Terminal Decline From Within- and Between-Person Perspectives, Accounting for Incident Dementia

Abstract

Objective.

The terminal cognitive decline hypothesis has been debated for almost 50 years. This hypothesis implies a change in rate of decline within an individual. Therefore, we examine the hypothesis from a within-person perspective using a time to death chronological structure.

Method.

Scores on a Swedish version of the Wechsler Adult Intelligence Scale Information and Block Design scores from 461 OCTO-Twin Study participants with confirmed death dates were modeled using quadratic growth curve models including both age and distance from death at study entry, sex, education, and dementia diagnosis as covariates of initial performance and of linear and quadratic change over time.

Results.

Information scores showed statistically significant evidence of slight within-person acceleration of declines in the no dementia group. Individuals with incident dementia declined more quickly, and those who were closer to death at study baseline had a stronger acceleration. Block Design scores declined but did not show evidence of such acceleration either within or across individuals. Decline was faster in incident cases closer to death at study entry.

Discussion.

Within-person evidence of terminal decline is not as strong as previously published between-person results. Strategies for focusing models on longitudinal aspects of available data and the extent to which lack of within-person evidence for terminal decline may stem from common data limitations are discussed.

THE terminal cognitive decline hypothesis (Kleemeier, 1962; Riegel & Riegel, 1972), which states that decline in cognitive functioning accelerates some number of years prior to death, has been a topic of research on aging for almost 50 years. It has implications for understanding aging, as it suggests that some proportion of the individual differences in cognitive change in later life could reflect distance to death rather than chronological age. Longitudinal studies, with individuals assessed for extended periods of time until their death, are essential for understanding both terminal decline and aging-related change from a within-person perspective (Kleemeier, 1962).

Although terminal decline implies a within-person process, it has until recently been studied mainly from a between-person perspective. While cross-sectional data contain between-person information only, longitudinal data contain both within-person (how an individual changes over time) and between-person (how an individual differs from those of different ages and distances from death) information. Despite the recent use of longitudinal data and longitudinal models (e.g., growth curve; Johansson et al., 2004; Laukka, MacDonald, & Bäckman, 2006, 2008; Sliwinski, Hofer, Hall, Buschke, & Lipton, 2003; Thorvaldsson, Hofer, & Johansson, 2006) including change-point models (Sliwinski et al., 2006; Thorvaldsson et al., 2008; Wilson, Beckett, Bienias, Evans, & Bennett, 2003), many reports addressing terminal decline continue to rely on between-person aspects of the data. Comparing level of performance or linear rate of change in deceased and surviving individuals (Laukka et al., 2006, 2008; Sliwinski et al., 2003) represents a comparison across individuals, rather than a focus within individuals. It addresses how people closer to death tend to differ from those farther from death but does not describe the cognitive path an individual takes when approaching death.

A strict definition of within-person change would be based on information regarding how each individual has changed over time, for example, on a change score or a growth curve model individual slope estimate. A strict definition of terminal decline as a within-person process implies an increase in the rate of (within-person) decline (i.e., acceleration), which could be approximated with a quadratic (e.g., Biesanz, Deeb-Sossa, Papdakis, Bollen, & Curran, 2004; Sliwinski et al., 2003) or other “nonlinear” trajectory (e.g., Cudeck & duToit, 2002) relative to the death event that would capture a change in rate of decline. This distinction between cross-sectional and longitudinal perspectives on “terminal changes” has been made before by Palmore and Cleveland (1976), who labeled the former “terminal decline” and the latter “terminal drop.” Both, however, imply within-person change in rate of change, unless the authors refer to linear declines starting in young adulthood, but there is good evidence of a period of stability in adult cognition (e.g., Schaie, 1996). In a time to death metric, an appropriate growth model addressing terminal decline would include curvature, in addition to intercept and linear slope terms.

For samples with baseline age heterogeneity, in addition to estimating a within-person curvature parameter, a term representing initial between-person age differences must be included in the model to account for variations in intercept, slope, and curvature attributable to cross-sectional, and possibly cohort-related, rather than developmental, differences. This is necessary to separate these cross-sectional influences from the longitudinal, within-person, possibly developmental, changes over time (Ware, 1985). By extension, in the context of studying terminal decline, when individuals are aligned according to time to death (rather than time since baseline or age), the model should also include a term that captures intercept, slope, and curvature differences in the trajectories of individuals entering the study at different distances from death (an alternate cross-sectional perspective on the data). In other words, cognitive scores should be modeled as a nonlinear function of within-person time to death at each interview, with individuals’ parameters adjusted for between-person differences in age at baseline and distance to death at baseline (see Technical Appendix). Without these two baseline covariates, the cross-sectional (between-person) and longitudinal (within-person) sources of chronology-related variance are confounded, and the resulting assumption is that baseline characteristics (age and distance from death) are not relevant—that the between- and within-person effects are equal or “convergent.” Aggregating the cross-sectional and longitudinal information in this way undermines the potential value of longitudinal data.

Separation of within-person changes from between-person differences is essential, as it is generally true that individuals of a particular age at baseline are healthier than those who reach that same age at a later date, having entered the study at a younger age (Mendes de Leon, 2007; Morrell, Brant, & Ferrucci, 2009), due likely to both initial selection and selective attrition. In other words, at a particular level of failing health, an individual is less likely to agree to initiate participation in a study than they are to agree to continue participation in that same study (initial selection). Furthermore, those who decline to a greater extent over the course of a study are more likely to drop out of the study (selective attrition). In the context of terminal decline (and whenever feasible), the impact of distance from death at baseline should be considered for similar reasons. All growth models should include an index of between-person alignment on time when such variation exists. This is clear when the longitudinal (within-person) dimension is represented by time since first assessment: if between-person age differences are not explicitly modeled, the restricting assumption of equal age (i.e., cross-sectional, between-person) and time (i.e., longitudinal, within-person) effects is imposed (Ware, 1985). This remains true for an age-based time structure: To not consider baseline age differences is to assume equality of the cross-sectional and longitudinal information (Mendes de Leon, 2007; Sliwinski, Hoffman, & Hofer, 2010). This applies equally to alternate time metrics, such as time to death. Following the same logic, between-person differences in proximity to death (or other relevant time metrics), when available, should also be explicitly modeled in order to address the impact of selection processes on the data.

Previous reports (see Table 1) vary in the inclusion of covariates representing between-person aspects of chronology, such as initial age (included in Laukka et al., 2006, 2008; Wilson et al., 2003) and proximity to death (included in Thorvaldsson et al., 2006). Early exploration of alternate time metrics (Sliwinski et al., 2003) did not address the convergence issue, most likely in the interest of comparing straightforward models. Although exclusion of age and distance from death at baseline reduces the number of parameters, between-person age differences and within-person changes across time (however structured) are confounded. Among the Sliwinski models, a significant quadratic trajectory was found for time to attrition but not for time to death, and it was suggested that modern medicine could extend the latter, so that the former may better reflect an individual’s state of health (Sliwinski et al., 2003). It would be interesting to compare the conclusions regarding these models once the between-person information was separated from the within-person information.

Table 1.

Characteristics of Studies Where Terminal Decline (TD) Was Examined Using Random Effects Models

Study and author	Dementia cases included	Outcome variable	Model Details	TD reported	TD from a within-person perspective
H70; Thorvaldsson and colleagues (2008)	Incident cases excluded	Verbal and spatial abilities; perceptual speed	Change point Metric: Age, time to death, serially BP information: none	Onset estimated at 6.5, 7.3, and 14.8 years. Before death for verbal ability, spatial ability, and perceptual speed	No
Kungsholmen Project; Laukka and colleagues (2008)	Demented at baseline excluded	Primary and episodic memory; word recognition; verbal and visuospatial ability	Linear rate of decline Metric: Years to event by group (dementia-free, impending death, demented group) BP information: Age	TD reported in primary memory, word recognition, verbal fluency. Impending death effects attenuated when patients with preclinical dementia removed	No
Swiss Interdisciplinary Longitudinal Study of the Oldest Old; Ghisletta (2008)	Included	Perceptual speed and word fluency	Joint linear longitudinal-survival. Metric: age BP information: none	Fluency predicted survival, change in fluency did not; Neither level nor change in speed predicted survival.	No
Rush Memory and Aging Project; Wilson and colleagues (2007)	Demented at baseline excluded	Composite and specific measures	Change point Metric: time to death BP information: Age	TD present in episodic memory (change point about 40 months before death). Weak evidence in other measures	No
Berlin Aging Study; Ghisletta and colleagues (2006)	Included	Perceptual speed; verbal knowledge; fluency; episodic memory	Joint linear longitudinal-survival Metric: age BP information: none	Yes, individuals with steeper decline reported to be closer to death	No
H70; Thordvalsson and colleagues (2006)	Demented at baseline excluded	Perceptual speed	Quadratic Metric: age and time to death separate and serially BP information: age at death	No	Yes
Kungsholmen Project; Laukka and colleagues (2006)	Demented at baseline excluded	MMSE	Linear rate of decline Metric: Years to event by group (dementia-free, impending death, demented group) BP information: Age	Yes, though disappeared after removal of demented and preclinical dementia cases	No
Bronx Aging Study; Sliwinski and colleagues (2006)	Nondemented sample	Episodic memory	Change point Metric: age, and time to death serially BP information: None	Terminal decline observed in episodic memory 8.4 years before death. Demented individuals had steeper post change point slopes.	No
Origins of Variance in the Old–Old (OCTO-Twin); Johansson and colleagues (2004)	Incident cases excluded	Knowledge; inductive reasoning; perceptual speed; visuospatial ability; memory	Quadratic Metric: time in study. BP information: Age, time to death	Weak support of TD hypothesis. Episodic memory characterized by linear decline; some evidence of accelerated decline for knowledge	No
Bronx Aging Study; Sliwinski and colleagues (2003)	Demented at baseline excluded	Memory performance	Quadratic Metric: time to death BP information: None	Time to death Increased rate of memory decline associated with death; accelerated decline not found; dementia accounted for most of memory loss	No
Religious Order Study; Wilson and colleagues(2003)	Demented at baseline excluded	MMSE, episodic; semantic and working memory; perceptual speed; visuospatial ability	Change point Metric: time, time to death, serially BP information: age	Onset of terminal decline ranged from 33 months (perceptual speed) to 72 months (visuospatial ability) before death.	No

Note: MMSE = Mini-Mental State Examination; BP = between-person.

A subsequent analysis including age and distance from death at baseline with a time-in-study (i.e., number of years since baseline assessment) time structure (Johansson et al., 2004) did reveal some quadratic terms, but these may not represent terminal decline, given the time metric used. The time-in-study structure modeled the association of baseline between-person age and time to death differences on initial level and rate of change in functioning relative to time since the baseline occasion rather than time to death.

A further development was to explicitly treat incident cases of dementia (Laukka et al., 2006, 2008), who should be either excluded (as in Johansson et al., 2004; Sliwinski et al., 2003) or modeled separately in order to avoid confusing terminal decline with incident dementia. Laukka and colleagues (2006, 2008) modeled time to death in individuals who died, time to diagnosis of dementia in those with incident dementia, and time to the mid-point between the second and third follow-up in those who neither died nor demented. This allowed comparison of rates of change prior to an event but did not specifically address terminal decline in the diagnosed group.

Thorvaldsson and colleagues’ (2006) extension of the alternate time metrics strategy appropriately included between-person (baseline) time to death as a covariate. (Baseline age was not needed as the sample was age homogeneous—all individuals started at the age of 70 years.) Incident cases, however, were not modeled separately, so the dementing process could have been misinterpreted as terminal decline. When the age (equal to time-in-study for this age homogeneous sample) and time to death structures were compared for fit with the data using the Bayesian information criterion (BIC), the time to death model provided a better fit, suggesting that it was a better metric than was age for characterizing within-person changes and between-person differences in late life (Thorvaldsson et al., 2006). Although the inclusion of incident cases of dementia weakens this argument, there are compelling theoretical reasons (Sliwinski et al., 2003) for specifying rate of change relative to a time structure that could plausibly represent a process rather than simply age. Similar models have been implemented to study terminal decline in life satisfaction (Gerstorf, Ram, Rocke, Lindenberger, & Smith, 2008) and self-perception of aging (Kotter-Gruehn, Kleinspehn-Ammerlahn, Gerstorf, & Smith, 2009).

Combining time metrics serially (e.g., age prior to the change, time to dementia, or death after), change point models (Gerstorf et al., 2008; Sliwinski et al., 2006; Thorvaldsson et al., 2008; Wilson, Beck, Bienias, & Bennett, 2007; Wilson et al., 2003) make use of both age and time to death metrics to account for acceleration of decline, as they allow a steeper, usually linear, slope after the change point. However, these models have assumed a change point common to all individuals—a strong assumption for studies with large age and age-at-death heterogeneity. Once random change points can be estimated in these models, as they have in Gerstorf and colleagues (2008) in the context of life satisfaction, they should be revisited for the study of terminal cognitive decline.

Another potential model, the joint longitudinal-survival model, uses parameter estimates from a longitudinal random effects model as covariates in a simultaneously estimated survival model (Ghisletta, 2008; Ghisletta, McArdle, & Lindenberger, 2006; Guo & Carlin, 2004; Henderson, Diggle, & Dobson, 2000). It is useful for analyzing data sets in which much of the mortality is unknown or has not yet occurred (i.e., is censored) and provides an estimate of the probability of surviving until a given age. Inclusion of between-person differences in baseline age and distance to death in the random effects portion of the estimation would be relevant in these models as well.

Our aim is to model differences in terminal decline separately in individuals who remained free of dementia and individuals diagnosed with dementia during the study (excluding those demented at baseline) with an emphasis on within-person aspects of the data. Exemplars of two cognitive abilities are considered, one “age vulnerable” and one “age maintained.” Although findings have been mixed (see Ghisletta et al., 2006 for review), some previous research has suggested that terminal decline is more evident in abilities that tend to show smaller age-related differences (White & Cunningham, 1988). Individuals are aligned on a theoretically relevant time to death metric. Dementia status is explicitly modeled. The significance of fixed and random quadratic effects is evaluated in order to focus on within-person increases in rate of change, rather than accepting steeper linear slopes in individuals closer to death (between-person information) as evidence for terminal decline. Finally, the effects of baseline differences in age and time to death are estimated in order to explicitly remove between-person characteristics (e.g., healthy participant effect) from the estimates of within-person change.

METHOD

Sample

Study participants were 461 elders with known death dates (as of 02/2009) from the population-based “Origins of Variance in the Old–old” (OCTO-Twin) study (McClearn et al., 1997). Initially, 737 pairs aged 80 years or older were sampled from the Swedish Twin Registry. The pairwise response rate, apart from nonresponse due to death of one or both twins in a pair (188 pairs), was 65%, resulting in 351 intact twin pairs aged 80 years or older (702 individuals: 149 monozygotic and 202 same-sex dizygotic pairs). These individuals were first interviewed between 1991 and 1993 and then at four further interviews conducted at two-year intervals. After accounting for mortality, only 10% of missing occasions are due to refusal to participate.

In the analysis sample, 355 individuals who remained free of dementia had data for both cognitive measures analyzed here at either the first or second occasion; 106 individuals with incident dementia had concurrent data on the two measures. Another 98 individuals had dementia before the beginning of the study but were excluded as very few had data on more than three occasions. Approximately two thirds of the sample is female (65% in nondementing and 60% in incident dementia group), comparable with the national ratio of 63% for this age range (Statistics Sweden, 2009).

Additional sample characteristics are provided in Table 2. Note that, in Sweden, at the beginning of the last century, only “folkskola,” essentially six years of elementary school, was compulsory. As in many countries, additional years were not mandatory until later.

Table 2.

Covariate and Outcome Means and Standard Deviations for Nondemented Individuals and Those With Incident Dementia

	Whole sample, N at T1 = 461, M (SD)	No dementia, N at T1 = 355, M (SD)	Incident dementia, N at T1 = 106, M (SD)
Years of education	7.24 (2.27)	7.32 (2.36)	6.96 (1.91)
Age at baseline	83.16 (2.70)	83.22(2.77)	82.92 (2.43)
Age at death	90.23 (4.23)	90.27 (4.35)	90.09 (3.77)
T1 Information	28.38 (11.18)	29.57 (10.51)	23.52 (12.56)
T2 Information	28.31 (11.45)	30.35 (10.10)	21.50 (12.97)
T3 Information	27.03 (12.48)	29.69 (11.02)	17.02 (12.85)
T4 Information	26.31 (12.99)	29.58 (11.31)	14.61 (12.08)
T5 Information	25.12 (11.43)	26.58 (10.46)	16.29 (12.95)
T1 Block Design	11.44 (7.08)	12.02 (7.10)	9.29 (6.62)
T2 Block Design	11.19 (7.12)	12.37 (6.72)	7.64 (7.12)
T3 Block Design	10.75 (7.06)	12.24 (6.53)	6.23 (6.73)
T4 Block Design	10.25 (7.12)	11.67 (6.64)	6.11 (6.91)
T5 Block Design	9.11 (7.13)	10.59 (6.67)	3.5 (5.97)

Procedure

Eleven cognitive tests were administered at the participants’ home by experienced registered nurses. Dementia was diagnosed by consensus according to the third edition of the Diagnostic and Statistical Manual of Mental Disorders. Sociodemographic information such as gender, years of education (number of years the individual went to school), and marital status were also collected. Date and cause of death were obtained from the Swedish Death Registry. Procedures were approved by the Gothenburg University ethical standards committee on human experimentation.

The two measures with the most complete data in this sample, best measurement properties, and which represent a straightforward division into age-maintained and age-vulnerable, were used for the current analysis.

Measures

The Swedish version of the Wechsler Adult Intelligence Scale (WAIS; Wechsler, 1981) Information test (Jonsson & Molander, 1964) and Koh's Block Design test (Dureman & Salde, 1959) were used to measure participants’ knowledge and visuospatial ability. The Information test includes questions of general knowledge and has a maximum score of 44. Block Design requires reproduction of a pattern shown on a set of cards using red and white blocks and has a maximum score of 42. Trajectories plotted against years to death for both measures are shown in Figure 1, separately for incident cases and those without a dementia diagnosis. Means and standard deviations for both measures at each occasion are displayed in Table 2.

Figure 1.

Observed time to death trajectories by measure and group.

Statistical Analyses

Information and Block Design scores were modeled using linear and quadratic time to death growth models with the intercept specified at two years before death. The number of years to death at each assessment was coded using negative values to correspond with traditional representations of number lines and time, which have values increasing to the right and with the progression of time. For instance, if an individual was interviewed at 6, 4, and 2 years before death, the corresponding centered time to death values were −4, −2, and 0, respectively. We did not center “time to death” at the actual date of death because it would not be possible to obtain a performance score at this point. Figure 2 shows the distribution of distance to death for the no-dementia group and for incident cases. Sixty-two percent of the individuals have their final interview within two years of death.

Figure 2.

Histograms of time to death by group.

All model parameters were adjusted for dementia diagnosis status and for an interaction term representing years to death in the incident dementia group. To further account for between-person effects, all model parameters were also adjusted by gender, years of education, initial age, and proximity to death at study entry. The reference characteristics were male and nondemented, with initial age of 83 years, initial distance from death 6 years, and education 7 years (the averages). With this specification, the intercept of a linear growth model represents the mean cognitive score 2 years before death for a man with 7 years of education who enters the study when he is 83 years old and 6 years from death. The linear term represents the mean rate of decline per year (at two years from death in the quadratic model) for someone with these characteristics, and the quadratic term, the rate of change in rate of decline.

The BIC was used to identify the model best describing the data in terms of goodness of fit and parsimony, with lower BIC indicating better fit.

All models were fitted in Mplus 5 (Muthen & Muthen, 2008), using maximum likelihood for the estimation of model parameters. Parameter estimates are robust against a missing at random missing data assumption (Little & Rubin, 1987). Models were adjusted for nesting within twin pairs by using “ANALYSIS: type = complex random” and “CLUSTER=PairID.”

RESULTS

There were no differences between dementia-free and incident case groups in terms of age at baseline, age at death, or years of education (t-tests all p > .05). This lack of difference is likely because the minimum age of the sample was 80 years, resulting in a small age range. Although the observed individual trajectories did not indicate strong evidence for curvature, both linear and quadratic change terms were considered, as a within-person perspective on terminal decline requires evidence of accelerated decline within, rather than across trajectories. Results of the final models are presented in Table 3.

Table 3.

Mean, Standard Error of the Estimates of the Effect of Risk Factors on Random Effects of Terminal Decline Model for WAIS Information and Block Design

	Information			Block Design
Fixed effects	Coefficient	SE	p Value	Coefficient	SE	p Value
Level: 2 years before death (intercept)
Never demented	28.75	0.83	<.001	9.80	0.50	<.001
Incident case vs. noncase	−11.33	1.19	<.001	−5.33	0.71	<.001
Years to death	0.75	0.15	<.001	−0.01	0.09	.89
Incident Case × Years to Death	−0.20	0.39	.61	0.12	0.22	.58
Baseline age	−0.66	0.18	<.001	−0.40	0.11	<.001
Years of education	1.95	0.20	<.001	0.64	0.13	<.001
Female	−4.08	0.99	<.001	0.54	0.60	.37
Rate of decline (linear slope)
Never demented	−1.13	0.22	<.001	−0.48	0.10	<.001
Incident case vs. noncase	−2.30	0.38	<.001	−0.86	0.16	<.001
Years to death	0.21	0.04	<.001	−0.01	0.02	.63
Incident Case × Years to Death	−0.54	0.11	<.001	−0.10	0.04	.007
Baseline age	−0.02	0.05	.72	−0.01	0.02	.63
Years of education	−0.00	0.05	.93	0.01	0.02	.78
Female	0.17	0.25	.50	0.10	0.09	.29
Acceleration (quadratic slope)
Never demented	−0.16	0.03	<.001	—	—	—
Incident case vs. noncase	−0.05	0.07	.45	—	—	—
Years to death	−0.01	0.004	.24	—	—	—
Incident Case × Years to Death	−0.03	0.01	.004	—	—	—
Baseline age	0.00	0.01	.59	—	—	—
Years of education	−0.00	0.01	.53	—	—	—
Female	−0.01	0.03	.68	—	—	—
Random effects
Score 2 years before death	86.62	6.90	<.001	28.62	2.51	<.001
Rate of decline	1.58	0.34	<.001	0.15	0.05	.004
Acceleration	0.007	0.002	<.001	—	—	—
Residual	13.92	0.80	<.001	10.83	0.59	<.001

Information

The estimated mean score two years before death for a dementia-free male participant enrolling in the study at 83 years of age, 6 years from death, with 7 years of education (i.e., reference values), was 28.75 (SE = 0.83), the rate of decline was −1.13 (SE = 0.22) per year and the rate of acceleration was −0.16 (SE = 0.03). Significant residual variances of cognitive performance (86.62; SE = 6.90), rate of decline (1.58; SE = 0.34), and acceleration (0.007; SE = 0.002) indicate heterogeneity across individuals about the fixed effects.

The expected score for those with incident dementia was 11.33 points (SE = 1.19), which is ¾ of a SD lower than for those remaining dementia free. In addition, for each year older on (between-person) baseline age, with the same initial distance from death, the Information score two years from death was estimated to be 0.66 lower. In contrast, for each year closer to death at study entry, the Information scores of initially like-aged nondementing individuals at two years from death were predicted to be 0.75 higher. This likely reflects a healthy participant effect, with better-off individuals more willing to participate later in their life span. Similarly, nondementing individuals closer to death at study initiation showed less decline over time. Individuals with more education performed better but did not differ on rate of decline or acceleration. Women scored an average of 4.08 points lower than men. Decline was faster in incident cases and in incident cases closer to death at study entry. To illustrate the average within-person trajectories of change in Information scores and to demonstrate the impact of baseline distance to death, the left panels of Figure 3 show mean estimated trajectories for prototypical nondemented and dementing 83-year-old men with 7 years of education, who were 6, 8, and 10 years from death at study entry.

Figure 3.

Model estimated mean curves by measure and group for different values of distance to death and baseline age at study entry.

Block Design

The model with a random quadratic term was not estimable for Block Design and the BIC for the linear-only model was lower than the model with quadratic variance fixed at zero (BIC_Fquad = 16,005, BIC_linear = 15,985), so the linear model was chosen. According to Raftery’s criteria (1995), a 10-point difference in BIC values suggests strong support of the model with the lowest BIC.

From the linear slope model, the estimated mean score two years before death for a dementia-free male participant enrolling at 83 years of age and 6 years to death, with 7 years of education, was 9.80 (SE = 0.50) and the rate of decline was −0.48 (SE = 0.10) per year. Significant residual variances of cognitive performance (28.62; SE = 2.51) and rate of decline (0.15; SE = 0.05) indicate heterogeneity across individuals.

Two years before death, incident cases were expected to score 5.33 points (SE = 0.71), which is 0.59 SDs below nondemented individuals. In addition, a one-year increase in between-person baseline age given the same baseline distance from death was associated with a 0.40 point lower Block Design score. Individuals with more education performed better but did not change at a different rate. Decline was faster in incident cases and for incident cases closer to death at study entry. The annual difference in rate of change for the incident group (−0.10) was 10-fold larger than the rate of decline of individuals who died without a dementia diagnosis (−0.01). To illustrate the average within-person trajectories of change in Block Design scores and to demonstrate the impact of baseline distance to death, the right panels of Figure 3 show mean estimated trajectories for prototypical nondemented and dementing 83-year-old men with 7 years of education, who were 6, 8, and 10 years from death at study entry.

Results for the fixed quadratic model were essentially the same, except that the incident case by baseline years to death interaction was not significant. The estimated quadratic term was −0.07, p = .01.

DISCUSSION

Given a conceptualization of terminal decline as a within-person process, it is worthwhile considering the results of analyses emphasizing within-person aspects of the data. In the literature, within-person change in rate of decline could not be addressed in reports fitting linear-only models (e.g., Laukka et al. 2006, 2008), and where nonlinear models were fitted, relevant between-person information was generally not included (e.g., Sliwinski et al., 2003, 2006), resulting in conclusions in which between-person and within-person effects were not separated. Despite this lack of separation, Sliwinski and colleagues (2003) also reported a lack of accelerated decline in memory associated with approach to death.

The current analyses explicitly addressed terminal decline from a within-person perspective by focusing specifically on the curvature of the individual trajectories and by separating the between-person differences from the within-person changes. Given this separation, the results can be viewed from both between- and within-person perspectives, neither of which showed strong terminal decline effects, though weak evidence of within-person terminal decline was evident for the Information measure.

The pairing of significant negative linear and quadratic terms for Information supports a within-person definition of the terminal decline hypothesis for the WAIS information subscale, which represents a typically “age-maintained” ability. This confirms and extends the earlier finding of a quadratic term in a different context but related data set (Johansson et al., 2004). Although the curves in Figure 3 appear far from striking, the parameter estimates are comparable with or larger than those of other studies reporting quadratic terms (e.g., Johansson et al., 2004; Sliwinski et al., 2003; Thorvaldsson et al, 2006).

Relying instead on the between-person information—whether an individual entered the study closer to death—there is also little evidence for terminal decline, as those who were closer to death at baseline showed less decline on average. Regression of the slope term on years to death at baseline represents the expected results for a typical analysis of the association of between-person nearness to death and rate of change in cognition, assuming statistical control of chronological age.

When change in Block Design is indexed by proximity to death, nondemented individuals in this sample, on average, are estimated as declining at a constant rate without experiencing a change in their rate of decline before death. This lack of acceleration for an “age-vulnerable” ability supports previous work, suggesting that terminal decline is seen primarily in “age-maintained” abilities. However, support for the terminal decline of a vulnerable ability is also missing from a between-person perspective for individuals not diagnosed with dementia, as steeper declines were not found in individuals of the same age but closer to death at baseline. This may be a function of the advanced age of the sample or of having included age as a covariate.

As expected, individuals with incident dementia had lower Block Design and Information scores than nondemented individuals, and they declined at a faster rate, with those closer to death declining most rapidly and, for Information, also showed greater acceleration in this decline. Although this faster decline appears to support the terminal decline hypothesis, it is based on between-person differences and, for Block Design, applies only to individuals who, by definition of their diagnosis, must be experiencing accelerated cognitive decline prior to death.

Previous lack of within-person longitudinal evidence for terminal decline in Block Design may have been a function of having a smaller number of occasions (Laukka et al., 2008), which is somewhat less of a factor here.

In contrast, a random effects model with a fixed change point, with time indexed by chronological age before the change point and proximity to death after the change point, suggested the existence of a change in rate of decline of spatial ability in a nondemented sample occurring about seven years prior to death, after which the rate of decline almost doubled (Thorvaldsson et al., 2008). Although it is possible that this finding was due to the relative weight of between-person information in the fixed change point analysis, it is a relevant comparison. In the current study, individuals were followed for up to eight years and entered the study at an advanced age. For Block Design, many individuals may already have entered a terminal decline phase prior to initiation of the study in which case the change in rate of decline would have occurred prior to data collection and could not be detected. It is also possible that people were not observed for long enough during the preterminal phase, so that acceleration of change could not be observed due to the left censoring. At the other extreme, given the 8-year longitudinal span, individuals farther than 12 years from death at baseline provide no data within four years of death. Regarding the suggestion that terminal decline may be specific, rather than pervasive (White & Cunningham, 1988), another answer may be that it depends on the distance from, and causes of, death in the sample.

Education has been identified as a protective factor in several studies of aging. However, its relationship with terminal decline is not often considered. In the time to death metric used here, education had a positive correlation with cognitive performance two years before death but did not predict rate of change. Laukka and colleagues (2006) similarly reported that education was related to individual differences in level of Mini-Mental State Examination scores but not to rate of change. These “level” differences, however, likely represent stable lifelong individual differences.

In the current analysis, between-person differences in proximity to death at the first occasion were included in the model to further separate between- and within-person chronology. These “time to death” terms are best described as representing the expected differences in intercept, slope, and acceleration for someone entering the study a year closer to death. As these terms have not generally been included in existing research, there is no straightforward comparison for these findings. For the model implemented here, inclusion of the between-person time to death by incident dementia interaction term means that the “time to death” term applies specifically to the nondementing individuals. At first glance, the finding of higher scores for individuals closer to death may seem counterintuitive but in fact is completely in line with expectations in the context of a healthy participant selection effect: For nondementing individuals of the same age, sex, and level of education, those entering the study closer to death scored higher, on average, than individuals expected to live longer. This coincides with the healthy participant effect reported in other longitudinal studies of aging (e.g., Mendes de Leon, 2007; Morrell et al., 2009). In the context of terminal decline, a person who joins the study closer to death is likely to perform better at that particular distance to death than someone with the same characteristics who reaches that distance to death some time after joining the study.

When terminal decline effects are found, one potential explanatory factor would be declines in the health of individuals approaching death. As health status likely changes over the course of a study, however, including initial health status only, as is often done in longitudinal analyses of cognition, may be of limited utility. It might be preferable, as we did with dementia, to include indicators of relevant incident pathologies. A more complex, but perhaps ideal option might be to include one or several time-varying covariates representing health and within-person changes in health over time. As we found little evidence for terminal decline here, we did not attempt to integrate health into our models.

Although we emphasized within-person aspects of the data, the influence of the initial between-person differences in age and distance from death cannot be completely eliminated. Standard treatment of missing data in models such as the one presented here inevitably rely on between-person as well as within-person associations. In addition, models such as the one we used explicitly align individuals along the proximity to death timeline and to the extent that people differ on this dimension, the overall curve is estimated based on the location of different individuals. In addition, inclusion of all individuals with death dates, rather than excluding those with only one interview, means that 85 individuals (18%) contribute only cross-sectional data to the analysis. Requiring a minimum of two occasions per participant prior to death led to estimation problems for the quadratic model, possibly indicating that despite best intensions, our analysis is still influenced by the relative quantity of between-person information.

Furthermore, including between-person differences in age and distance from death as covariates in the model, while addressing the convergence assumption, is not without assumptions either. We are—implicitly or explicitly—implying that the association between these initial differences and our outcomes of interest are linear (based on the general linear model). It would be possible to also explore the association of the outcomes with quadratic or other forms of these cross-sectional covariates.

The current study combines a number of important previous distinctions in the study of terminal decline: theoretically relevant time metric (Laukka et al., 2006; Sliwinski et al., 2003; Thorvaldsson et al., 2006), explicit treatment of incident dementia (Laukka et al., 2006, 2008; Sliwinski et al., 2003), statistical separation of between-person effects in terms of both age and years to death from baseline (Johansson et al., 2004), and comparison of age-vulnerable and age-maintained abilities (White & Cunningham, 1988). This study also adds an emphasis on a within-person definition of terminal decline. This combination of features makes better use of the available longitudinal information.

However, the current study also shares limitations with the other research. First, if, by definition, a person who declines tends to be diagnosed as demented, then, by corollary, the nondementing group includes those who are for the most part not declining. The terminal decline phenomenon, which was noted prior to virtually all modern work on dementia, may be driven primarily by declines in cognition due to dementia in a subset of the population. In the sample studied here, however, additional curvature was not seen in the incident dementia group.

Second, it is awkward to attribute curvature solely to terminal decline, when other factors may also contribute to observed nonlinearity of trajectories. For example, retest gains, in a situation where declines would otherwise be observed, would also contribute to a curved trajectory. Ceiling effects at earlier but not later occasions could also artificially induce curvature. It is possible, as well, although incident dementia over the course of the study was treated separately, that some of the individuals in the no-dementia group entered the preclinical phase of dementia during this time but were diagnosed only after data collection ended.

Third, a two-year interval between assessments may be insufficient to identify within-person acceleration in change related to health change and subsequent mortality, as estimation of accelerated change in the months or years prior to death is limited by temporal resolution (Bäckman & MacDonald, 2006).

Fourth, identification of the accelerated change implied by the concept of terminal decline requires an adequate number of occasions close enough to death with which to model a quadratic within-person curve or change point (at least four; Bollen & Curran, 2006; Wilson et al., 2007; and likely significantly more: Gerstorf et al., 2008). The current study, along with most existing longitudinal studies of aging, does not meet this last criterion, at least not in a large enough proportion of the sample, without combining between-person and within-person effects in an age-based model.

As more longitudinal studies of aging become complete, it may become possible to more fully address the issue of terminal decline. In the meantime, we can give more thought to how we interpret terminal decline and accelerated changes from a within-person perspective and we should include initial between-person age differences as a covariate in our longitudinal growth models.

FUNDING

This work was supported by the National Institute on Aging at the National Institutes of Health (grant number AG026453) and the UK Medical Research Council WBS (grant numbers U. 1052.00.013.00003, U.1052.00.013.00001). The OCTO-Twin study was funded by the National Institute on Aging at the National Institutes of Health (grant number AG08861), The Swedish Council for Working Life and Social Research, The Adlerbertska Foundation, The Hjalmar Svensson Foundation, The Knut and Alice Wallenberg Foundation, The Wenner-Gren Foundations, and The Wilhelm and Martina Lundgrens Foundation.

TECHNICAL APPENDIX

In a time to death (ttd) metric, an appropriate growth model (with standard distributional assumptions), expressed here with intercept, slope, and curvature-related terms grouped for clarity (BP = between-person; WP = within-person), is:

where ${\mathrm{WPttd}}^2$ represents individual-level curvature (with negative WP_ttd and negative ${\mathrm{WPttd}}^2$, together, indicating “accelerating” decline).

Estimates associated with BPage represent between-person (i.e., cross-sectional) age differences in expected level, slope, and trajectory curvature, at the specified intercept, for individuals entering the study at different ages. Similarly, BPttd provides expected intercept, slope, and curvature differences for the trajectories of individuals entering the study at different distances from death.