Psychology and Aging
2004, Vol. 19, No. 1, 145–156
Copyright 2004 by the American Psychological Association, Inc.
0882-7974/04/$12.00 DOI: 10.1037/0882-7974.19.1.145
Change in Cognitive Capabilities in the Oldest Old: The Effects of
Proximity to Death in Genetically Related Individuals Over a
6-Year Period
Boo Johansson
Scott M. Hofer, Jason C. Allaire,
Mildred M. Maldonado-Molina, and
Andrea M. Piccinin
University of Göteborg, Jönköping University, and
Pennsylvania State University
Pennsylvania State University
Stig Berg
Nancy L. Pedersen
Jönköping University and Pennsylvania State University
Karolinska Institutet and University of Southern California,
Los Angeles
Gerald E. McClearn
Pennsylvania State University
Change in cognitive abilities was assessed over a 6-year period in a sample of monozygotic and same-sex
dizygotic twin pairs (N ⫽ 507 individuals), aged 80 and older (mean age ⫽ 83.3 years; SD ⫽ 3.1), who
remained nondemented over the course of the study. Latent growth models (LGMs) show that chronological age and time to death are consistent predictors of decline in measures of memory, reasoning,
speed, and verbal abilities. Multivariate LGM analysis resulted in weak and often negative correlations
among rates of change between individuals within twin pairs, indicating greater differential change
within twin pairs than occurs on average across twin pairs. These findings highlight several challenges
for estimating genetic sources of variance in the context of compromised health and mortality-related
change.
There is increased recognition of the importance of longitudinal
studies for the description, prediction, and explanation of individual differences in patterns of development and aging (e.g., Schaie
& Hofer, 2001). Indeed, there are currently more than 35 major
longitudinal studies of older adults with at least partial focus on
psychological aging, a number of which have focused on the oldest
old: individuals older than 80 years (e.g., Bäckman & Wahlin,
1997; Johansson, Zarit, & Berg, 1992; Nyberg, Baeckman, Erngrund, Olofsson, & Nilsson, 1996; Poon et al., 1992; Smith &
Baltes, 1993). The study of the oldest old, however, poses numerous challenges to the understanding of aging, related to design
issues and sample characteristics, including differential survival
and declining health status (e.g., Vaupel & Yashin, 1985). In
addition, the sources and timing of influences on individual dif-
Boo Johansson, Department of Psychology, University of Göteborg,
Göteborg, Sweden; Institute of Gerontology, School of Health Sciences,
Jönköping University, Jönköping, Sweden; and Department of Biobehavioral Health, Pennsylvania State University; Scott M. Hofer, Department of
Human Development and Family Studies and Center for Developmental
and Health Genetics, Pennsylvania State University; Jason C. Allaire,
Center for Developmental and Health Genetics, Pennsylvania State University; Mildred M. Maldonado-Molina, Department of Human Development and Family Studies, Pennsylvania State University; Andrea M. Piccinin, Department of Statistics, Pennsylvania State University; Stig Berg,
Institute of Gerontology, School of Health Sciences, Jönköping University
and Department of Biobehavioral Health, Pennsylvania State University;
Nancy L. Pedersen, Department of Medical Epidemiology, Karolinska
Institutet, Stockholm, Sweden, and Department of Psychology, University
of Southern California, Los Angeles; Gerald E. McClearn, Center for
Developmental and Health Genetics and Department of Biobehavioral
Health, Pennsylvania State University.
The study is supported by National Institute on Aging Grant AG 08861.
The OCTO Twin Study is an ongoing longitudinal study conducted at the
Institute of Gerontology, School of Health Sciences, Jönköping University,
Jönköping, Sweden, in collaboration with Center for Developmental and
Health Genetics, Pennsylvania State University, and Department of Medical Epidemiology, Karolinska Institutet, Stockholm, Sweden. We are
greatly indebted to the Lene Ahlbäck (1991–2002), Agneta Carlholt (1992–
2003), Gunilla Hjalmarsson (1991–1993), Eva Georgsson (1993–1995),
and Anna-Lena Wetterholm (1993–1994), who traveled throughout the
country and examined the twins. Invaluable help in coordinating the study
was provided by Inger Cronholm and Ingegerd Brandström, Institute of
Gerontology, Jönköping University, and Elana Pyle, Pennsylvania State
University.
Correspondence concerning this article should be addressed to either
Boo Johansson, Department of Psychology, University of Göteborg, Box
500, S-405 30 Göteborg, Sweden, E-mail: [email protected], or
Scott M. Hofer, Department of Human Development and Family Studies,
110 Henderson South Building, The Pennsylvania State University, University Park, PA 16802, E-mail: [email protected]
145
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JOHANSSON ET AL.
ferences of change in aging-related outcomes are highly dimensional and involve combinations and interactions among genetic
influences, lifelong contextual effects, and health-related factors.
Therefore, the pattern and timing of change in aging-related outcomes will likely differ considerably, even across genetically
identical individuals.
The twin literature provides support for a substantial genetic
influence on cognitive abilities across the life span (e.g., McClearn
et al., 1997; Pedersen & Lichtenstein, 1997), although less for
memory functioning (Johansson et al., 1999). The evidence for
substantial genetic influences is based on cross-sectional estimates.
Whether the genetic proportions of influence remain in very late
life and in longitudinal designs is also largely unknown. Compromised health and differential survival become even more of a
challenge in studies of oldest-old twins and increase the likelihood
that intrapair resemblance will decrease in later life and over time
in a longitudinal study context.
In this study, we focus first on the pattern and magnitude of
change for a range of measures assessing various domains of
cognitive functioning at the level of the individual. We examine
how particular individual characteristics are related to differences
in initial status and rate of change. In particular, we evaluate the
effect of proximity to death (proxy for compromised health) as a
predictor of accelerated decline in cognitive functioning. Additionally, we evaluate the effect of differential attrition based on survival status (i.e., participant dropout) on twin similarity (correlations within twin pair) at previous occasions when the twin pairs
were intact. Estimates of correlations among initial status and rate
of change within monozygotic (MZ) and dizygotic (DZ) twin pairs
for each of these cognitive outcomes are provided to further
evaluate the effect of differential change within twin pair.
Accelerated Change in Cognitive Functions Before Death
Numerous studies have provided evidence for accelerated decline in a broad range of human abilities over a period immediately
before death. These changes have been attributed to general decline in physiological and health-related status. In studies focusing
on cognitive functioning, this empirical finding has been termed
terminal decline or terminal drop and observed as accelerated or
abrupt decline, respectively, in cognitive functioning before death
(for reviews see Berg, 1996; Bosworth & Siegler, 2002; Siegler,
1975; Small & Bäckman, 1999). Evidence in support of terminal
decline has been found in longitudinal studies in which the spans
between measurement occasions have typically been 5 years or
less (e.g., Deeg, Hofman, & van Zonneveld, 1990; Johansson &
Berg, 1989; Rabbitt et al., 2002; Smits, Deeg, Kriegsman, &
Schmand, 1999). Although many of these studies have emphasized
average change in a sample of individuals, an alternative method
is to analyze the association of time to death with rate of change in
the outcome variable (Botwinick, West, & Storandt, 1978). Figure
1 shows a set of hypothetical trajectories for individuals of different ages aligned on the point of mortality. Accelerated change
before death is seen relative to rate of change at earlier points in
time for most of the trajectories. These patterns are indicative of an
association between rate of change and proximity to death.
In studies of late-life cognitive functioning, the high prevalence
(e.g., Heeren, Lagaay, Hijmans, & Rooymans, 1992; Skoog, Nilsson, Palmertz, Andreasson, & Svanborg, 1993) and incidence
rates of dementia (e.g., Johansson & Zarit, 1995) in the oldest old
Figure 1. Hypothesized effect of terminal decline on cognitive capabilities independent of age.
make it necessary to examine whether individuals have or later
develop disease. Dementia represents the most devastating type of
disease with deleterious effects on episodic memory (Bondi et al.,
1994; Sliwinski, Lipton, Buschke, & Stewart, 1996) and other
cognitive abilities (Johansson & Zarit, 1997). Because dementia
contributes to both severe cognitive decline and increased risk of
mortality (e.g., Heeren, van Hermert, & Rooymans, 1991; Johansson & Zarit, 1997), it is essential either to evaluate the terminal
decline hypothesis in nondemented samples (e.g., Bosworth,
Schaie, Willis, & Siegler, 1999; Small & Bäckman, 1999) or to use
designs and statistical analysis that include information about
prevalence and subsequent incidence of dementia (e.g., Gatz, Pedersen, Crowe, & Fiske, 2000).
Besides dementia, there is a long list of other potential diseases
in late life (e.g., Nilsson, Johansson, Berg, Karlsson, & McClearn,
2002) that may compromise cognitive functioning (e.g., Hassing et
al., 2002). The more complex morbidity patterns and the increased
probability of death with age provide a challenging problem for
understanding normal age changes and the impact of pathological
changes. Indeed, distinguishing between primary and secondary
aging (e.g., Birren & Cunningham, 1985) becomes more problematic in late life because physiological changes lead to a greater
propensity for disease-related changes. Also, comorbidity increases with age (Nilsson et al., 2002), making it even more
difficult to evaluate the relative importance of specific healthrelated changes such as those related to diabetes, hypertension,
stroke, depression, and hearing loss (Hassing et al., 2002). Thus, it
is difficult to propose a composite health-related marker or an
overall physiological indicator of health status in late life. Considered in this way, proximity to death may be the most valid,
although indirect, marker of overall health and vitality.
The Current Study
The purpose of the current investigation was to characterize the
longitudinal pattern and rate of change in memory and other
CHANGE IN COGNITIVE CAPABILITIES
cognitive abilities over a 6-year period in a sample of oldest-old
twins. Individual variation in initial level at the first study occasion
and rate of change over the course of the study were evaluated as
a function of age, proximity to death, sex, and education. In
addition, we evaluated the effect of proximity to death on the
concordance of cognitive outcomes in both MZ and DZ twin pairs
based on subgroup analysis stratifying on intact pair status across
occasions of measurement. It was expected that the resemblance
among twin pairs would decrease longitudinally because of differential exposures and timing of health-related changes and proximity to death.
Method
Sample
The participants for this study included 507 community-dwelling elders
(male ⫽ 178, female ⫽ 329) drawn from the ongoing longitudinal study,
“Origins of Variance in the Old-Old” (OCTO Twin Study; McClearn et al.,
1997). This is a subsample of the 702 individuals (351 complete twin pairs;
149 MZ pairs and 202 same-sex DZ pairs) who were not diagnosed with
dementia over the 6-year course of the study according to the Diagnostic
and Statistical Manual of Mental Disorders (third edition, revised; American Psychiatric Association, 1987) criteria. Participants were assessed at
four different occasions spaced by a 2-year interval. At the baseline
occasion of measurement, participants ranged in age from 79 to 98 years
(M ⫽ 83.2 years; SD ⫽ 2.98) and had a mean of 7 years of education
(SD ⫽ 2.42 years, range ⫽ 0 –23 years). The gender ratio, education,
socioeconomic status, marital status, and housing of the OCTO twin
sample correspond to population statistics for this age segment of the
Swedish population (Simmons, Johansson, Zarit, Ljungquist, Plomin, &
McClearn, 1997).
Measures
The OCTO Twin Study includes a broad spectrum of biobehavioral
measures of health and functional capacity, personality, well-being, and
interpersonal functioning. Cognitive functioning is assessed with a widely
used Swedish psychometric battery (Dureman & Sälde, 1959) composed of
a number of tests assessing abilities from the broad fluid and crystallized
domains (e.g., Horn & Hofer, 1992) as well as memory. In a small
percentage of individuals (fewer than 25 at any particular wave), the
second parts of some of these two-part tests were not administered because
of time and fatigue of the individual. For purposes of analyses here, scores
for both parts of the tests were required and were combined for a total
score. The analyses focus on the cognitive test level because of limitations
in modeling latent factors, with at most two indicators per factor. (For
further details about these tests, see Johansson et al., 1999, and McClearn
et al., 1997.)
Knowledge. Two tests derived from the Wechsler Adult Intelligence
Scale (WAIS; Wechsler, 1991) were administered: the Swedish version
of the Information Task (Jonsson & Molander, 1964), including questions of general knowledge, and the Synonyms test, a verbal meaning
test that requires finding a synonym among five alternatives that match
a target word. The maximum scores on these tests are 44 and 30,
respectively.
Inductive reasoning. The Figure Logic task (Dureman & Sälde, 1959)
requires the person to identify one figure out of five in a row that is
different in concept from the rest. Maximum score is 30.
Perceptual speed. A modified version of the speeded Digit–Symbol
Substitution Test (WAIS; Wechsler, 1991) was used. This Digit–Symbol
test requires a verbal response indicating what digits match the symbols
within a 90-s period. The maximum score is 100, which basically reflects
no upper limit in this timed test.
147
Visuospatial ability. In Koh’s Block Design Test (Dureman & Sälde,
1959), the participant is presented with red and white blocks and several
patterns written on cards. The task is to reproduce the pattern shown on the
cards by assembling the proper blocks and arranging them to form the
design shown on the card. The maximum score is 42.
Memory. The memory battery represents the short-term and long-term
memory systems, involving episodic memory processing of verbal and
nonverbal material, with different demands on the retrieval mechanisms
(recall and recognition). The following tests were used in the current study.
The Digit Span Forward and Backward Test measures short-term memory for orally presented digits (Wechsler, 1991). In the forward part,
participants are asked to recall the digits in the same order as they were
presented, whereas in the backward part, they are instructed to recall the
digits in reverse order. The maximum score is 9 for the forward and 8 for
the backward part of the test.
The Prose Recall test is a verbal memory test in which participants
are asked for immediate free recall of a brief (100 words) story that has
a humorous point (Johansson et al., 1992). Responses are coded for the
amount of information recalled in a manner similar to the Wechsler
Memory Scale (Wechsler, 1991). The maximum score is 16.
Thurstone’s Picture Memory test is a nonverbal, long-term memory test
(Thurstone & Thurstone, 1949). Participants are shown 28 pictures and
then asked for recognition of these among three lures. The pictures were
enlarged from the original version to minimize visual problems. The
maximum score is 28.
Procedures
The twins were assessed in their place of residence by registered nurses
who where specially trained for the study and regularly supervised. A
complete testing session typically lasted approximately 3.5 to 4.0 hr and
included several rest periods. Scheduling was arranged to minimize geographical, age, or gender order effects, and different nurses assessed the
members in a pair within 1 month of the cotwin’s test date. The nurses were
deliberately kept unaware of zygosity of the twins to avoid expectation
biases. In pairs in whom zygosity was unknown, a diagnosis was based on
a DNA test.
Statistical Analysis
Predictors of initial status and change. Predictors of change in memory and cognitive functioning were chronological age, sex, and level of
education. Proximity to death was included, calculated as the number of
years from the age at initial measurement to age at death for each individual (these values were missing for surviving individuals).
Standardization. All memory and cognitive measures at baseline were
standardized to a pseudo t score (M ⫽ 50; SD ⫽ 10). To preserve mean and
variance changes over time, the variables at each subsequent occasion were
transformed to a pseudo t-score metric, using the baseline mean and
standard deviation as the standardization base. The t scores were used to
facilitate comparison of effect magnitudes across variables with different
scales.
Latent growth curve analysis. Latent growth curve (LGC) analysis is a
method of longitudinal data analysis emphasizing individual trajectories of
change from initial status. Briefly, growth curve analysis involves estimating within-individual regressions of performance on time. This summarizes
individual-level data in terms of “true” initial level of performance (intercept), linear and curvilinear slope (decline or rate of change), and error
(residual) parameters.
Figure 2 shows a graphic representation of the LGC model used in this
study for one cognitive variable and the set of included covariates. By
incorporating information from multiple occasions of measurement, it goes
beyond traditional difference score analysis, emphasizing rate rather than
the amount of change. As the number of occasions of measurement
increases, parameter estimates of initial level and change become more
precise. Detailed descriptions of these methods (Willett, 1989) and exam-
148
JOHANSSON ET AL.
Figure 2. Diagram of latent growth curve model with initial performance
level (Level), linear slope (Slope_L), and quadratic slope (Slope_Q) at
each measurement occasion (var_t1, var_t2, etc.) and covariates (age
[AGE1], sex, education [EDUC], and time to death [D_Time]) labeled.
Conditional mean (m_L, m_Sl, m_Sq) and variance (v_L, v_Sl, v_Sq)
estimates are shown as latent factors level (vL), linear slope (vSl), and
quadratic slope (vSq).
ples of their computation using structural equation modeling programs are
available elsewhere (McArdle & Epstein, 1987; McArdle & Hamagami,
1992; Willett & Sayer, 1994).
The covariates (age, sex, education, and time to death) account for systematic differences in the initial level as well as rate of change and represent the
partial effects given the other covariates included in the model. Figure 2 shows
the fixed-design parameters, which specify the level (values fixed to 1.0) and
slope (fixed to 0 at Time 1 and then to 2, 4, and 6 for corresponding
measurement occasions, each separated by 2 years). The quadratic slope was
centered on the median time in study (Year 3) and fixed to the squared values
(9, 1, 1, 9) across occasions to minimize collinearity with the linear slope
function. Unlabeled directed arrows indicate estimated parameters.
LGC models were first used to evaluate the pattern of change across
occasions and to determine whether there was significant variance in the
rate of change parameter that would indicate sufficient variance for covariate prediction. For each of the cognitive tests, the model-fitting procedure used a full model, including estimated level (i.e., initial status), linear
slope, and quadratic slope. If the parameter representing the mean and
variance of the quadratic slope was statistically nonsignificant, indicating
the absence of quadratic change and individual differences in change, a
reduced linear-only model was estimated. Similarly, the presence of linear
change in the reduced model was determined by examining the significance of the mean and variance for the linear slope. Furthermore, if the
variance estimates for linear or quadratic slopes were nonsignificant but the
mean slopes were significant, variance terms were fixed to zero and
predictors on these slope estimates were not evaluated. The LGC analysis
was performed using Mplus (Muthén & Muthén, 2001), a program that
uses full-information maximum likelihood parameter estimation and permits analysis of incomplete data within and across occasions.
Full-information maximum likelihood was used to estimate model parameters that yields a ⫺2LL fit function. For nested models, the difference
between the fit functions is distributed as chi-square with degrees of
freedom equal to the difference in the number of parameters estimated
between the models. The adequacy of model fit was assessed by this
chi-square statistic, or discrepancy function, and a number of relative fit
indexes, including comparative fit index (CFI; Bentler, 1990), nonnormed
fit index (NNFI; Bentler & Bonett, 1980), and root-mean-square error of
approximation (RMSEA; Browne & Cudeck, 1992). Values larger than .90
are desirable on the CFI and NNFI. Browne and Cudeck (1992) suggest
that values of the RMSEA below .08 (preferably below .05) are indicative
of acceptable model fit.
Intraclass correlations across occasions. Correlations were calculated
for MZ and DZ twin pairs separately to provide an estimate of twin
resemblance for the MZ and DZ twin pairs (sharing 100% and 50% of their
segregating genes, respectively). A higher correlation indicates a greater
similarity, whereas the differences in MZ and DZ correlations provide an
estimate of familiality, including genetic influences. The computation of
phenotypic correlations is typically only a first step in examining twin data,
aiming at the estimation of the relative contribution of genetic and environmental influences by using quantitative genetic modeling. For the
purpose of the current investigation, however, the analysis is restricted to
examining stability and change in intraclass correlations in MZ and DZ
twin pairs across the four measurement occasions. The basic assumption is
that of greater similarity in MZ than in DZ twins, including higher
intraclass correlations over time among MZ pairs.
Multivariate analysis of change within twin pair. Multivariate LGC
models were used to estimate correlations among level and rate of change
within twin pair for each cognitive outcome in the combined sample and
separately for MZ and DZ status. Identical sample inclusion criteria were
used for these models that were based on simultaneous analysis of level
and slope estimates for each member of the twin pair. The multivariate
approach permits direct assessment of correlated level and rate of change
and is an alternative to the multilevel modeling approach, which would
provide intraclass correlations at the level of twin pair (Guo & Wang, 2002).
Treatment of missing data. The majority of participant nonresponse
over the course of this study was due to mortality. Once mortality is taken
into account, less than 10% is due to refusal to participate, which is related
mainly to frailty and compromised health. Incomplete data in a longitudinal
study present problems, and issues related to attrition are especially pertinent to twin studies of aging. For example, we might expect that change in
functioning would not occur simultaneously for both individuals within a
twin pair but would rather be differential in that one individual within a
twin pair exhibits change at a different age and at a different rate than the
twin partner. Individual change is related to sample selection at the initiation of this study but also to differential attrition within the study sample
over time, and this would have an effect on intraclass correlations at each
occasion as well as on multivariate models of change within twin pair. We
attempt to deal with some of these issues by evaluating intraclass correlations among twins as a function of intact pair status and in our longitudinal
modeling of change within twin pairs. However, in the longitudinal modeling of these data, we apply likelihood-based statistical methods for
treating missing data. This method of estimation is currently a standard
treatment for obtaining the unbiased and efficient population estimates
under particular assumptions of participant nonresponse. These methods
have been shown to provide less biased estimates of population parameters
than traditional methods relying on complete cases, available pairwise, mean
imputation, or single-imputation regression methods (Graham, Hofer, & Piccinin, 1994; Little & Rubin, 1987; Schafer, 1997; Schafer & Graham, 2002).
Following the work of Little and Rubin (1987; Diggle & Kenward, 1994;
Diggle, Liang, & Zeger, 1994; Rubin, 1976), a distinction is made between
participant nonresponse that is missing completely at random (MCAR),
missing at random (MAR), and not missing at random (NMAR). The key
distinction is whether the cause of the missingness is related directly to
levels of the missing outcome variable (NMAR) or whether the missingness is due to other variables that are either irrelevant (MCAR) or measured and included in the model (MAR). Whether valid inferences can be
drawn from analysis of longitudinal data with participant loss depends on
the relationship between the outcome variables and the dropout mechanism
(i.e., the reason for dropout), whether the dropout mechanism has been
measured and included in the analysis, and the specific method of analysis
(e.g., maximum likelihood). Inferences derived from likelihood-based
methods are both unbiased and efficient when the data are at least MAR.
The utility of these methods has been demonstrated in a number of studies
(e.g., Graham, Hofer, & MacKinnon, 1996; Graham et al., 1994; McArdle,
CHANGE IN COGNITIVE CAPABILITIES
1994; McArdle & Hamagami, 1992). The parameter estimates provided in
this study assume MAR and are based on included covariates and available
outcomes at previous occasions of measurement before dropout.
The analysis of twin resemblance based on correlations across individuals within twin pairs (above) requires data from complete twin pairs at
each measurement occasion. The restriction imposed by the MZ–DZ comparisons also means that nonresponses for reasons other than mortality
(attrition) may influence the calculations of the intraclass correlation. The
low nonresponse rate in this study makes this a minor problem. Of greater
importance is that once a participating member has been unable to perform
a certain test because of fatigue and health-related problems, including
sensory, motor, and other handicaps, the number of available pairs is
consequently reduced, and the remaining pairs are more likely to have
superior overall vitality and health.
Dependencies related to the analysis of twin pairs. In the first set of
longitudinal analyses, the twins were treated as unrelated singletons. Therefore, it is important to note that the parameters obtained in the analysis will be
unbiased estimates of the population parameters. However, under conditions of
positive and moderate to substantial intraclass correlations, standard errors of
these parameters will be downwardly biased because of the dependencies
associated with analyzing cotwins simultaneously. For example, if the twins
were phenotypically exact replicas of one another such that the intraclass
correlation was 1.0, the singleton sample would be identical to entering the
identical data for each individual twice. However, in the case of these octogenarian twins, the intraclass association at the first occasion is low to moderate and decreases across occasions, and so would have little to no influence
on the significance of the results. The second set of analyses of twin resemblance across measurement occasions is based on the comparison of intraclass
correlations across intact MZ and DZ twin pairs. Consequently, these analyses
are restricted to the number of available pairs in which both have a performance score on a specific test.
Results
We first present the results from the LGC models that examined
the pattern as well as the rate of change for each cognitive
measure. Second, the relationship of participants’ time to death
with initial level and rate of change, controlling for sociodemographic characteristics, was examined for each cognitive outcome.
Finally, the within-pair similarity at each time point was examined
separately by intact pair status.
Longitudinal Change Trajectories
Table 1 shows that the fit for each of the final estimated
models was quite adequate, with fit indexes exceeding .95 for
149
most outcomes (with the exception of .85 in the linear plus
quadratic model for Figure Logic) and an RMSEA less than or
equal to .05 (Browne & Cudeck, 1992). The absolute fit
index showed good model fit for many of the final models
(nonsignificance indicative of no significant differences between the observed and expected covariance matrices) with a
couple of exceptions (i.e., Figure Logic, Prose Recall). A linear
slope model best represented the pattern of change for the
majority of the cognitive variables with the exception of the
Information, Figure Logic, and Digit–Symbol tests, for which
evidence of quadratic change was found. However, significant
random effects (individual differences) in this quadratic trend
were found only for the Figure Logic test. These findings
generally support the evaluation of predictors of initial status
(level) and linear-only change and so permit a more direct
comparison across tests under the same linear change model
characteristics.
Table 2 contains the mean and variance estimates for initial
level and linear slopes (as well as models including quadratic
slopes when these are significant) for each of the cognitive tests.
The estimates for the expected initial level closely approximate the
standardization imposed across all four occasions that was based
on the mean and standard deviation at the first occasion of measurement. These estimates are, however, not exact because they are
the fitted or expected estimates of initial status (level) at Time 1
given the linear (or linear plus quadratic) model imposed on the
data. However, the estimated variance in initial level reflects a fair
amount of heterogeneity, with estimates ranging from 44.68 to
90.05.
As mentioned, change in performance on most of the cognitive variables was best characterized by a linear pattern. As
can be seen in Table 2, the pattern of linear decline was
significant and ranged in magnitude from ⫺.11 to ⫺.85, with
the exception of the Figure Logic test (.05, p ⬎ .05). Additionally, heterogeneity in individual differences about these average
slopes was observed across variables as evidenced by the significant variance estimates for the linear slope (with the exception of Figure Logic). The estimates of mean linear change
presented in Table 2 reflect the per year change in performance
based on a t-score metric with a mean of 50 and a standard
deviation of 10.
Table 1
Fit Indices for Latent Growth Models
Test
CFI
NNFI
RMSEA (LB, UB)
␹2
df
p
Synonymsa
Informationb
Figure Logicb
Block Designa
Digit–Symbolb
Digit Span Forwarda
Digit Span Backwarda
Picture Memorya
Prose Recalla
1.00
1.00
0.97
1.00
1.00
1.00
0.99
1.00
0.97
0.99
0.98
0.85
1.00
1.01
1.00
0.98
0.99
0.94
.02 (0.00, 0.05)
.04 (0.00, 0.07)
.05 (0.01, 0.09)
.00 (0.00, 0.04)
.00 (0.00, 0.05)
.00 (0.00, 0.04)
.02 (0.00, 0.05)
.01 (0.00, 0.05)
.05 (0.03, 0.07)
15.39
14.81
11.85
12.99
4.09
10.70
15.16
14.38
35.33
13
8
5
13
6
13
13
13
16
.28
.06
.04
.45
.67
.64
.30
.35
.003
Note. CFI ⫽ comparative fit index; NNFI ⫽ nonnormed fit index; RMSEA ⫽ root-mean-square error of
approximation; LB, UB ⫽ lower and upper bound.
a
Linear model. b Quadratic model.
JOHANSSON ET AL.
150
Table 2
Mean and Variance (Var) Estimates for Significant Level and
Slope Parameters
Level
performance scores were related to longer life spans from age at
the first occasion (controlling for age at the first occasion). Also,
distance to death was related to rate of change in the Synonyms
Linear slope
Quadratic
slope
Test
M
Var
M
Var
M
Var
Synonyms
Information
Informationa
Figure Logic
Figure Logica
Block Design
Digit–Symbol
Digit–Symbola
Digit Span Forward
Digit Span Backward
Picture Memory
Prose Recall
49.64
50.34
50.05
50.89
50.06
49.84
49.71
49.39
49.76
50.09
49.34
49.09
78.79
90.03
90.05
61.81
53.06
78.78
80.41
83.91
56.11
44.68
64.39
64.61
⫺.11
⫺.44
⫺.41
⫺.02
.05 (ns)
⫺.34
⫺.31
⫺.26
⫺.57
⫺.32
⫺.85
⫺.82
.50
.93
.88
2.06
.11 (ns)
.66
.78
.81
.89
.78
2.64
2.65
—
⫺.05
—
⫺.15
—
—
⫺.06
—
—
—
—
—
—
—
—
.27
—
—
—
—
—
—
—
—
Note. Linear effects are shown for all models, regardless of statistical
significance, whereas quadratic effects were omitted from models if these
were found to not be statistically significant. Dashes represent parameters
fixed to zero in the model.
a
Linear only.
Predictors of Cognitive Change
Analyses next turned to determining the predictors of cognitive
change, with a particular focus on the predictive salience of proximity to death in accounting for individual differences in intraindividual change. Table 3 provides the parameter estimates of the
covariate associations with initial status and slope. Both unstandardized and standardized partial effects (statistically controlling for
other included covariates) are given.
Chronological age was negatively associated with level in all
tests (although Synonyms was not statistically significant). Chronological age was not consistently related to the linear effect of
slope, which would indicate steeper slopes for older individuals,
and observed only for Information Task (␤ ⫽ ⫺.20) and Picture
Memory (␤ ⫽ ⫺.21). This relative inconsistency in age effects on
slope parameters indicates that accelerated change in later ages is
not strongly apparent in this rather age-homogeneous sample of
the oldest old.
The results indicate that differences between sexes are negligible for initial level, except for the Information Task and Digit Span
Backward and Prose Recall tests. Men have higher initial scores on
the Information Task but also exhibit greater decline in performance over time. In the Digit Span Backward and Prose Recall
tests, women show better performance at the initial level but no
differential decline compared with men. A significant slope is
observed for the Synonyms test, although sex is unrelated to initial
status. Education was a significant predictor of level across all
tests, with the exception of the Picture Memory test. The standardized independent prediction of level of functioning ranged from
0.08 to 0.54, with the expected highest associations with the
crystallized knowledge measures of Synonyms (␤ ⫽ 0.54) and
Information (␤ ⫽ 0.42). Education was, however, not associated
with individual differences in rate of change in any cognitive
outcome variable.
Proximity to death was related to the initial level in Block
Design (␤ ⫽ 0.15) and Digit Span Backward (␤ ⫽ 0.18); higher
Table 3
Covariate Regressions on Level and Slope Parameters
Level
Test and covariate
Synonyms
Age
Sex
Education
T1-Death
R2
Information
Age
Sex
Education
T1-Death
R2
Figure Logic
Age
Sex
Education
T1-Death
R2
Block Design
Age
Sex
Education
T1-Death
R2
Digit–Symbol
Age
Sex
Education
T1-Death
R2
Digit Span Forward
Age
Sex
Education
T1-Death
R2
Digit Span Backward
Age
Sex
Education
T1-Death
R2
Picture Memory
Age
Sex
Education
T1-Death
R2
Prose Recall
Age
Sex
Education
T1-Death
R2
Slope
Partial
Std. partial
Partial
Std. partial
⫺0.16
1.38
1.99a
0.28
—
⫺.06
.07
.54a
.07
.31
⫺.01
.40a
⫺.01
⫺.13a
—
⫺.03
.27a
⫺.04
⫺.41a
.23
⫺0.51a
⫺3.51a
1.64a
⫺0.07
—
⫺.16a
⫺.18a
.42a
⫺.02
.26
⫺.06a
.31a
.04
⫺.09
—
⫺.20a
.16a
.09
⫺.21
.10
⫺0.61a
0.22
0.64a
0.27
—
⫺.25a
.01
.21a
.09
.13
⫺.01
.20
⫺.05
⫺.13
—
⫺.03
.09
⫺.11
⫺.27
.10
⫺0.61a
1.28
0.83a
0.57a
—
⫺.20a
.07
.23a
.15a
.13
⫺.03
.14
.04
⫺.10
—
⫺.12
.08
.11
⫺.27
.10
⫺0.74a
1.30
1.42a
0.19
—
⫺.24a
.07
.38a
.05
.22
.01
.19
.01
⫺.13
—
.05
.10
.03
⫺.34
.13
⫺0.52a
⫺0.95
0.76a
0.44
—
⫺.21a
⫺.06
.26a
.14
.15
.00
.35
.01
⫺.14
—
.00
.19
.02
⫺.35
.15
⫺0.45a
1.76a
0.81a
0.51a
—
.21a
.13a
.30a
.18a
.19
.03
.03
.04
⫺.17a
—
.07
.01
.08
⫺.36a
.14
⫺0.51a
2.87
0.28
0.37
—
⫺.19a
.17
.08
.11
.08
⫺.11a
.45
.10
⫺.19
—
⫺.21a
.13
.14
⫺.27
.14
⫺0.56a
3.17a
1.16a
0.37
—
⫺.20a
.18a
.34a
.10
.19
⫺.02
.20
⫺.01
⫺.17a
—
⫺.07
.09
⫺.02
⫺.38a
.15
Note. R2 indicates the standardized variance explained. Cells containing
dashes refer to negative parameter estimates. T1-Death is the span (in
years) from age at first occasion of measurement to age at death. Std.
partial ⫽ standardized partial regression estimates.
a
Significant parameter estimates ( p ⬍ .05) are based on significance of the
unstandardized partial estimate.
CHANGE IN COGNITIVE CAPABILITIES
151
(␤ ⫽ ⫺.41), Digit Span Backward (␤ ⫽ ⫺.36), and Prose Recall
(␤ ⫽ ⫺.38) tests. Trends were observed in standardized regression
parameters for the other tests, but these were not statistically
significant.
Intraclass Correlations as a Function of Intact Pair
Status Across Occasions
The observed variation in change in memory and cognitive
functioning at the individual level should have an impact on the
association between genetically related individuals, here in the
similarity between MZ and DZ twins. Given interindividual differences in intraindividual change (e.g., Allaire, 2001; Hofer,
Sliwinski, & Flaherty, 2002), we computed intraclass correlations,
partialed for age and sex (McGue & Bouchard, 1984), for intact
MZ and DZ pairs stratified by intact pair status across occasions.
Pairs were defined as intact at each occasion based on the criteria
that both twins in a pair participated and were not classified with
dementia over the course of the study. The intraclass correlations
for each test are shown in Figures 3, 4, 5, 6, 7, 8, 9, 10, and 11.
As can be seen in the figures, there is a tendency for the
correlations of intact twin pairs to decrease at occasions more
proximal to the occasion when one member of the pair drops from
the study. This implies that the twins are becoming less similar at
the preceding occasion and that differential decline in functioning
is occurring within the twin pair. For example, the Digit–Symbol
test shows high concordance in the MZ twins at the first occasion
but exhibits a decline over the occasions in nearly all intact pair
groups. This general pattern is somewhat mixed across groups for
intact pair status, however.
Multivariate Analysis of Within-Pair Correlations of
Initial Status and Rate of Change
Multivariate models permit simultaneous estimation of level and
slope for each member of the twin pair and estimates of association
Figure 3. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Synonyms by intact pair status.
Figure 4. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Information Task by intact pair status.
across individuals within MZ and DZ pairs. Within-twin pair
estimates of correlations between levels and rates of change for the
combined sample and separately for MZ and DZ twins are shown
in Table 4. The correlations between estimates of level are high
and follow the general pattern of higher MZ compared with DZ
intraclass correlations. These model-based estimates of association
are based on the predicted level (Time 1) performance expectations from the linear slope model. The MZ correlations are mod-
Figure 5. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Figure Logic by intact pair status.
152
JOHANSSON ET AL.
Figure 6. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Block Design by intact pair status.
Figure 8. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Digit Span Forward by intact pair status.
erate to high; most values are above .60 and range from .43 to .84.
Estimates of level correlations for DZ are systematically lower
than for MZ and range from .23 to .51.
Estimates of within-pair correlations for rate of change are low
and are often negative in the case of DZ twins. Weak correlations
among slope estimates within twin pairs would indicate that
change is relatively independent at the twin pair level, whereas
negative correlations would indicate significant differential change
among individuals within twin pairs. In general, correlations
among rates of change for MZ twins are weak, generally positive
in direction, and not statistically significant (except for Synonyms). Slope correlations for the DZ group, however, tend to be
negative in direction and weak to moderate in magnitude with
several statistically significant negative correlations. It is not uncommon for variance estimates of this type to be negative for
particular parameterizations of the intraclass correlation (i.e.,
Figure 7. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Digit–Symbol by intact pair status.
Figure 9. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Digit Span Backward by intact pair status.
CHANGE IN COGNITIVE CAPABILITIES
153
Table 4
Within-Pair Correlations Among Level (L) and Slope (S) for
Combined Zygosity, Monozygotic, and Dizygotic Groups
Combined
Monozygotic
Dizygotic
Test
L
S
L
S
L
S
Synonyms
Information
Figure Logic
Block Design
Digit–Symbol
Digit Span Forward
Digit Span Backward
Picture Memory
Prose Recall
.55a
.58a
.44a
.51a
.52a
.50a
.48a
.39a
.54a
.13
⫺.06
.04
⫺.10
⫺.10
.20
.04
.19a
⫺.09
.71a
.78a
.67a
.68a
.72a
.60a
.84a
.43a
.57a
.48a
.10
.12
⫺.16
.15
.24
.25
.15
.06
.43a
.44a
.32a
.37a
.36a
.42a
.23
.36a
.51a
⫺.41a
⫺.30a
.03
⫺.09
⫺.91a
⫺.25
⫺.16
.38a
⫺.38a
a
Figure 10. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Picture Memory by intact pair status.
Searle, 1971) and are interpreted as greater variability in rates of
change within twin pairs than occurs on average across twin pairs.
These weak or negative estimates of slope correspond to the
general pattern of decline in cross-sectional correlations proximal
to dropout status.
Discussion
In this study we addressed questions concerning the nature of
change in memory and cognitive functioning in old-old individu-
Figure 11. Monozygotic (MZ) and dizygotic (DZ) intraclass correlations
for Prose Recall by intact pair status.
Significant parameter estimates ( p ⬍ .05).
als—whether the pattern is one of stability or decline and the
degree of interindividual differences in rate of change, including
the impact of age, gender, education, and proximity to death.
Given that the current sample was composed of MZ and same-sex
DZ twins, we examined how the differential rate of change might
affect measures of intrapair twin similarity and thus the basic
information for estimation of genetic sources of variance.
Results from the growth curve modeling analyses revealed that
change in cognitive functioning was predominately characterized
by linear decline over the 6-year period. Although decline in
cognitive functioning in old age is a well-supported finding (e.g.,
Baltes, 1987; Horn & Hofer, 1992; Schaie, 1996), the results from
the current study are informative regarding the magnitude of
cognitive change in the oldest old, the age segment of the elderly
population that so far has received less empirical attention. In
addition, these findings clearly show that decline in cognitive
performance becomes ubiquitous in the oldest old, encompassing
cognitive abilities that tend to be less age vulnerable, such as
verbal abilities. Given the metric of change over the 6-year study
period, only one test was found to exhibit random effects in a
quadratic trend: the measure of inductive reasoning, the Figure
Logic test.
Education was consistently associated with level of cognitive
functioning, with its highest association with verbal abilities. It is
noteworthy that education exhibited no association with rate of
decline. This finding is consistent with other results (Christensen et
al., 2001), although several longitudinal studies have reported
associations with cognitive decline (for review, see Anstey &
Christensen, 2000; Christensen et al., 2001). As Christensen et al.
(2001) indicated, the numerous propositions for an association
between education and cognitive functioning are typically referred
to as the reserve capacity hypothesis (Kliegl & Baltes, 1987). This
hypothesis does not, however, predict a direct association between
differential change in cognitive functioning because of education
level. Rather, the association between education and cognitive
capabilities may be mediated through numerous protective as well
as risk factors (e.g., socioeconomic status, nutrition, lifetime health
and exposures), genetic vulnerability (Lichtenstein & Pedersen,
1997), as well as learning and compensatory strategies. Also, Gatz
et al.’s (2001) twin study suggested that low education is a risk
factor for Alzheimer’s disease when analyzed in a classic case–
control manner, whereas a matched-pair analysis on the same
154
JOHANSSON ET AL.
sample revealed no effects of education. Thus, controlling for
genetic and other familial influences tends to provide less evidence
for education as a marker of cognitive reserve in later life or an
indicator of lifelong exposure to intellectual challenges.
The results demonstrate that proximity to death is predictive of
decline on indicators of crystallized knowledge and verbal abilities
with some evidence of an association with working memory (i.e.,
Digit Span Backward). This partially replicates the findings of a
number of studies (e.g., Bosworth, Schaie, & Willis, 1999; Reimanis & Green, 1971; Siegler, McCarty, & Logue, 1982; White &
Cunningham, 1988) but not of others that suggest that distance to
death has a more pervasive effect on cognition (e.g., Johansson &
Berg, 1989; Ljungqvist, Berg, & Steen, 1996; Maier & Smith,
1999). In a 2002 study across an extended age range (49 –93
years), terminal change effects in cognitive performance were
found to predict mortality over 11 years independently of manifest
health, cause of death, gender, and socioeconomic status (Rabbitt
et al., 2002). Thus, the evidence for an association between cognition and proximity to death seems valid not only in later life but
also in adulthood and in individuals with less compromised health.
Results from the analysis of initial status in cognitive functioning confirmed previous cross-sectional findings suggesting significant familiality among genetically related individuals (McClearn
et al., 1997). The estimates presented here are based on predicted
estimates at the first occasion that were implied by the LGC model.
Inspection of Time 1 intraclass correlations stratified by intact pair
status found differences in magnitude of twin similarity, with pairs
more proximal to becoming “nonintact” exhibiting lower intraclass
correlations. Evidence of this type is indicative of a differential
decline that leads to one twin dropping out of the study (e.g.,
proximity to death). The trend of lower correlations across time
implies a decreasing role of genetic and familial influences in
terms of age of onset and magnitude of decline processes (Reynolds, Gatz, & Pedersen, 2002).
The decreasing intraclass correlations across time in study and
stratified by intact status of the twin pair is a function of differential rate of change within twin pair. In the multivariate analysis
of twins within MZ and DZ pairs, the correlations among rates of
change within twin pairs were weak for both MZ and DZ twin
samples and often negative for the DZ twin sample. These findings
provide strong evidence for nongenetic influences on change and
correspond with results from other twin studies of older adults
(McGue & Christensen, 2002). It should be noted that the multivariate analysis of twin pair correlation provided an explicit means
of evaluating similarity for initial status and rate of change. A
three-level structure could have been used to model the dependency between twins within a pair and structured as occasions of
measurement (Level 1) nested within individuals (Level 2), which
are further nested within MZ or DZ twin pair (Level 3). Analysis
of a three-level model specification often resulted in negative
intraclass correlations (after removing the default boundary constraints on the variance components), and these are in concordance
with results from the multivariate model in which the concordance
among initial status and rate of change was modeled directly. That
variance components of this type should be negative is not unusual
(i.e., Searle, 1971) and simply describes the fact that there is
greater differential change within twin pairs than is occurring on
average across twin pairs.
The LGC models were based on a time-in-study metric and
would require that onset and magnitude of decline be highly
congruent for positive intraclass correlations among rate of change
to be observed. Intraclass correlations based on this time-in-study
metric exhibit decreases across time in study and by dropout status
(intact pair groups) because of heterogeneity in decline of functioning within pairs. If a broader window of change status is
evaluated, discordance may, for example, later turn into concordance if the partner also becomes affected or exhibits change in
functioning. Genetic influences on dementia and other diseases
are, therefore, often studied in terms of concordance among twins
over a broader time-sampling framework (see Gatz et al., 2000).
We regard the observation of declining intraclass correlations
longitudinally and for weak or negative correlations in rate of
change as indicative of heterogeneity in timing and specificity of
cause and outcome in the aging process. This provides further
evidence that the pattern and rate of loss associated with aging are
influenced by factors that are unique to the individual and in some
sense stochastic (Finch & Kirkwood, 2000). Further analysis of
change processes in late life needs to be sensitive to appropriate
within-person measurement models for structuring change and
permit reasonable correlations among change in twins and across
variables (e.g., Sliwinski, Hofer, & Hall, 2003).
These findings are informative not only in the context of understanding differential rates of intraindividual change in cognitive
performance but also for understanding the role of compromised
health and change before mortality in the estimation of genetic
sources of variance. The role of genetic influences under conditions of differential intraindividual change relative to other individuals is vital and will be examined in greater detail in subsequent
research on this sample. Indeed, the findings of this study suggest
that high (and often increasing) cross-sectional estimates of heritability in older age groups are, in part, an artifact of sample
selectivity. Of course, analysis of genetic and environmental influences on aging-related change is not limited to synchronously
measured attributes, which would be foreclosed by the death of
one partner. Of equal or greater importance are conditions for
which age of onset is an important consideration. Among the most
central in understanding cognitive aging is dementia and specific
medical conditions that may affect the central nervous system in
the still undercharacterized realm of the old-old and oldest-old
individuals.
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Received June 4, 2002
Revision received July 24, 2003
Accepted July 24, 2003 䡲