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a Saint Louis University School of Public Health, St. Louis, MO
b Saint Louis University School of Public Health, St. Louis, MO
c Saint Louis University School of Medicine, St. Louis, MO
Correspondence: Fredric D. Wolinsky, PhD, Saint Louis University School of Public Health, 3663 Lindell Boulevard, Suite 240B, St. Louis, MO 63108-3342. E-mail: wolinsky{at}slu.edu.
Decision Editor: Vernon L. Greene, PhD
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and two Nagi 1976 items, asked of 12,998 older adults who participated in up to seven waves of data collection as part of the Established Populations for the Epidemiologic Study of the Elderly, are used to illustrate this approach, emphasizing both its conceptual and pragmatic advantages. The results provide greater clarity in terms of those who become functionally limited, take on more functional limitations, or recover as well as those who are likely to be lost to follow-up and in terms of the outcomes associated with those individuals over time.
Key Words: Trajectories • Transitions • Functional limitations • Health status • Older adults
Functional limitations involve situation-free activities (Verbrugge and Jette 1994), or the capacity to perform fundamental physical actions such as reaching out or up, walking a half mile, or climbing a flight of stairs. In contrast, disabilities involve situation-dependent activities (Verbrugge and Jette 1994), such as the capacity to perform basic tasks associated with daily living like bathing and toileting, or to perform instrumental tasks such as money management and shopping. Taken together, functional limitations and disabilities are among the most frequently studied issues in gerontology and geriatrics. This can be readily demonstrated in two ways. One involves reviewing the work that has appeared in the journals published by The Gerontological Society of America during calendar years 1995–1998. Of the 1,120 Medline entries for The Gerontologist and the Journals of Gerontology, 145 or one eighth could be identified simply from the single subject heading (i.e., MeSH term) for activities of daily living (ADLs). The other way to demonstrate the interest in functional limitation and disability in gerontology and geriatrics is to review the number of instruments used to measure these constructs. Cohen and McHorney 1998 recently identified more than 75 such instruments that have been developed since 1945. Because their list was restricted to generic (i.e., not disease specific) functional assessment tools, this is actually a conservative estimate.
A frequent theme in studies of functional limitation and disability are transitions over time. Indeed, Stuck and colleagues 1999 recently identified 78 longitudinal studies conducted between 1985 and 1997 that focused on risk factors for such transitions. Generally speaking, research on transitions in functional limitation and disability may be placed into three categories. The first category of studies looks at transitions between one state and another state on just one item. For example, this could involve the onset of a particular disability item, such as bathing. Given the dichotomous (limited vs not limited) nature of most ADL items, this approach typically involves using a binomial logistic regression model in which several risk factors are used to predict going from an independent to a dependent state in terms of bathing. The second category of studies looks at changes in categorical dependence levels from one state based on the basis of several items. An example of this approach would be the transition from one combinatorial state of ADL and/or instrumental ADL (IADL) limitations (e.g., having only one IADL limitation and no ADL limitations) to another combinatorial state (e.g., having any two IADL limitations and/or any one ADL limitation). Because there are frequently more than two possible combinatorial states, this approach often involves multinomial logistic regression or grade of membership models. The third category of transition studies looks at change score analyses of aggregated indices. This approach frequently involves general linear modeling of changes in the simple summed number of either ADLs or IADLs.
Although all three of these categories of research on transitions in functional limitation and disability have made important contributions to our understanding of the onset of and recovery from functional limitations, at least three important issues remain unresolved. First, state transitions involving only one item (e.g., shopping) examine that transition in isolation from state transitions on other items (e.g., money management and transportation). This is not entirely realistic inasmuch as the ability to shop is (or should be) at least partly conditioned on the ability to maintain personal finances and get to stores. Second, changes in both categorical dependence models and change score analyses of aggregated indices are somewhat removed from the original item transitions. That is, with these approaches it is not known which of the particular individual states (e.g., ADLs or IADLs) have been exited or entered. Indeed, compositional change in the individual states (e.g., going from bathing and dressing limitations to eating and toileting limitations) that results in the same combinatorial classification (i.e., two ADL limitations) is conceptually and statistically treated as stability. Third, all three categories of transition modeling approaches focus mostly on differences between only two points in time, such as baseline and a specifically targeted follow-up. As a result, there is no characterization of the trajectory pattern. This is both conceptually limiting and empirically unfortunate, given the increasing number of multiwave data sets available for analysis.
Even recent and sophisticated analyses suffer from these limitations. This can be quickly illustrated with just two examples of some of the best work that has been done in recent years. First, consider the work of Rudberg, Parzen, Leonard, and Cassel 1996. Writing in this journal, they reported on using wave-to-wave probabilities to examine ADL transitions across the 1984 baseline and 1986, 1988, and 1990 re-interviews of the respondents in the Longitudinal Study of Aging (LSOA). Although Rudberg and colleagues focused on seven states (i.e., 0, 1, 2, 3, 4, or 5 limited activities, or death), real transitions within three of those states (i.e., the 2, 3, or 4 limited activities states) would mistakenly be viewed as stability if the transition resulted in the same numerical count. Second, consider the work of Mendes de Leon and colleagues 1999. Writing in another of The Gerontological Society of America's journals, they reported using Markov models to estimate one-year disability transitions in ADLs across eight waves of data from the Yale Health and Aging Project (one of the four sites of the Established Populations for the Epidemiologic Study of the Elderly, or EPESE). In those analyses, a two-state transition was modeled reflecting entrance into one or more of the six ADL disabilities, or return from one or more of the six ADL disabilities to no disabilities. As such, that work only reflects the two most extreme transitions (i.e., the initial onset of the first disability, or complete recovery).
It would seem, then, that most of the work done to date on changes in functional limitation and disability over time has focused on single transitions devoid of context rather than on the pattern of transitions over time that constitute trajectories. The purpose of this Forum article, therefore, is to suggest reorienting both conceptual and empirical work toward trajectories. The essential element underlying our approach involves a different way of characterizing trajectory patterns. To illustrate this approach, consider the data used by Rudberg and colleagues 1996. They examined five dichotomous ADL items: bathing, dressing, eating, getting in and out of a bed or chair, and toileting. These ADLs were observed over the four waves of the LSOA. Thus, at baseline there were 32 possible combinations (i.e., 25) in their data, assuming that there were no missing data at the item level. Three additional combinations were possible at each follow-up, reflecting respondents who had died, who were re-interviewed but did not answer all five of the ADL items, or who were otherwise lost. To appreciate the myriad possible trajectory patterns, visualize four 6 x 6 grids on which each of the 32 possible baseline or 35 possible follow-up combinations can be located (i.e., one grid per wave of data). Arrange the cells on these grids such that at baseline the most densely populated cells (limitations on none or only one or two ADLs) are at the outer edges, and the least densely populated cells (such as death and lost to follow-up, which are by definition empty at baseline) are at the center. Layer the grids in a three-dimensional space in which the baseline grid is on top and the close-out grid is on the bottom, much like a three-dimensional tic-tac-toe or chess game.
This approach has some intuitive appeal. Consider the simplistic case in which there was very little limitation at baseline, followed by incrementing disabilities over the three follow-up periods, resulting in institutionalization or death. Under those circumstances, a graphical portrayal of the cell densities would resemble a tornado pattern, with the intensity (i.e., rate of progression) of the funneling dependent on how well the observed longitudinal run corresponds to the natural pattern of decline. However, regardless of whether such a tornado pattern (symmetrical or otherwise) emerges, it becomes evident that there is nearly an infinite number of possible trajectories (i.e., approximately 353 or about 40,000). Of these, it will be the most densely traveled paths that represent the patterns of interest that should ultimately be modeled using multivariable methods to identify salient risk factors.
Rather than use the ADL items in the LSOA as an empirical example of this perspective, we have chosen five of the lower body functional limitation questions taken from the Rosow and Breslau 1966 and Nagi 1976 measures that were included in the EPESE. There were three reasons for the selection of these measures and data. First, as Lawrence and Jette 1996 have eloquently argued, functional limitations (as opposed to disabilities, or situation-free versus situation-dependent activities) are what drive the disablement process from both the theoretical and practical standpoints. Thus, improvements in the public health of older adults will be most closely tied to understanding functional limitation trajectories (Branch 1996). Second, despite the availability of lower body functional items in the LSOA, no attempt was made to re-interview nearly one third of the LSOA respondents in 1986 because of budgetary constraints (Kovar, Fitti, and Chyba 1992). As a result, the utility of the LSOA for assessing trajectory patterns is substantially diminished (Lawrence and Jette 1996; Rudberg et al. 1996). Third, the November 1998 public use version of the EPESE available from the Inter-University Consortium for Political and Social Research includes the first seven waves of data collected from all four sites as well as the associated mortality data (Taylor, Wallace, Ostfeld, and Blazer 1998). As such, the EPESE is the largest and longest-run multiwave data set currently available for public use. Use of these data expands the number of grids in our demonstration from four to seven, and it concomitantly increases the number of unique trajectories that are possible to approximately 1 billion (i.e., about 356).
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). Data were elicited from persons 65 years old and older who resided in four catchment areas: East Boston, Massachusetts; New Haven, Connecticut; Iowa and Washington Counties, Iowa; and north central North Carolina. Sampling approaches varied by site and involved the following: (a) a total community census in East Boston; (b) Agency on Aging enumeration lists in Iowa; (c) residential stratification within private and public age-restricted housing and general community areas in New Haven; and (d) area sampling in North Carolina. Because of the different and complex sampling designs used at each site, traditional estimation procedures that assume random selection might underestimate standard errors and result in inflated significance levels in the absence of adjustments for the design effects. For the descriptive and illustrative purposes of this Forum article, however, such design adjustments are not necessary.
At baseline, the response rates for those eligible (given the above sampling approaches) were 
in North Carolina, yielding a combined sample of 14,456 older adults. With some exceptions (206 telephone interviews in Iowa), the baseline interviews were conducted face-to-face in 1982 for East Boston, Iowa, and New Haven, and in 1986 for North Carolina. Subsequently, at each site there were two consecutive cycles of three annual follow-ups involving two rounds of telephone interviews and one face-to-face interview. Therefore, a total of seven waves of data are available for use. Because the focus of this Forum article is on annual changes in physical limitations, no adjustment is made for the potential period confound associated with the later start of the North Carolina data series.
The EPESE included five lower body functional limitations questions: three items from the Rosow and Breslau 1966 scale, and two items from the Nagi 1976 scale. The Rosow and Breslau items were as follows: (1) "Are you able to do heavy work around the house like (shoveling snow), washing windows, walls, or floors without help?" (2) "Are you able to walk up and down stairs to the second floor without help?" and (3) "Are you able to walk half a mile without help?" Response options were "yes" or "no." "No" responses were coded as limitations. The Nagi items were as follows: (4) "How much difficulty, if any, do you have pulling or pushing large objects like a living room chair?" and (5) "What about stooping, crouching, or kneeling?" Response options were "no difficulty at all," "a little or some difficulty," "a lot of difficulty," or "just unable to do it." The latter two responses were coded as limitations.
One of the three Rosow and Breslau 1966 items warrants further discussion. This is the heavy housework question, which is a noticeably less discreet indicator of lower body limitations. Indeed, the ability to do heavy housework is the least situationally free of the five items and, as such, it taps disability in addition to functional limitation. The complexity of the heavy housework item notwithstanding, it remains widely used as an indicator of lower body functional limitation (Stuck et al. 1999) because the primary exertional force is derived from the legs, regardless of which particular housework activity is involved. Therefore, we retain it in the current analysis. Note that these measurement shortcomings are minimized by our focus on patterns of serial combinatorial transitions rather than traditional marginal change score models.
Because the Nagi items were not asked of 250 Iowa proxy-respondents or 206 Iowa telephone respondents at baseline, it was necessary to reduce the eligible analytic sample to 14,000. Frequency distributions for the five lower body physical limitation questions are shown in Table 1 by wave of data collection. Missing data at baseline reflect item nonresponse. Subsequent missing data reflect both item nonresponse and loss to follow-up other than mortality. Mortality data were obtained by carefully monitoring hospital admissions, obituaries, state death indexes, and follow-up interviews with collateral persons previously identified by the deceased respondents. Reported deaths were verified by matches with death certificates in 99.2% of all cases.
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To simplify reference to the 32 possible combinations among the five items at baseline and the 35 possible combinations at each of the six follow-ups, a notational system was selected. It labels each combination of the five items at each wave by using a five-digit sequence. Ones or zeroes reflect the presence or absence, respectively, of the limitation in question. At all waves, the limitations are sequenced from left to right in ascending order on the basis of their prevalence at baseline (i.e., easiest to most difficult to perform tasks; see Table 1 ). Therefore, the first number (i.e., the leftmost 0 or 1) refers to a limitation in walking up one flight of stairs, the second to a limitation in pushing or pulling large objects, the third to a limitation in walking one-half mile, the fourth to a limitation in stooping, and the last to a limitation in doing heavy housework. For example, the sequence (or state) 00101 denotes a person whose only limitations are walking one-half mile and doing heavy housework. The analysis is limited, for simplicity, to the 12,998 EPESE persons with complete data for all five items at baseline. Persons lost to follow-up are assigned a numeric code of 77777. A numeric code of 88888 is used for persons who were re-interviewed but had missing data on one or more of the five items. Decedents are noted with the numeric code of 99999.
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of the EPESE analytic sample at baseline and the last follow-up, respectively. At baseline, 77.3% (8,557/11,074) of these older adults were in states completely congruent with a hierarchy or Guttman scale (Dunn-Rankin 1983; Lazaridis, Rudberg, Furner, and Cassel 1994; Rosow and Breslau 1966; Torgerson 1962) based on the prevalence data sequence (i.e., 00000, 00001, 00011, 00111, 01111, and 11111). Excluding those lost to follow-up, having missing data, or deceased, the percentage was similar at the final follow-up (i.e., 70.7% or 5,472/7,736).
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, Manton, Corder, and Stallard 1997; Mendes de Leon et al. 1999; Wolinsky, Stump, Callahan, and Johnson 1996) due to the fact that mortality is a fully absorbing state in transition models (Crimmins, Hayward, and Saito 1994). The second point worth noting in Table 2 concerning functional limitation pathways involves the 30 other states possible at baseline (i.e., excluding states 77777 and 88888). Being limited only in heavy housework (i.e., state 00001) or only in stooping (i.e., state 00010) are by far the two most densely populated of these 30 states. Their percentage shares are reduced by about one half from wave 1 to wave 7. The absolute numbers of persons in the 28 remaining states, however, did not change appreciably over the observation period. This includes those with all five functional limitations (i.e., state 11111), who represented 7.4% of the analytic sample at baseline and 7.8% at final follow-up. Thus, from a sequential cross-sectional standpoint, it would appear plausible to conclude that considerable distributional stability existed.
A third important point worth observing in the data shown in Table 2 involves those who were completely lost to follow-up at each particular wave of data collection (i.e., state 77777) and those who were re-interviewed at each particular wave but had missing data on one or more of the functional limitations questions (i.e., state 88888). The lost to follow-up state increases in a three-step fashion, going from about 3% at waves 2 and 3, to about 5% at waves 4, 5, and 6, to about 8% at the final follow-up. This is consistent with previous reports that those completely lost to follow-up at any particular wave of data collection are at increased risk of staying lost at subsequent waves and, if simply excluded from longitudinal analyses, may result in substantial attrition bias (Dubin and Rivers 1990; Little and Rubin 1990; Little and Schenker 1995). At the same time, however, it is clear that being lost to follow-up is not a fully absorbing state among older adults (Mihelic and Crimmins 1997). In contrast, the percentage of those who were re-interviewed at a particular wave but had missing data on one or more of the functional status questions (i.e., state 88888) shows a noticeable dip at waves 5 and 6 but is otherwise relatively stable at about 5%. Although consistent with an interpretation that those who have missing data at the functional limitations item level at any particular wave of data may be at increased risk of doing so repeatedly over time, these data are only definitive about the existence of considerable cross-sequential distributional stability.
What the data in Table 2 do not provide is much of a picture of either wave-to-wave transitions or overall trajectories. One way to do this would be to draw a flow diagram showing the migration paths (depicted by arrows) from each state at each wave to each state at the next wave, with the number of EPESE sample persons making each transition listed on each arrow. Even if such a flow diagram were restricted to only the 13 most common states, however, this would be incredibly complex. There are 130 (i.e., 10 states to 13 states) possible arrows from wave 1 to wave 2, and 157 (i.e., 12 states to 13 states, plus the single state-to-state transition for those already deceased) possible arrows for each of the five remaining contiguous wave-to-wave transitions, resulting in 915 possible arrows overall. A less cumbersome approach is to present the frequency distributions for the 13 most common states at waves 1 to 7 for those persons residing in the most densely populated origin or destination states. Table 3 , Table 4 , Table 5 , Table 6 , and Table 7 do this for two origin states and three destination states. The origin states involve those who had no functional limitations at baseline (00000) and those who had all five functional limitations at baseline (11111). These two origin states account for 57.0% (7,407/12,998) of the EPESE analytical sample. The three destination states involve those who had no functional limitations at the last follow-up (00000), those who had all five functional limitations at the last follow-up (11111), and those who were deceased at the last follow-up (99999). These three destination states account for 60.3% (7,837/12,998) of the EPESE analytical sample.
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The frequency distributions across all seven waves for the 964 EPESE sample persons who had all five functional limitations (i.e., state 11111) at baseline are shown in Table 4 . These data reveal a very different pattern. Although some recovery did occur, including the restoration of all functional abilities, this was rather rare. Furthermore, although 20% of those with all five functional limitations at baseline were not found in one of the 13 most common states at wave 2, this is merely an artifact. Recall that four of the states with four functional limitations were so uncommon that they were not included in the table. Ninety-five of the persons with all five functional limitations at baseline migrated to one of these four less common states with four functional limitations at wave 2. However, by the final follow-up, 90.5% of the 964 older adults who had all five functional limitations at baseline were still limited (24.0%), lost to follow-up (6.7%), had missing items (4.7%), or were dead (55.1%, or about a 9% annual mortality rate). Thus, there is considerable evidence that those with the most functional limitations at baseline are most likely to retain those limitations or to die.
Table 5 contains the frequency distributions across all seven waves for the 3,257 EPESE sample persons who had no functional limitations at the last follow-up. Of these individuals, 84.7% were also without any functional limitations at baseline. Moreover, another 8.6% had only one functional limitation at baseline (i.e., state 00001, 00010, or 00100). Thus, the evidence suggests that nearly all of those who were in robust health at the end of the observation period were rather hardy when it started. It is also important to note that about 3-4% of those persons who had no functional limitations at the last follow-up were either lost to follow-up (i.e., state 77777) or had missing data on one or more items (i.e., state 88888) at one of the intervening waves, illustrating the potential attrition bias that can occur by excluding those with missing data.
The frequency distributions across all seven waves for the 1,011 EPESE sample persons who had all five functional limitations at the last follow-up are shown in Table 6 . A very different pattern is revealed here. Less than one fourth of these individuals had all five functional limitations at baseline. Moreover, only about one half had all five functional limitations at wave 6, suggesting considerable wave-to-wave transition into this state. This is further reflected by the fact that 7.3% of those having all five functional limitations at the final follow-up had either none or only one such limitation the year before (i.e., state 00001, 00010, or 00100 at wave 6). It is also important to note that only 7.5% of those with all five limitations at the last follow-up were either lost to follow-up (i.e., state 77777) the year before or had some missing data (i.e., state 88888) at that point. This represents only 5.1% (34/669) and 15.2% (41/270), respectively, of all such EPESE sample persons, suggesting that few individuals lost to follow-up at a preceding wave were found to have all five functional limitations at the next wave.
In addition, close inspection of Table 6 reveals something not found in any of the preceding tables. Fully 22% (224/1,011) of those who had all five functional limitations at the final follow-up were not to be found in any of the 13 most common states at the preceding follow-up (i.e., wave 6). Neither were similar percentages to be found in any of the 13 most common states involving any previous wave-to-wave transition. When coupled with the above observation that less than one half of the persons who had all five functional limitations at the final follow-up were in that state (i.e., 11111) at wave 6, this indicates an unusually large migration into this state from the less common states that only occurs at wave 7.
Table 7 contains the frequency distributions across all seven waves for the 3,579 EPESE sample persons who were deceased at the last follow-up. In addition to demonstrating that this is a fully absorbing state, these data show that the majority of those who died at a given wave either had all five functional limitations in the previous wave or were lost to follow-up. That is, of the 658 (3,579-2,921) new deaths between waves 6 and 7, 37.2% (245) had five functional limitations and 18.5% (122) were lost to follow-up. At the same time, 10.3% (68) of the new deaths between waves 6 and 7 involved persons with no functional limitations at all, and another 4.3% (28) involved persons with only one functional limitation. Moreover, nearly one half of those who were dead by wave 7 had either no limitation or just one functional limitation at baseline. This reflects the fact that although there is a dose–response relationship between functional limitations and mortality, even those in robust health face sizeable risks.
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Pragmatically, rethinking functional limitation pathways to focus on trajectories reveals a clearer picture of what is taking place. Specifically, it provides greater clarity in terms of who becomes functionally limited, who takes on more functional limitations, and who recovers as well as who is likely to be lost to follow-up, and what happens to those individuals over time. For example, previous studies have shown that both the onset of functional limitations and complete recovery occur among older adults, although the former happens with greater frequency than the latter (Manton et al. 1993, Manton et al. 1997; Mendes de Leon et al. 1999; Wolinsky et al. 1996). The trajectories shown here, however, further indicate that patterns of decline and recovery (i.e., transitions) are not the same for all origin states. This is clearly reflected in a comparison of Table 4 and Table 5 . Table 4 indicates that there was very little recovery of any magnitude among those with all five functional limitations at baseline, whereas Table 5 indicates that 1 out of 6 older adults who had no functional limitations at the final follow-up had at least one functional limitation at baseline. These distinctions are completely masked in more traditional transition models.
Moreover, as one would expect, it is also the case that the greatest amount of wave-to-wave fluctuation occurs among those with two, three, or four functional limitations at baseline (data not shown). Such oscillation patterns could reflect either of two distinct possibilities, one positive and one negative. On the positive side, these fluctuation patterns may accurately reflect the ebb and flow of functional limitations over time for older adults. On the negative side, it is possible that these oscillations reflect more on the unreliability of the five functional limitation items. Either explanation should prompt a reconsideration of more traditional transition models because those approaches (especially transition models involving only two points in time) infer more meaning to these observed changes than is probably warranted.
Focusing on trajectories also has implications for the treatment of those lost to follow-up. These data suggest that although those lost to follow-up at one wave may be more likely to be lost to follow-up at subsequent waves, this is clearly not always the case (Mihelic and Crimmins 1997). As a result, the exclusion of those lost to follow-up at any wave of data collection is likely to bias the understanding of functional status pathways (Dubin and Rivers 1990; Little and Rubin 1990; Little and Schenker 1995). The same can be said for those who were successfully re-interviewed at any given wave of data collection but failed to answer one or more of the functional limitation questions.
Rethinking functional limitation pathways, however, has a price. That price involves having no straightforward methods for deriving simple statistical summaries of the approximately 1 billion pathways possible in these data and predicting who will travel down them. The development and application of such statistical techniques is sorely needed. In their absence, only part of the trajectory story can be told. For example, the simple analysis presented here, which focused on the 13 most common states, results in ignoring up to one fourth of the persons residing in the selected origin or destination states in the out-waves.
Until more appropriate statistical techniques are available, it will be necessary to take intermediate approaches that restrict attention to comparing and contrasting the risk factors associated with particularly intriguing trajectories emanating from a common origin state. One example of such a targeted and relatively primitive contrast would involve focusing on the 6,443 older adults in these data who had no functional limitations at baseline (i.e., state 00000). By using a variety of background, personal, social, economic, and disease history measures, researchers could estimate multinomial logistic regression models in which those with no functional limitations at the final follow-up were contrasted with those in the next six most common final destination states (i.e., states 99999, 77777, 88888, 00001, 11111, and 00010). Although this would not take into consideration the intervening serial transitions involving waves 2 through 6, it would provide the opportunity to identify differential risk factors associated with the most common ultimate destination states for those older adults originating in the most common states. At least, that would be a beginning.
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Received for publication June 28, 1999. Accepted for publication December 7, 1999.
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