clinical trial phase were important contributory factors to the placebo
response. A limitation of the Weibull model is that it lacks the flexibility to describe
the worsening of the disease condition after initial improvement or vice versa. To
overcome this deficit, Gomeni et al.[55] proposed a mixed Weibull model with an
additional linear function (with a slope parameter called DRIFT) to describe the
placebo response in a major depressive disorder trial of paroxetine (equation 9):
(Eq. 9)
This model is generic and therefore appropriate for modelling other diseases like
depression and Alzheimer’s disease. The Weibull model may be one of the best
choices to model data that show initial improvement followed by a plateau (as is
often seen in placebo groups in antipsychotic drug trials). In addition, the Weibull
model also takes into account the individuals with a flat placebo response.
Furthermore, a linear or other suitable function has to be added to the basic
Weibull function in order to describe the data that has a parabolic shape.
Polynomial Function
The mathematical expression of a polynomial function is shown in equation 10:
(Eq. 10)
where SLOP and QUAD are the linear and the quadratic coefficients, respectively.
A polynomial function was used to describe the time course of the MADRS
Placebo-Response Modelling in Schizophrenia
score following venlafaxine treatment in depression.[79] The model predicted
the time course of the MADRS score reasonably well after including plasma
drug concentration as a covariate. Gomeni and Merlo-Pich[13] attempted various
longitudinal placebo models to describe the HAMD-17 scores in depression, one
of them being the polynomial function. It is not clear from this paper whether
the polynomial function described the HAMD-17 scores adequately. The presence
of the QUAD parameter in equation 10 helps to account for the curvature in the
response and allows worsening of the disease after initial improvement, or vice
versa.
Inverse Bateman Function
The mathematical model of the IBF is shown in equation 11:
(Eq. 11)
The IBF contains two exponential expressions. The first exponential expression
describes the improvement with a placebo treatment, while the second
exponential expression is used to account for worsening of disease. In this
function, krec is the rate constant of improvement after placebo dosing, kon is the
rate constant of score worsening, and the DREC parameter reflects the amplitude
of score improvement during recovery. The placebo response is assumed to be
due to the time course of a hypothetical placebo concentration (CEON) after a
placebo dose at time zero (the start of the trial). A basic pharmacokinetic firstorder absorption and elimination model is then used to describe the placebo
effect. Differences in the rate of response appearance and loss of response are
determined by the absorption and elimination half-lives. Originally, Holford and
Peace[76,80] proposed IBF to predict the hypothetical CEON. The predicted CEON
was then used to model the time course of the Alzheimer’s Disease Assessment
Scale-Cognitive (ADASC) score in Alzheimer’s disease.
Recently, many authors[13,65,72,73] have used the IBF to predict the time course of
the disease score without the need to predict the CEON. Holford et al.[73] used the
IBF to account for the placebo response in depression, mainly due to the cyclical
nature of the disease, and an expectation of improvement and worsening of the
score over time. Since the IBF is empirical in nature, there are no requirements
for model parameter estimates to be positive and to constrain the initial estimates
that allow description of the patients worsening at an early stage and then
improving at a later stage.
In placebo-controlled studies, placebo response is usually dominant at the
beginning of the treatment but decreases as the time progresses. kon and its
derived parameter, ton (the half-life of worsening), which is calculated by equation
12 may not be identifiable with shorter-duration trials, which lack information
on relapse.
53
3
54
Table V. Parameter values for various placebo models used to assess the placebo effects in
neuropsychiatric diseases.
Structural parameters
3
Model
Disease
Linear
Schizophrenia
Bi-linear
Schizophrenia
Power
Schizophrenia
Exponential Schizophrenia
Weibull
Weibull +
linear
Schizophrenia
Depression
continued on next page
Rating
scale
Parameter
(units)
BASL
SLOP (h–1)
RUV (% CV)
BASL
SLOP1 (units/day)
PANSS SLOP2 (units/day)
BREAK (days)
RUV (% CV)
BASL
SLOP
PANSS
POW
RUV (% CV)
BASL
PE (units)
PANSS
k (week–1)
RUV (% CV)
BASL
PEmax
PANSS
TD (days)
POW
RUV (SD)
BASL
TD
DRIFT
HAMD-17
POW
RUV (% CV)
BPRS
Parameter
value
38.6
−0.0077
31
90.2
−0.73
0.17
10
NA
85.6
−1.04
0.371
9
92.1
11
0.3
29
90.5
0.085
13.2
1.24
3.5
23
7.2
0.91
0.51
NA
Interindividual
variability
(%CV)
Ref.
52
132
−
−
165
365
−
−
−
8
−
−
14
32
−
−
13 (SD)
0.16 (SD)
−
−
44
10
12
52
88
−
66
68
67
69
14
13
(Eq. 12)
IBF could be a useful model for longer-duration trials that might have enough
information on the relapse of disease conditions. However, correlations among
the rate constant parameters are common and should be considered during
optimization of a clinical trial using a simulation approach. IBF parameter
estimates are usually dependent on study duration. Like the Weibull model, this
model has been extensively used in various disease conditions like depression,
Alzheimer’s disease and Parkinson’s disease. The use of the IBF for the modelling
of placebo response in schizophrenia has not been reported.
Placebo-Response Modelling in Schizophrenia
55
Table V. Parameter values for various placebo models used to assess the placebo effects in
neuropsychiatric diseases.
Structural parameters
Model
Disease
Rating
scale
Polynomial
Depression
MADRS
IBF
Depression
HAMD-17
IRM
Depression
HAMD-17
Transit
model
Depression
HAMD-17
Parameter
(units)
Parameter
value
BASL
SLOP
QUAD
RUV (SD)
BASL
DREC
krec
kon
RUV (SD)
kin (day–1)
kout (day–1)
SLOP
RUV (SD)
34.1
−2.22
0.046
4.6
21.6
7.65
0.72
0.037
3
0.11
0.005
0.94
3.4
BASL
MTT (days)
SLOP
RUV (SD)
21.8
10
0.06
4
Interindividual
variability
(%CV)
Ref.
4.9 (SD)
1 (SD)
0.04 (SD)
−
−
77
178
51
−
8
−
223
−
3
−
181
−
13
13
72
72
BASL = baseline score; BPRS = Brief Psychiatric Rating Scale; BREAK = transition between two
slopes; CV = coefficient of variation; DREC = amplitude of score improvement during recovery;
DRIFT = slope parameter; HAMD-17 = 17-item Hamilton Depression Rating Scale; IBF = inverse
Bateman function; IRM = indirect-response model; k = rate of change in disease severity;
kin = zero-order rate constant; kon = rate constant of score worsening; kout = first-order rate
constant; krec = rate constant of improvement after placebo dosing; MADRS = MontgomeryÅsberg Depression Rating Scale; MTT = mean transit time; PANSS = Positive and Negative
Syndrome Scale; PE = magnitude of the placebo effect; PEmax = maximum placebo effect;
POW = shape parameter; QUAD = quadratic coefficient; RUV = residual unexplained variability;
SD = standard deviation; SLOP = slope; TD = time when 63.2% of maximum change from
baseline is reached.
Semi-Mechanistic Models
The IRM and transit models are semi-mechanistic in a pharmacological sense
for a drug treatment but are not necessarily semi-mechanistic for a placebo
effect. These models for the placebo treatment are still rather empirical in
nature with a hypothetical CEON but may be considered as semi-mechanistic
models when the mechanism of placebo effect is known. Benedetti[22] reviewed
possible mechanisms of placebo treatment in many CNS diseases. Increased
understanding of placebo-response mechanisms in recent years creates a
challenging opportunity for pharmacometricans to gather such data, account for
the mechanism(s) of the placebo effect via pharmacokinetic-pharmacodynamic
modelling and subsequently link it to the clinical endpoint.
3
56
3
Indirect-Response Model (IRM)
The IRM describes the change in disease severity score as the net result of the rate
of worsening (as reflected in the zero-order rate constant [kin]) and the rate of
improvement (as reflected in the first-order rate constant [kout]) processes. In this
model a pharmacokinetic driving function is used to reflect the time course of the
hypothetical CEON, which is assumed to affect either kout or k in (i.e. a stimulatory
effect on kout or an inhibitory effect on kin). Shang et al.[72] have successfully used
equation 13 to model the natural course of the HAMD-17 score.
(Eq. 13)
A hypothetical steady-state CEON allowed kout to be affected linearly with a SLOP
parameter or nonlinearly (e.g. with Emax model parameters). The model was found
to be over parameterized, hence BASL was not considered as a model parameter
and the system was initialized to the BASL. Alternatively, one of the rate constants
and the BASL may be estimated as parameters, and the other rate constant can
then be derived indirectly from equation 14, assuming steady-state conditions.
(Eq. 14)
Various approaches to estimate the time course of CEON have been proposed in
the literature. The first approach by Shang et al.[72] used a one-compartment linear
placebo pharmacokinetic model with a multiple bolus dose of placebo (1 unit)
and first-order elimination (equation 15). The values of the clearance (CLplacebo)
and the volume of distribution (Vplacebo) were fixed to certain values in order to
derive the elimination rate constant (ke):
(Eq. 15)
The second approach was called the kinetic pharmacodynamic (K-PD) model,[81]
where ke was estimated in order to derive the hypothetical CEON values. The
third approach by Post[82] used an exponential infusion type of K-PD function to
predict CEON following a placebo dose at the beginning of the trial. The CEON
was assumed to increase as an infusion input and remain at a steady-state
concentration of 1 unit until the end of the study (equation 16):
(Eq. 16)
Placebo-Response Modelling in Schizophrenia
The pharmacokinetic input for placebo treatment depends on an onset function
presented in equation 16, where the switch, PLAC, initializes the placebo
treatment effect with PLAC( 0| 1) = 1, if t > tstart. The parameter ke gave the
elimination rate constant for the placebo dosing. However, usually the values of
the ke and kout parameters are correlated, which limits the use of this approach. To
overcome this parameter-correlation issue, one could fix the value of ke based on
the simulations and estimate only kout. Our NONMEM data analysis showed that
the exponential infusion type of the K-PD function seems to have fewer numerical
difficulties and a shorter run time compared with other approaches.[83]
In schizophrenia, Ortega et al.[70] proposed a complex IRM to describe the
time course of PANSS following placebo/paliperidone treatment. The change
in the clinical score of the patient was described by a balance between the rate
of deterioration and the rate of amelioration of the disease. Amelioration was
assumed to be proportional to the current value of the score and the proportionality
coefficient, K. Deterioration was assumed to be proportional to the asymptotic
value (at time ∞) of the score (RP) with the same K of amelioration (equation 17):
(Eq. 17)
At the beginning of a trial, i.e. at time zero, SCORE = BASL. It was assumed that
the treatment reduces RP and thereby the rate of deterioration. If RP > BASL
the patient’s condition deteriorated, and RP < BASL indicated improvement
in the patient’s condition. Hence, RP was considered a composite parameter
incorporating disease progression, PE, drug effect and effect of dropouts. RP
was constrained within the PANSS score boundaries (30–210), using logit
transformation.
To model the PE and to account for the tolerance in placebo response, Ortega
et al.[70] used an exponential model with a parameter, tlag, that described the time
after which the placebo effect decreased with a first-order rate constant (kt). As
the tolerance was not observed in all patients, they employ a mixture model on
the kt parameter to differentiate the patients who were tolerant or non-tolerant of
placebo treatment (equation 18):
(Eq. 18)
Moreover, Ortega et al.[70] also accounted for time-dependent changes in the
dynamics of disease progression of schizophrenia. An asymptotic change in the
PANSS score from the baseline of 23 units was reported with a disease progression
rate constant of 0.0294/day. This decreased disease severity could be explained
by stabilization of the acute schizophrenic episode. They also reported that no
clinically relevant covariates could be identified with their final placebo model.
57
3
58
3
The IRM model is still rather empirical in nature with a hypothetical CEON,
but it may be considered as a semi-mechanistic model when the mechanism of
placebo effect is known[22] or when a drug component is included in the model.
For example, in schizophrenia, D2 receptor binding is believed to influence the
clinical outcome. Therefore, linking rate of improvement (or deterioration) to
D2 receptor occupancy rather than to plasma concentration may lead to better
results. Alternatively, one could use predicted drug concentration in biophase
(e.g. using preclinical data via a translational approach). A generic schematic IRM
is shown in figure 8.
Transit Model
Shang et al.[72] and Mould et al.[74] used a transit model to describe the time course
of the HAMD-17 score in depression. Two transit compartments were used to
describe the change in HAMD-17 scores over time. A pertinent feature of a transit
model is that it incorporates a parameter called mean transit time (MTT), which
describes the delay in the placebo effect (equation 19):
(Eq. 19)
where n = number of transitions and kTC is the first-order rate constant between
transit compartments.
Figure 9 and equation 20 depicts the transit model structure and its differential
equations:
Fig. 8. Indirect-response model used to describe the change in score over time.
Cp = concentration in plasma; kin = zero-order rate constant; kout = first-order rate constant.
Placebo-Response Modelling in Schizophrenia
(Eq. 20)
where PRE represents the precursor status.
The influence of placebo was handled by creating a pharmacokinetic driving
function for the placebo effect as described above for the IRM. When there is one
transit compartment, the transit model and IRM are interchangeable. Shang et
al.[72] reported that the transit model performed slightly better than the IRM in
describing the HAMD-17 score in depression. A transit model may be a better model
to describe the delay in treatment response as is usually seen in depression trials,
unlike schizophrenia trials.
Dropout Models
Dropouts are common events in longitudinal clinical trials. Subjects may drop out
of an ongoing clinical trial due to several reasons. Missing data based on the reasons
why patients drop out could be of three basic types.[84,85] The first type is ‘missing
completely at random’ (MCAR), also commonly known in the pharmacokineticpharmacodynamic area as CRD, where the missingness is independent of the
observed data and/or covariates. The estimation-based inferences, model
evaluation and clinical trial simulation results are usually unaffected if the missing
mechanism is MCAR. However, the MCAR mechanism affects the standard errors
as the sample size is lower. Consequently, the confidence intervals predicted
through simulations would be larger. The second type is ‘missing at random’
(MAR) or ‘random dropout’ (RD), where the missingness is related to the observed
Fig. 9. Schematic representation of the transit compartment model used to describe the
change in scores over time.[74] kTC = first-order rate constant between transit compartments;
PRE = precursor status; TC1 = transit compartment 1; TC2 = transit compartment 2; TCn = transit
compartment n.
59
3
60
3
response (such as drug concentration or clinical endpoint) and/or covariates. The
estimation-based inferences are usually not influenced by the MAR mechanism if
appropriate modelling methodology (e.g. likelihood-based methods) is used to
estimate the model parameters. However, the results of model evaluation and
clinical trial simulations are influenced if the missing mechanism is MAR. The
third type is ‘missing not at random’ (MNAR) or informative dropout, where the
dropout is related to one or more predicted (unobserved) response variables.
The results of estimation-based inferences, model evaluation and clinical trial
simulation results are potentially affected if the missing mechanism is MNAR.
Often, MAR and MNAR are regarded as informative dropout as the missing data
contains information on the disease progression, drug efficacy and safety.
Wu and Carroll[86] jointly modelled disease progression and probability of
dropping out, using a statistical generalized linear model approach. Since disease
progression, pharmacokinetic and pharmacodynamic observations frequently
show nonlinear trends, Hu and Sale[85] extended the joint modelling efforts, using
a nonlinear pharmacokinetic-pharmacodynamic modelling approach along with
statistical principles to evaluate whether the dropout mechanism is MCAR, MAR
or MNAR. Parametric time-to-event (TTE) and logistic regression models are
commonly used to investigate the relationship between the clinical response and
the dropout event.
Time-to-Event Dropout Models
TTE models predict the probability of a patient dropping out by describing the
hazard for the event. Hazard is the instantaneous rate of the dropout event: H(t).
The cumulative hazard (CHZ) predicts the risk of a patient dropping out from a
study over the time interval, which is obtained by integrating the hazard with
respect to time: The probability of survival (not dropping out) can be predicted
from the CHZ: exp(–CHZ). Hazard over time is usually integrated numerically
using software programs (e.g. NONMEM, WINBUGS, R, etc.) with the help of userdefined differential equations. The commonly used TTE models in the area of brain
disorders are the exponential dropout model (Parkinson’s disease, schizophrenia,
Alzheimer’s disease and depression),[55,65,69,87] the Gompertz dropout model
(generalized anxiety disorder)[54] and the Weibull dropout model (depression).[88]
The exponential dropout model assumes the probability of dropout to be constant
over time for the entire study duration. In contrast, a time factor is considered in
the Gompertz and the Weibull dropout model. Further basic discussions on various
models to account for missing data can be found elsewhere.[89-91]
In schizophrenia, Goyal[69] used an exponential dropout model to integrate with
clinical efficacy (the MNAR pattern). In depression, Parkinson’s and Alzheimer’s
diseases the most commonly used TTE was the exponential dropout model.[55,65,69,87]
Recently, the Weibull dropout model has been also evaluated in depression trials.
[88]
No dropout models have been reported with power[67] and polynomial[13,79]
placebo models.
Placebo-Response Modelling in Schizophrenia
61
Longitudinal Logistic Regression Dropout Model
The longitudinal logistic regression model describes a probability (P) of a patient
dropping out, which always lies in the range between zero and one. The general
form of the longitudinal logistic regression model is shown in equation 21:[92]
(Eq. 21)
The logit transformation transforms the 0 to 1 probability scale to a −∞ to +∞
scale, allowing for the development of linear models to describe the relationship
between the success probability and various predictors. In equation 21, α
denotes the probability of a patient dropping out at the time of trial initiation,
while β determines the change in P(X) relating to one or more predictor
variables (X). As in linear regression, a value of zero for β indicates that the score
is independent of X. The logistic regression model is shown to be advantageous
in adding extensions to the model to test for nonlinear functions, interactions
between covariate effects or other more complicated functions within the same
general framework.
In schizophrenia, the longitudinal logistic regression model has been used by
Friberg et al.[14] and Petersson et al.[68] Both authors used an empirical description
of the PANSS time course and combined it with a logistic regression model of
dropout to improve their model fit. The important predictors of dropout were
found to be the study site (US or non-US), hospitalization, the change in the PANSS
score from baseline, the time since start of study, the score on previous occasion
and the difference between the last two scores. The logistic regression dropout
model is flexible and allows inclusion of many predictors at a time. No integrated
logistic regression dropout model with a drug-effect model has been reported for
depression, Alzheimer’s disease or Parkinson’s disease.
Instead of the above-mentioned TTE models and logistic dropout modelling
approach, Ortega et al.[70] have used a simple linear dropout model to account for
dropouts in an antipsychotic drug trial. They used the following model structure
(equation 22):
(Eq. 22)
where tLO is the time from the commencement of the study to the last PANSS
observation for each patient, tES is the scheduled trial duration and kLO is a
parameter that determines the dropout effect. The dropout effect was then
3
62
allowed to influence the PANSS score via the RP function as shown in equation 17.
For further details see Ortega et al.[70]
Discussion and Conclusions
3
Developing a new drug for CNS disorders has always been challenging, and
even if the research and development groups have managed to come up with a
‘promising’ molecule, they have often failed to prove its efficacy in clinical trials.
Clinical trials aiming to prove the efficacy of drugs in CNS diseases typically
compare the efficacy of the newly developed molecule to placebo treatment in
placebo-controlled trials. However, many clinical trials fail to prove the superiority
of the molecule – for example, failure rates of up to 50% have been reported in
clinical trials conducted for antidepressants which were introduced later on to
the market.[68,93]
Important possible reasons for such high failure rates are considerable
magnitude and variability in placebo response, high dropout rates and low
sensitivity of the subjective rating scales used for assessing the treatment effect.
Usually, non-model-based approaches make the general assumption that both
the placebo effect and disease progression are constant over time, which is often
not factual and could lead to a biased trial outcome. Conversely, using advanced
model-based assessment tools with higher sensitivity, such as pharmacokineticpharmacodynamic modelling and simulation-based approaches, would increase
the power and the chance of discriminating among the disease progression,
placebo and drug effects. This would also help in designing highly powered studies
with the need for less money and time spent on studies with a large number
of subjects. The FDA and the European Medicines Agency have appreciated
the potential of pharmacokinetic-pharmacodynamic modelling and its impact
on decision-making by publishing the guidance to industry.[94-96]Examples of
psychiatric drugs where the pharmacokinetic-pharmacodynamic model-based
approaches have been utilized in the NDA to obtain regulatory approvals are
aripiprazole[67] and asenapine.[97]
Placebo response is a ‘background noise’ that impedes the likelihood of
detecting the signal of an effective drug. Addressing the placebo-response issue
is one of the most important challenges facing the future of psychiatric drug
development. Variable placebo response is a big problem with multi-centred
clinical trials. Different magnitudes of placebo response in different trial centres
may affect the detection of drug effects. The definition of dose/exposure response
and the comparison of drug response across studies would require normalization
of the quantifiable treatment effect by the level of placebo response. In modelling,
one should consider possible differences in the study designs, study centres,
patient characteristics and other important factors such as dropouts and disease
progression.
Placebo-Response Modelling in Schizophrenia
The empirical placebo models demonstrated their potential to predict
the clinical trial results via a simulation approach, but sometimes parameter
estimates are dependent on the study design and study duration. In contrast,
the parameter estimates of semi-mechanistic or mechanistic models are often
more robust, uncorrelated and independent of the study design and duration.
In addition, the parameters will be more clinically meaningful by considering
physiological mechanisms. For instance, clinical translation of pharmacological
mechanisms of treatment effects to their efficacy and safety can be implemented
using mechanism-based models, while it is difficult with empirical models. Post
et al.[98] and de Winter et al.[99] have successfully shown the advantages of the
mechanistic models over the empirical models with data on antidiabetic drugs.
However, mechanism-based models usually, but not always, require the use of
differential equations, leading to longer run times (e.g. using NONMEM) and
numerical difficulties. Currently, there is a scarcity of (semi)-mechanistic models
in neuropsychiatric disorders as they require better understanding of the disease
and the mechanism of treatment effects. However, a few semi-mechanism-based
models have been published in the area of schizophrenia[100] and depression.[101]
Della Pasqua et al.[59] and Gobburu and Lesko[102] emphasized in their reviews
that the development of mechanism-based models in neuropsychiatric disorders
is essential. Such models can be developed by integrating specific features
of a disease (e.g. individual symptoms or items in a clinical rating scale) with
information from the disease biomarkers (e.g. hippocampal volume reduction,
tryptophan depletion in depressive patients).
Recently, Nucci et al.[103] reviewed various model-based approaches to increase
the efficiency of drug development in schizophrenia. They proposed evaluation of
the empirical placebo models that performed the best in depression trials, i.e. IBF,
a mixed Weibull and linear function, and a mixed exponential and linear function.
Based on our modelling experience, the Weibull model and the IRM[14,72,83] were
the best models among all the above-reviewed placebo models to describe the
time course of the PANSS score.
In addition to the large placebo response, high dropout rates may blunt the
placebo-drug differences. Dropout events are often used as an outcome measure
in clinical trials of CNS medications and they are usually related to the change in
the clinical score from the baseline or between the last two visits. Patients can
perceive the treatment effect (whether improvement or deterioration) relative
to the disease status at the beginning of the trial, and this might lead to dropout.
Ignoring missing data due to dropouts may bias the model-simulated trial outcome
(thus biasing the prediction of future trial results). In the pharmacokineticpharmacodynamic modelling area, TTE dropout models are preferred over
logistic regression models when exposure information is available. In many trials,
covariate information is available. During the drug development process, we are
typically interested in identifying the covariates that lead to increased probability
63
3
64
3
of dropout and the effect of these covariates that are known to influence the
probability of dropout (i.e. the magnitude of the covariate effect). TTE models
pose numerical difficulties as the number of covariates increase in the model.
Conversely, logistic regression dropout models have fewer numerical difficulties
and can accommodate many covariates.[104] Integration of the dropout model with
the clinical-response model is often helpful in making the right decisions with
respect to selection of dose, dosing regimen and dosage adjustment.
To solve the issue of low sensitivity of the subjective rating scales used for
assessing the treatment effect, one should look further into the currently used
rating scales and explore components separately to try and find out which one
is more sensitive than the others. Such an approach has already been used in
depression by Santen et al.[60,61] and in schizophrenia by Lader[62] and Santor
et al.[38] In depression, Santen et al.[60,61] have shown that the use of change in
the HAMD-17 from baseline as the primary endpoint contributes to failures in
the assessment of treatment efficacy. They successfully managed to come up
with a subscale (HAMD-7) derived from the original HAMD-17 rating scale of
depression. This subscale was composed of the most sensitive individual items
and it showed higher sensitivity to detect the drug effect than the HAMD-17 rating
scale. Similarly, in schizophrenia, Lader[62] and Santor et al.[38] have suggested
that not all of the PANSS items are sufficiently sensitive to detect true treatment
effects. The positive and negative subscales are more sensitive to change than the
PANSS total score and, thus, they may constitute a ‘mini PANSS’ that may be more
reliable for future research. To further examine the findings of Santor et al.[38]
we are currently investigating the performance of the different PANSS subscales
separately and individual items utilizing pharmacokinetic-pharmacodynamic and
simulation tools. Such a study could yield the most sensitive individual items that
are capable of better detecting changes due to treatment.
Complete integration of disease-progression models, placebo-response
models, drug-response models, covariate models and dropout models enables
reliable prediction of the outcome of future trials through model-based simulation
with consideration of various predictors of the placebo response and dropout.
Model-based simulations help in determining the appropriate clinical trial design
by selecting the right population, treatment duration, disease condition, etc., and
thereby improve the detection of the signal of the drug effect by maximizing drugand placebo-effect differences. As there is growing knowledge of the mechanisms
of the placebo response in brain diseases, one can adopt several conceptual,
statistical and mathematical approaches to confine different aspects of this
biological system. Finally, we believe there is a need for a repository of disease
progression models, placebo response models and dropout models, using pooled
clinical data to identify the potential sources of higher placebo responses and
dropout rates in failed clinical trials.
Placebo-Response Modelling in Schizophrenia
65
Acknowledgements
We would like to thank Ahmed Abbas Suleiman, Gijs Santen, Lena Friberg, Nisha
Kuzhuppilly Ramakrishnan and Teun Post for their suggestions. We also thank the
referees of an earlier version of this paper for valuable comments and suggestions,
which have been incorporated into this version.
This review was performed within the framework of project no. D2-104 of the
Dutch Top Institute Pharma (Leiden, the Netherlands; www.tipharma.com). The
authors have no conflicts of interest that are directly relevant to the content of
this review.
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