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The Journals of Gerontology Series B: Psychological Sciences and Social Sciences logoLink to The Journals of Gerontology Series B: Psychological Sciences and Social Sciences
. 2015 Mar 3;70(5):745–752. doi: 10.1093/geronb/gbu182

Disability Trajectories at the End of Life: A “Countdown” Model

Douglas A Wolf 1,✉, Vicki A Freedman 2, Jan I Ondrich 3, Christopher L Seplaki 4, Brenda C Spillman 5
PMCID: PMC4635644  PMID: 25740918

Abstract

Objectives.

Studies of late-life disablement typically address the role of advancing age as a factor in developing disability, and in some cases have pointed out the importance of time to death (TTD) in understanding changes in functioning. However, few studies have addressed both factors simultaneously, and none have dealt satisfactorily with the problem of missing data on TTD in panel studies.

Methods.

We fit latent-class trajectory models of disablement using data from the Health and Retirement Study. Among survivors (~20% of the sample), TTD is unknown, producing a missing-data problem. We use an auxiliary regression equation to impute TTD and employ multiple imputation techniques to obtain final parameter estimates and standard errors.

Results.

Our best-fitting model has 3 latent classes. In all 3 classes, the probability of having a disability increases with nearness to death; however, in only 2 of the 3 classes is age associated with disability. We find gender, race, and educational differences in class-membership probabilities.

Discussion.

The model reveals a complex pattern of age- and time-dependent heterogeneity in late-life disablement. The techniques developed here could be applied to other phenomena known to depend on TTD, such as cognitive change, weight loss, and health care spending.

Key Words: Disability, Latent classes, Time to death, Trajectories

Background

Popular culture, mass media, and everyday life all present abundant images of late-life change, whether in type and location of residence, in family and social networks, in social engagement, in economic circumstances, or in health and functioning. These widespread images of change nevertheless compete with messages devoted to stability—to the maintenance of health and functioning, vigor and fitness, and “successful aging.” These aspects of everyday life are paralleled in scholarly research, where research on both the change in functioning associated with the disablement process (Verbrugge & Jette, 1994), as well as on the maintenance of functioning associated with a possible compression of morbidity (Fries, 1980) or extension of life expectancy (Oeppen & Vaupel, 2002), is widespread.

It is, therefore, unsurprising that the research literature on trajectories—that is, representations of the shape and direction of change over time—of late-life health and functioning has grown very rapidly in recent years. This growth has been facilitated by the increasing availability of individual-level panel data, permitting analysts to plot the time paths of various health or disability indicators at the person level. It has also been facilitated by the availability of several computer programs tailored to the estimation of alternative models of individual- and group-level pathways of change.

As George (2009) points out, trajectory analyses can be either transition based or level based; transitions are nearly always understood to coincide with “events” that produce a change of status in a discrete-state system, whereas levels can be associated with either continuous or discrete indicators of someone’s point-in-time status. In practice, most health or disability trajectory analyses are level based, and use models that imply a continuous pathway for the expected value of the outcome variable, whether the outcome employs a continuous or a discrete measure. An appealing feature of these types of trajectory analyses is that they allow researchers to use a sequence of current status measures—the type typically produced by panel surveys—to analyze developmental pathways, without making strong assumptions about the number and timing of intervening health or disability events. In contrast, analytic approaches that use transition rates or transition probabilities derived from current status data often require the adoption of strong, untestable, and in some cases unwarranted assumptions about the occurrence or nonoccurrence of health or disability transitions between assessment times (Wolf & Gill, 2009).

Many analyses of late-life disability trajectories have appeared in recent years. Some studies have used latent growth curve models to represent between-person variability in these pathways (Shaw, Liang, Krause, Gallant, & McGeever, 2010; Yang & Lee, 2010). Other studies have used discrete mixture models, in which each individual is assumed to belong to one of a (typically) small number of latent classes, each of which has a distinctive average trajectory (Liang, Xu, Bennett, Ye, & Quiñones, 2009; Taylor & Lynch, 2011). A common feature of these models is their representation of change along a time dimension that runs “forwards,” whether measured by an individual’s chronological age, or by elapsed time since experiencing a major event such as a hip fracture (Tseng, Shyu, & Liang, 2012), or by time since an arbitrary event such as the initial measurement in a panel survey (Dodge, Du, Saxton, & Ganguli, 2006). In contrast, several studies have conceptualized change as it relates to remaining lifetime—that is, time to death (TTD)—thus invoking a notion of time that runs “backwards.”

The idea of describing patterns of functional trajectories with respect to TTD rather than age appears to have originated in Glaser and Strauss (1968), who focused on hospital care for terminally ill patients. They defined trajectories as “perceived courses of dying” (p. 6) that begin when medical staff realize that the patient is on a pathway to death and distinguished several types of trajectories: abrupt and unexpected transitions to death; expected yet swift passages to death; “suspended-sentence” trajectories in which patients thought to be near death instead recover sufficiently to be discharged; and “entry–reentry” pathways that involve fluctuating levels of function, possibly associated with a series of hospitalizations. More recently, an influential paper by Lunney, Lynn, Foley, Lipson, and Guralnik (2003) classified decedents from a panel study into one of four predetermined trajectory groups (“sudden death,” “terminal illness,” “organ failure,” and “frailty”) based on disease diagnosis, cause of death, or nursing home residence (along with a fifth, “other,” group of unassigned cases).

Empirical disability trajectory models formulated on a TTD axis have often used samples of decedents identified either retrospectively or prospectively. Teno, Weitzen, Fennell, and Mor (2001), for example, used a mortality follow-back survey administered to kin of a 1993 sample of decedents. Examples of prospective designs include Lunney and colleagues (2003), who used decedents from four sites in the Established Populations for Epidemiologic Studies of the Elderly study; Gill, Gahbauer, Han, and Allore (2010), who used decedents from the Precipitating Events Project; and Schoeni, Freedman, and Wallace (2002), who used National Health Interview Survey (NHIS) respondents (1986–1994) linked to National Death Index (NDI) records (1986–1997). Studies that use the prospective designs must, of necessity, discard all observations on individuals that survive past the last wave of panel-data collection (or, in the case of Schoeni et al., NHIS respondents that do not link to NDI death records); this, in turn, raises questions of possible selection bias. The main source of potential selection bias arises from the fact that those who die in a given year (or within the period of a panel study) are probably in worse health, and also more likely to have a disability, than those who survive that year (or the study’s observation period), creating systematic differences between the decedents and the survivors.

An obvious problem with an analysis that uses TTD as an organizing principle is that for living individuals, TTD is typically unknown. Even among those who on the basis of clinical observation are expected to live only a short time, predictions about the length of remaining lifetime are highly uncertain and often quite inaccurate (Minne, Ludikhuize, de Rooij, & Abu-Hanna, 2011). Prospective and panel studies frequently record subjects’ deaths during a follow-up period, but in nearly all cases, there are numerous subjects that remain alive (e.g., have right-censored lifetimes) at the end of the study period. Only in very rare cases (e.g., Romoren & Blekeseaune, 2003) have the members of a sample been followed prospectively until all have died, eliminating the right-censoring problem.

Recent research reveals the usefulness of biomarkers of aging (Butler et al., 2004) as predictors of TTD, whether used individually as covariates (Goldman et al., 2006) or combined into a single index of “biological age” (Levine, 2013). In these studies, biomarkers are shown to predict TTD independently of chronological age. Other studies have also shown biomarkers to be strongly predictive of disability (Jenny et al., 2012). Most existing studies of late-life disability trajectories, however, have accounted for chronological age while ignoring TTD as well as the underlying biomarkers that predict it, or have focused on TTD while paying little or no attention to age differences. The main purpose of this article is to present a method for modeling late-life disability trajectories that permits simultaneous assessment of the relative contribution of both age and TTD to the likelihood of having a disability, in the context of a multiple class trajectory model.

Disability trajectory models that control for chronological age but not for an extensive set of biomarkers that would, in theory, completely characterize biological age—in other words, nearly all existing disability trajectory research—are likely to produce biased estimates of age effects because chronological age is strongly correlated with the omitted variable, biological age. In the absence of such biomarker information, if complete data on TTD were available—as in a cohort or panel study that tracks its sample to extinction—then including TTD as a proxy for biological age might still produce biased parameter estimates because TTD is not perfectly predicted by biomarkers, but would surely be a substantial improvement over the age-only model typically used. The more common situation, which is the situation we address, is one in which panel data fails to include biomarker data but does have partial (i.e., right censored) measures of TTD. We address the problem of missing information on TTD using multiple imputation (MI) techniques. By permitting observations with otherwise missing information on TTD to be included in the analysis, we address potential selection-bias issues. This approach also increases effective sample size, producing more precise statistical estimates.

Our goal is not to determine whether chronological age, or alternatively TTD, is the “better” predictor of having a disability; rather, we wish to explore the possibility that there are multiple and distinct disability trajectories, each of which may to varying degrees reflect the process of age-related disease, terminal decline, or both. Because we incorporate a backwards-running time-to-death variable along with age, we refer to this as a “countdown” model. We also emphasize that ours is a descriptive model of disability pathways. Just as chronological age should not be viewed as a causal variable (Ferraro, 2013), neither should TTD be viewed as causal, but rather as a proxy for unobserved biological processes of aging.

Our approach requires a series of analytic steps. We first estimate a predictive model of TTD, using interval regression (Cameron and Trivedi, 2009). We treat unobserved TTD as missing data and impute multiple plausible values of TTD to each right-censored case, producing a number of probabilistically identical (but numerically different) complete data files. Using each complete data file, we then estimate a latent-class disability trajectory model, using the well-known SAS PROC TRAJ routine (Jones, Nagin, & Roeder, 2001). The final step is to combine the alternative sets of estimated model parameters into a single set of estimates and standard errors using standard MI tools (Rubin, 1987).

Method

Sample

Our analysis uses a sample of individuals from what was originally called the Asset and Health Dynamics of the Oldest-Old (AHEAD) panel study (Soldo, Hurd, Rodgers, & Wallace, 1997). AHEAD began in 1993 and was incorporated into the Health and Retirement Study in 1998 (National Institute on Aging, n.d.). For this study, we include respondents with a complete 1995 interview who were born between 1890 and 1923. We begin with the 1995 interview because the wording of survey items we use to code disability changed between 1993 and 1995. A total of 6,269 individuals meet our inclusion criteria; after exclusions for missing values on outcome and explanatory variables, the sample is reduced (by 1.6%) to 6,168.

We use outcome measures from eight waves of the survey (1995–2010). Our sample-selection criteria ensure that disability status is observed at least once (in 1995) for all individuals. We include observations from all waves in which the sample members (or their proxy informants) provided complete interviews; there are 25,566 such person waves of data, with each sample member appearing about 4.1 times on average. Information on the timing of deaths comes from either the designated informant in a so-called “exit interview,” administered in each wave of data collection, for cases where the attempt to re-interview a previous respondent revealed that the respondent had died (94% of the cases with observed TTD in our sample) or from a 2006 match (attempted for all presumed decedents up to that time) to NDI records (6% of cases). The last occasion at which deaths can be detected is the 2010 interview; thus, deceased members of the sample provide from one to seven panel observations on disability status prior to death. Sample members can be lost to follow up at any point after the 1995 interview; however, about 20% of our sample individuals remain alive, and have an observed disability indicator, in 2010.

Measures

Having a disability

We use a binary indicator of disability status, one that indicates the receipt of help from another person with any of six activities of daily living (ADLs). The questions on ADL help are asked in each interview and come from a sequence in which respondents are first asked “[b]ecause of a health or memory problem do you have any difficulty with dressing” or, in separate questions, “walking across a room,” “bathing or showering,” “eating,” “getting in or out of bed,” or “using the toilet.” In each case, those responding affirmatively are then asked whether anyone ever helps with the respective activity. We use both self-reported and proxy-reported help with ADLs to code our disability outcome.

Age and TTD

Using data on the month and year of birth and (when observed) death as well as the month and year in which each interview occurred, we constructed measures of age and TTD (in years and months) at each interview. All age variables were expressed relative to age 70 (in other words, chronological age minus 70). When TTD is known, it can never exceed 15 years (i.e., 2010–1995). And, in the 1995 interview (but not in later interviews) those known to be alive in 2010 are also known to have an unobserved value of TTD that exceeds 15. To deal with the fact that true TTD (if it were known) would predict missingness, we created two variables to represent TTD. The first, TTDB (for “bounded above at 15”) equals TTD conditional on TTD less than or equal to 15. The second, TTDD, is a dummy variable indicating TTD greater than 15. When TTDD is one, TTDB is zero, and when TTDB is nonzero, TTDD is zero. Both are sometimes missing, and both must therefore be imputed.

For cases with unknown TTD, we used random imputation methods to fill in the missing values of TTDB and TTDD; details are provided subsequently. A handful of cases (n = 48) are recorded as “known dead” as of some follow-up interview, but their timing of death is unknown. For these cases, the date of death is bounded below by the last interview in which they were alive and bounded above by the date of the first interview in which they were reported to have died. The timing of death for those never reported to be dead, including those still alive at the time of the 2010 interview, is bounded below by the month of their last complete interview and (by assumption) bounded above by the month in which they would become 112, which is 1 year older than the oldest recorded death in our sample.

Time-varying predictors of disability status

In addition to age and TTD, our disability trajectory equations included several time-varying explanatory variables. In particular, we controlled for the presence of six chronic conditions (high blood pressure, cancer, lung disease, heart disease, stroke, and arthritis). These chronic conditions are among those most often named as causes of disability (Freedman, Schoeni, Martin, & Cornman, 2007). The chronic conditions variables were coded using responses to questions about whether a doctor had “ever told” the sample person that they had each such condition. Although many individuals already had one or more such conditions in 1995, new cases of these chronic diseases were reported by anywhere from 6% (for lung disease) to 19% (for arthritis) of the sample over the period of follow up. We also controlled for current smoking status and for widowhood (~19% of individuals not initially widowed experienced widowhood during the period of follow up).

Time-invariant predictors of trajectory class.

The latent-class trajectory model also includes several time-invariant explanatory variables, which are used to predict class membership. These include indicators of gender (women), race (Black), ethnicity (Hispanic), whether the sample member ever smoked, and two categorical indicators of educational attainment (college degree and less than high school education). These variables capture several domains shown in many past studies to be associated with between-group differences in health and disability.

Statistical Analysis

Imputing TTD

Imputations are based on a regression of the logarithm of TTD on an extensive set of explanatory variables (including disability status). With the additional assumption that residuals are normally distributed, this is a type of accelerated failure time model (Klein & Moeschberger, 1997). For cases with missing TTD, the lower bound of the missing variable is always known. For example, for someone still alive in 2010, we know that TTD exceeds 15 in 1995, TTD exceeds 12 in 1998, TTD exceeds 10 in 2000, and so on. We also assumed that missing values of TTD were bounded above by the number of years it would take to reach age 112. Knowing the bounds on TTD when it is missing allows us to use all cases when estimating the equation used to impute TTD, rather than only the complete-case subset as is true in typical applications of MI. We pooled all person waves of data for this auxiliary regression and used Stata’s intreg procedure, with standard errors clustered at the person level, to obtain parameter estimates along with their variances and covariances. Our approach ensures that the range of permissible values of both TTD variables is the same within the observed values subsample and the missing values subsample, a necessary (although not sufficient) condition for the missing data to be considered missing at random (MAR, Rubin, 1987).

The explanatory variables used in the TTD regression include dummy variables for single year of age through age 99, and a linear term in age for ages 100 and older. We also included the disability measure, measures of several chronic condition, and measures of gender, race, ethnicity, education, marital status, and change in self-reported health. Parameter estimates for these predictive equations are not of substantive interest so are not included here (but are available from D. A. Wolf on request).

We used a “proper” MI procedure (Raghunathan, 2004). Each set of imputed values depends on a different randomly selected array of regression coefficients, drawn from the (estimated) posterior multivariate normal distribution produced by the maximum-likelihood estimation algorithm, and, at the individual level, an independently drawn value from the fitted distribution of regression errors. Thus, our final model estimates reflect two sources of uncertainty about the value of imputed TTD: uncertainty about the true values of the predictive model parameters, and uncertainty about the value of unobserved individual-level factors associated with remaining lifetime conditional on the values of explanatory variables included in the predictive equation. The equation we use to impute TTD produces imputed values of both TTDB and TTDD, ensuring internal consistency among the variables included in the trajectory models. White, Royston, and Wood (2011) recommend using as many imputations as the percentage of missing data in the sample. About 20% of our sample members have an unknown TTD; accordingly, our final model estimates are based on 20 imputed values.

Model of Disability Trajectories

For each of the 20 imputed complete data files, we estimated a latent-class trajectory model using SAS PROC TRAJ. In a model with J latent classes, the probability of having an ADL limitation (Dt) at interview t, conditional on age, TTD, and membership in latent class j, is given by a logistic regression,

ln[Pj(Dt=1)/Pj(Dt=0)]=β0j+β1jAget+β2jAget2+β3jTTDtB+β4j[TTDtB] 2+β5TTDtD,

which allows for quadratic age and TTD effects on disability (the equation also includes additional time-varying covariates, not shown). The probability of being in latent trajectory class j is πj and is related to a set of fixed explanatory variables using a multinomial logistic expression. In our model, the class-membership probabilities depend on gender, race, ethnicity, and education. Note that as a cohort ages, the mix of trajectory classes can change due to differences in the death rates associated with each trajectory class.

Because the number of latent classes is unknown, the usual procedure is to estimate models with a range of theoretically appropriate numbers of potentially distinct trajectories. Based on both theoretical considerations (Lunney, Lynn, & Hogan, 2002) and prior empirical studies (e.g., Han et al., 2013; Liang et al., 2009; Taylor & Lynch, 2011; Wickrama, Mancini, Kwag, & Kwon, 2013), we estimated models with 2 through 5 trajectory classes. Although a number of statistical criteria for selecting the final number of classes have been suggested, the Bayesian Information Criterion (BIC), which depends on the value of the likelihood function, the sample size, and the number of estimated parameters, seems to be most widely used (Nagin, 2005). However, there appears to be no way to combine BIC statistics across estimates from multiply imputed data sets (White et al., 2011). In our case, the BIC statistic favored the 3-class model in all 20 sets of imputed data. Statistical inference for the final model requires combining parameter estimates and standard errors from the separate estimates that correspond to each set of imputed time-to-death variables into a single set of estimates, using procedures introduced by Rubin (1987).

Results

Sample Characteristics

Summary statistics for our analysis sample appear in Table 1. Sample individuals range in age from 72 to 109 over the eight waves of survey data used, averaging about 83 years old. Average remaining lifetime is about 5 years, conditional on it being no more than 15 years; about 13% of cases, however, have TTD more than 15 years. Chronic conditions (which can predate or be contracted within the panel period) are present at levels ranging from about 10% (for lung disease) to about 57% (for high blood pressure) of the sample. A majority of the sample is women, and a majority has also ever smoked (although fewer than 6% of person-wave observations are for current smokers). Educational attainment is modest in this sample, with nearly 45% having failed to obtain a high school degree.

Table 1.

Summary Statistics

Sample average Standard deviation
Time-varying characteristicsa
 Age 83.40 5.86
 TTDB 4.97b 4.14
 TTDD 13.2%b
 High blood pressure 56.9%
 Cancer 17.5%
 Lung disease 9.6%
 Heart disease 36.9%
 Stroke 16.0%
 Arthritis 63.8%
 Current smoker 5.6%
 Widowed 51.6%
Fixed characteristicsc
 Female 61.6%
 Black 13.2%
 Hispanic 5.4%
 Ever smoked 52.0%
 College degree 11.2%
 Less than high school 44.7%
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Notes. TTD = time to death.

aAveraged over pooled sample of 26,108 person-wave observations; TTDB = TTD conditional on TTD ≤ 15; TTDD = 1 if TTD > 15.

bAveraged over 20 multiply imputed values for each person-wave observation.

cAveraged over 6,214 individuals.

Latent-Class Trajectory Model

The full set of parameters for the best-fitting model, which identifies three latent classes, is shown in Table 2. The upper part of the table shows coefficients describing trajectory classes, and the lower part of the table shows coefficients for class-membership probabilities. We find significant, although modest, age effects in classes 1 and 2, but we find substantial and significant TTD effects in all three classes. Holding age constant, the probability of having a disability declines as TTD increases and is predicted to be quite low among those with more than 15 years of remaining lifetime. Two of the health conditions—stroke and arthritis—have significant effects on the log-odds of having an ADL limitation in all three trajectory classes, whereas lung disease and heart disease are significant in two of the three classes. Note also that the magnitudes of these coefficients differ across classes.

Table 2.

Estimates of Three-Class Trajectory Model Parameters

Class 1 Class 2 Class 3
Coefficient Standard error Coefficient Standard error Coefficient Standard error
Trajectory equations
 Intercept −1.812 0.558** −0.079 0.386 0.913 0.561
 Age −0.101 0.058 −0.084 0.043 0.124 0.068
 Age2 0.006 0.002** 0.006 0.001* −0.001 0.002
 TTDB −1.052 0.105*** −0.693 0.065*** −0.415 0.125***
 [TTDB]2 0.056 0.008*** 0.029 0.005*** 0.011 0.007
 TTDD −6.542 315.3 −4.017 0.389*** −4.274 0.622***
 High blood pressure 0.219 0.152 0.024 0.110 −0.079 0.154
 Cancer −0.163 0.165 0.022 0.131 0.006 0.251
 Lung disease 0.420 0.181* 0.444 0.159** 0.634 0.412
 Heart disease 0.083 0.147 0.309 0.113** 0.550 0.176**
 Stroke 1.625 0.155*** 2.072 0.154*** 2.821 0.710***
 Arthritis 0.595 0.191** 0.982 0.119*** 0.865 0.187***
 Current smoker −1.153 0.756 −0.260 0.214 −0.036 0.324
 Widowed −0.039 0.154 −0.188 0.113 −0.342 0.167*
Class-membership equations
 Intercept −0.997 0.205*** −2.755 0.243***
 Female 0.686 0.122*** 1.191 0.156***
 Black 0.328 0.168 0.886 0.147***
 Hispanic 0.265 0.240 0.837 0.206***
 Ever smoked −0.002 0.115 −0.285 0.131*
 College degree −0.085 0.173 −0.001 0.226
 Less than high school 0.411 0.114*** 0.822 0.129***
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Notes. TTD = time to death.

*p < .05. **p < .01. ***p < .001.

Because the trajectories depend on both age and TTD, and because at any age there is considerable heterogeneity in TTD, there are in fact numerous pathways being followed in the population at any given time. Figure 1 illustrates these patterns. To facilitate comparability with past studies focused on functional decline (Dodge et al., 2006; Lunney et al., 2003), we show the probability of having no ADL limitation (i.e., one minus the probability of having an ADL limitation) in each of the three classes. Figure 1 illustrates the trajectories followed by people from ages 70 to 85, given that they die at age 85 (i.e., although age ranges over the values 70, 71, … , 85, TTD ranges over the values 15, 14, … , 0). This choice of illustrative values reflects the fact that 85 approximates the average age at death of those that survive to age 70, according to the 2001 life table published by the National Center for Health Statistics (Arias, 2004). The predicted probabilities are all computed for a nonsmoking, nonwidowed individual with none of the chronic conditions.

Figure 1.

Figure 1.

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Probability of being without disability by age and trajectory class, for age at death = 85.

As shown in Figure 1, Class 1 consists of a group that is essentially disability free until the last few years of life, at which time a pattern of decline begins to appear. In Class 2, the period of decline extends over a 6- or 7-year period and is correspondingly more gradual. People in Class 3 already have modest chances of experiencing an ADL limitation a full 15 years prior to death and experience gradual further declines at a relatively steady rate throughout their remaining lifetime. This third group seems to coincide with the “geriatric frailty” group described in Lunney and colleagues (2003).

The coefficients for the class-membership probabilities (shown at the bottom of Table 2) can be used to calculate predicted probabilities of following each of the three trajectories. Calculating these probabilities at the individual level and averaging over the sample, we find that about 52% of the sample falls into Class 1, 36% falls into Class 2, and 12% into Class 3. There is, however, considerable heterogeneity in these class-membership probabilities. Women, for example, are more than twice as likely as men to be in the frailty group, and one third more likely than men to be in the intermediate-decline group. Thus, according to these results, women are at much greater risk than men of spending many years receiving help with ADL limitations prior to their death. Furthermore, Blacks and Hispanics, as well as those who failed to graduate from high school, are also at considerably greater risk (compared with Whites or high school graduates, respectively) of following the “frailty” trajectory and slightly greater risk of being in the intermediate-decline class.

Discussion

We have shown that in the older population there are distinctive subgroups in which changing levels of disability depend on both the aging process (marked by age) and the dying process (indicated by remaining lifetime). Our application of latent-class trajectory modeling uncovered three trajectory classes, which could be labeled “rapid decline,” “moderate decline,” and a gradually declining “frailty” trajectory. Importantly, we have shown for the first time that a clear majority of older adults are found in trajectory classes in which TTD is much more influential than age in driving the disablement process. We view TTD as a proxy for “biological age,” itself a construct that reflects the combined effects of a broad set of measures of biological aging processes; the fact that TTD appears to have a stronger association with disability than does chronological age suggests the great heterogeneity in biological aging that accompanies advancement in chronological age.

Our finding of three disablement classes that differ with respect to the rapidity of decline fits reasonably well with the existing literature. In previous work on late-life disability, researchers have found two (e.g., Stock, Mahoney, Reece, & Cesario, 2008) to five (Gill et al., 2010; Liang et al., 2009) disability trajectories. Note also that the group-level average pathways, all of which exhibit monotonically declining disability, do not rule out the possibility of recovery of function at the individual level. Indeed, Nagin and Tremblay (2005) offer an interpretation of latent classes as categorical representations of an underlying continuum of individual-level trajectories; by this interpretation, our finding of three classes also seems quite reasonable.

One limitation of our work is that we have relied on a binary indicator of disability, measured on a semiannual schedule. With shorter measurement intervals, it might be possible to see differing degrees of curvature across trajectory types, whereas with a more finely graded outcome measure, smaller differences in the level of disability at any point in the age-TTD process might be detected. The literature does not appear to offer guidance on this point, which makes it a promising area for further methodological investigation. A second issue concerns the need to assume that TTD is MAR, conditional on the variables used to predict it for purposes of imputation. Although we included an extensive set of significant predictors of TTD in the imputation equation, we cannot rule out the possibility that there remains some uncontrolled differences between those for whom TTD is and is not observed, producing biases of unknown size and direction in our trajectory model. Given the inevitability of censoring of TTD in any panel study, this remains an issue that cannot be fully resolved. Moreover, as indicated earlier, even if there were no missing values for TTD, using it as proxy for biological age would introduce acknowledged omitted-variable bias, yet we maintain that any such bias would be preferable to the biases present in an age-only model.

Despite these limitations, our results have implications for practitioners focused on improving the end-of-life experience. By bringing both age and TTD into one model, we are able to demonstrate that for most people the dying process is more influential than the aging process in determining functional trajectories. This finding in turn suggests that efforts to focus on end-of-life trajectories, rather than age, as a way to shape appropriate care (Lynn & Adamson, 2003) are well founded.

Moreover, our findings suggest that related areas of end-of-life research might benefit from incorporating both aging and dying processes into a latent-class modeling approach. Research on cognitive aging, for example, has demonstrated a strong association between age and several aspects of cognition, such as speed of processing and primary working memory (Verhaeghen & Salthouse, 1997). However, researchers have also called attention to the phenomenon of “terminal decline” or “terminal drop” (Palmore & Cleveland, 1976). Some have argued that TTD is more important than age in explaining cognitive change (Thorvaldsson, Hofer, Hassing, & Johannson, 2008), and others have attempted to identify a “change point” on the age axis, at which the influence of age on cognition ceases, or is outweighed by the influence of TTD (Sliwinski et al., 2006). Our findings on activity limitations could be extended to explore the relative importance of aging versus dying for cognitive decline. Other phenomena for which distinctive end-of-life patterns have been observed but for which the relative importance of aging versus dying have not yet been explored include oral health (Chen, Clark, Preisser, Naorungroj, & Shuman, 2013), visual acuity (Gerstorf, Ram, Lindenberger, & Smith, 2013), and weight change (Alley et al., 2010).

Our findings with respect to disability also may help focus research that has attempted to understand the forces that underlie end-of-life patterns of heath care costs. Zweifel, Felder, and Meiers (1999) suggested that once TTD is controlled, current period health expenditures do not depend on current age. Spillman and Lubitz (2000) have shown that health care costs in the last 2 years of life actually fall as age at death increases, although this decline is more than offset by rising nursing home costs. Others have documented very different cost histories for “sudden death,” “terminal disease,” “organ failure,” and “frailty” groups (Lunney et al., 2002). Our findings suggest it may be worthwhile to investigate whether both age (“aging”) and TTD (“dying”) are driving costs within particular trajectories.

Finally, this article makes a methodological contribution to end-of-life trajectory modeling. Our approach shares many of the objectives and features of a recently published extension of latent-class trajectory models aimed at addressing nonrandom attrition (Haviland, Jones, & Nagin, 2011) and used by Zimmer, Martin, Nagin, and Jones (2012) to study functional trajectories in China. But we have combined existing tools and software in a new way. We have shown how to use MI to overcome the problem of unknown TTD in panel data, permitting the estimation of a latent-class trajectory model of late-life disablement that depends on both age and distance from death. By developing a predictive model for TTD, we can overcome the sample-selection issues that have confronted past time-to-death studies that used either decedent samples or the uncensored subset of cases from a panel study.

Funding

This work was supported by the National Institute on Aging (R01 AG029260 and R01 AG34455 to D. A. Wolf). Dr. C. L. Seplaki is supported by Mentored Research Scientist Development Award (K01AG031332) from the National Institute on Aging.

Acknowledgements

The authors acknowledge the helpful comments provided by the editor and three anonymous reviewers.

The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institute on Aging or the National Institutes of Health.

D. A. Wolf, V. A. Freedman, C. L. Seplaki, and B. C. Spillman developed the conceptual framework; D. A. Wolf and J. I. Ondrich developed the estimation methodology; D. A. Wolf wrote and ran the computer programs used; D. A. Wolf wrote the first draft of the manuscript, and all authors contributed to the refinement and finalization of the manuscript.

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