1 Division of Epidemiology, School of Public Health, University of California, Berkeley, CA
2 Division of Research, Kaiser Permanente Medical Care Program, Oakland, CA
3 Department of Statistics, University of California, Berkeley, CA
4 Division of Biostatistics, School of Public Health, University of California, Berkeley, CA
Correspondence to Thaddeus J. Haight, Division of Epidemiology, School of Public Health, University of California, Berkeley, 140 Warren Hall, #7360, Berkeley, CA 94720-7360 (e-mail: tad{at}stat.berkeley.edu).
Received for publication November 12, 2004. Accepted for publication April 13, 2005.
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ABSTRACT |
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aging; body composition; causality; exercise; stochastic processes
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INTRODUCTION |
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Previous studies have elaborated on the underlying risk factors (biologic, demographic, social, environmental attributes) that influence the underlying physiology and subsequent events along the pathway to disablement (1, 6
, 7
) and the complex network of intermediary factors that contribute to the disablement process (2
). Of particular interest is the role of physical activity in the prevention of diseases that could lead to limitation or to reduction in the occurrence of functional limitation in healthy elders (8
12
). Additionally, studies based on surrogates of underlying physiologic processes in the disablement process (measures of obesity in relation to impaired insulin metabolism) attempt to shed light on the roles and the potential mitigating effects of physical activity on the progress of disablement (4
, 13
).
Recently, leisure-time physical activity (LTPA) and ratio of lean body mass to fat mass (L/F) were examined for their associated and causal effects on self-reported functioning. In a cross-sectional analysis (3), L/F was associated with faster walking speed and improved functioning. Moreover, a relative measure of lean to fat mass, rather than lean body mass alone, was the more important factor related to physical performance and physical functioning. A subsequent longitudinal analysis evaluated the combined causal effects of L/F and LTPA on physical functioning (4
); L/F had a greater effect than LTPA on the reduction of the log-odds of functional limitation, except in the presence of obesity. Those studies suggested that the beneficial effects of physical activity were most likely mediated through reduction of fat mass relative to lean mass. In addition, in the presence of obesity, it was found that improvement in muscle mass had little effect on preservation of functioning (4
).
Transitions between various levels of physical function and disability in elderly subjects have been described (1419
). Beckett et al. (14
) showed that the decline in mean level of physical function in their elderly subjects did not imply that all subjects followed a steady course of decline; some subjects recovered from disability even at the oldest ages. Anderson et al. (15
) emphasized the heterogeneity of transitions between states of disability that can occur in elderly subjects and demonstrated the importance of the incorporation of knowledge about previous patterns of disability into estimations of the probability of subsequent transitions in disability status. Other studies (16
19
) emphasize the prognostic importance of prior disability episodes on new episodes and the high rates of recovery from disability that older subjects experience. The implication of the later findings supports the argument that additional efforts could extend the recovery and independence of older subjects at high risk of recurring disability (17
, 19
).
The present investigation was undertaken to extend current understanding of transitions between states of functioning in the elderly within the context of the disablement model by the application of marginal structural models (MSMs) (20, 21
). MSMs provide less biased estimates of the effects of interest in the presence of the time-dependent confounding inherent in the disablement model, and they permit more direct population-level inferences than can be derived from more conventional statistical approaches (4
, 22
). Application of statistical methods for causal inference provides the opportunity to unravel the complex causal associations in the disablement model to an extent not easily achieved or even possible with standard statistical methods.
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MATERIALS AND METHODS |
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The 1,655 subjects were those for whom bioelectric impedance measurement, physical performance, and physical function data were available at the baseline evaluation (May 1993December 1994). Full details of the protocol have been published previously (2325
). Data from the present analysis were derived from the baseline and three subsequent evaluations (September 1995November 1996, June 1998October 1999, and February 2000March 2001). Complete data from all four evaluations and from the first three and the first two evaluations were available for 648, 884, and 1,236 subjects, respectively.
Assessment of functional limitation
Self-reported functional limitation was based on 10 questions (appendix 1) that assessed the degree of difficulty that a participant reported in various domains of physical function (upper- and lower-body domains of varying complexity) (3, 26
29
). Participants who reported having "a lot of difficulty" doing one or more of the functions or not doing at least one because they were unable or were advised by a physician not to do so were classified as having self-reported limitation.
Measurement of body composition
Estimates of fat mass and lean mass were derived from resistance and reactance measured by bioelectric impedance (BIA101Q Quantum Body Composition Analyzer System; RJL Systems, Clinton Township, Michigan) based on study-specific validation equations (3). The total variances in lean mass accounted for by these regressions were 0.85 for men and 0.80 for women. Similar regressions were performed for lean plus bone mass. Fat mass (in kilograms) was obtained by the subtraction of lean plus bone mass from body weight. L/F was defined as the ratio of lean body mass to fat mass (both in kilograms). Measurements of appendicular fat-free mass were not available.
Measurement of LTPA
At each evaluation, subjects reported their average weekly participation over the past 12 months (average number of times per week for each activity) in 22 specific physical activities that spanned a wide range of energy expenditures (24). Each activity was assigned a metabolic equivalent (MET) value (1 MET
oxygen consumption of 3.5 ml/kg minute1) from a standard compendium of MET values (30
). Two separate classifications of LTPA were created.
A continuous LTPA variable was derived based on a weighted sum of the frequency and MET values of the 22 activities for each subject: (no. of times/week x METs)i, i = 1, ..., 22 (24
). On the basis of recommended levels of physical activity (31
), we created a four-level categorical variable that corresponded to 1) no LTPA (0 METs/week); 2) insufficiently active (>022.5 METs/week, where 22.5 METs/week represents the minimum recommended level based on the MET value for brisk walking (4.5)); 3) meeting the minimum recommendation (>22.5<35 METs/week); 4) and highly active (
35 METs/week).
At baseline, subjects were asked whether their level of physical activity had changed in the preceding 510 years. Responses were recorded as a dichotomous variable (1 = report of any decline, 0 = no change or increase).
Other covariates
Weight and height were measured by using a standard protocol at each visit, and body mass index was calculated as weight in kilograms divided by height in meters squared. We categorized body mass index into three groups (<25, 25<30, 30 kg/m2) (32
, 33
). At each survey, subjects were classified as having none, one, or more than one chronic disease based on the new or past occurrence of self-reported cancer, cardiovascular disease, cerebrovascular disease, diabetes mellitus, kidney disease, liver disease, or Parkinson's disease. The presence of depression was based on a score of 16 or more on the Center for Epidemiologic Studies Depression Scale (34
) and/or current use of an antidepressant medication (direct inspection of all medications was conducted at each interview). At each survey, smoking was classified as never, current, or former (24
). Subjects rated their overall health (excellent, good, fair, or poor, which was summarized as a dichotomous variable: 0 = excellent/good, 1 = fair/poor). Living arrangements were defined for each subject as living alone, living with a spouse, or living with a nonspouse (35
). Walking speed (feet per second; 1 foot = 0.3 m) was measured by the number of feet walked in 60 seconds (24
).
Statistical analysis
Description.
Functioning in the elderly was evaluated as a stochastic process (36) that changes over time. For example, Y(t)
(0, 1), t = 1, ..., 4 can be viewed as a discrete-time process during which a person might or might not exhibit signs {Y(t) = 1, Y(t) = 0, 1 = limitation, 0 = no limitation} associated with functional limitation at observation times t. We can represent this stochastic process with a multivariate vector
Thus, we can evaluate the process as different "histories" or "courses" of disablement (transitions) defined on an interval (t = 1, ..., 4) and having a distribution,
and state-space
= 16 possible realizations (24 combinations of impaired/not impaired over four time points). We are interested in how the distribution
might vary given underlying factors that occur in the disablement process that can lead to different transitions, in particular, the marginal (unconditional) effects of L/F and LTPA.
We applied MSMs, as in previous studies (3739
), to evaluate the effects of exposure variables (e.g., L/F, LTPA) in the presence of time-dependent confounders (e.g., walking speed, health status) that are affected by previous levels of the exposure variables. Standard approaches, under these circumstances, would yield biased estimates of the effects (40
). The covariates described above are assumed to represent all of the measurable confounders of LTPA and L/F. In the MSM framework, we control for the effects of these confounders relative to L/F and LTPA through time-specific exposure ("treatment") models. In addition, we can control for selection bias from various sources of loss to follow-up by the use of censoring models at each time point. From these respective models, we obtain subject-specific, time-specific weights (20
), which can be applied in an MSM to obtain unbiased estimates of the marginal effects of L/F and LTPA.
Application of the MSM.
MSMs are based on the concept of counterfactual variables. An exposure-specific counterfactual (potential outcome) variable is a random variable that represents a subject's set of outcomes had the subject, contrary to fact, had an exposure history other than the one actually observed (20). Formal presentation of the theory, assumptions, and applications of MSMs toward epidemiologic research has been reported extensively (4
, 20
22
, 38
41
). A formal data analysis that assessed the marginal effects of L/F and LTPA on functional limitation is available (4
). We have listed the restrictions/assumptions required to identify causal effects with MSMs in appendix 2.
We assume a generalized MSM for the marginal distribution of :
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is defined as the multivariate vector that represents different transitions, or histories of functioning, if, contrary to fact, subjects had followed joint exposure history
We assume that
has a joint probability distribution:
To formulate the MSM model, we factorize
as the product
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Regressions were implemented with standard logistic regression software (PROC LOGISTIC, SAS version 8.2; SAS Institute, Inc., Cary, North Carolina) with weights.
Computation of counterfactual transition distributions.
To compute the distribution of transitions in functioning, ), for a counterfactual exposure history,
we first estimate the marginal distributions of functional status
for each time t based on the time-specific parameter estimates ß1t, ß2t; second, we compute the product of these marginal distributions of functional status from t = 1, ..., 4:
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Confidence intervals (95 percent) for each transition probability were calculated with the standard error based on a bootstrap distribution of 1,000 estimates for each of the different transitions. If the distributions were not normal, the 2.5 and 97.5 percentiles of the distribution were selected (42).
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RESULTS |
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If, contrary to fact, subjects reported at all surveys that they exercised at high aerobic levels (35 METs/week), the likely onset of functional limitation without recovery would be expected to decrease (tables 2 and 3, column 5). We observed a reduction of 53 percent (7.4
3.5 percent) in women's chances of developing a functional limitation at the last survey compared with their actual observed history (table 2, row 2, column 5 vs. column 3). Furthermore, high, sustained levels of aerobic exercise play a role in the delay of the onset of functional limitation (table 2, rows 3 and 4). For example, the risk for women who experience functional decline at the second and third surveys is reduced approximately 38 percent and 45 percent, respectively (4.7
2.9 percent, second survey; 4.2
2.3 percent, third survey). Although a reduction in late-stage limitation occurs for the men who participate in increased levels of exercise, functional decline does not appear to be reduced at earlier stages of the process (table 3, rows 3 and 4). High levels of physical activity improved the chances of full recovery in subjects with limitation at baseline (table 4, rows 1 and 2, column 5 vs. column 3). For women, the percentage increase in recovery for higher levels of physical activity over the levels of physical activity in the observed data was 43.8 percent (6.9 percent vs. 4.8 percent); for men, the increase was onefold (7.1 percent vs. 3.4 percent). The estimates used to calculate these percentage increases were imprecisely estimated (column 5); therefore, the increases are not statistically significant. Nonetheless, there is an indication that recovery from functional limitation would increase with higher levels of physical activity.
A lower risk of functional decline and a higher chance of recovery from functional limitation are not attributable solely to consistent participation in high levels of LTPA. If women were initially sedentary at baseline but increased their levels of physical activity over time (table 2, column 7), with the likely associated benefits of higher L/F, their chances of functional decline would not differ significantly from those if they had maintained high levels of LTPA (table 2, column 5) throughout the study. For men, a similar comparison of these two exposure histories suggests a further reduced risk of functional limitation when L/F levels increase with increasing exercise over time (table 3, column 7 vs. column 5). In the counterfactual world where the population experienced a faster rate of decline in their physical activity (column 8) and, consequently, a lower L/F, the risk of functional decline would be as large as that if they did not exercise at all.
We also examined the distribution of functioning over time if subjects were not physically active but if, contrary to fact, their L/F was one unit greater than their observed L/F (column 6). The effects appear to vary somewhat for men and women. For women (table 2), we observed an increase in the proportion of subjects without functional limitation (row 1, column 3 vs. column 6, 50.5 63.9 percent) and subjects who experienced a delayed functional limitation (row 2, 7.4
10.1 percent), although these were both estimated imprecisely. In addition, we observed significant reductions in the proportions of women who experienced limitation a majority of time during the study period (rows 35: 4.2
2.1 percent; 4.7
1.2 percent; 8.7
3.0 percent). The benefits of higher L/F in the absence of physical activity with respect to function occur for men but to a lesser extent than in women (table 3). The proportion of men living without functional limitation during the study increased to 73 percent (table 3, row 1, column 6) because fewer men experienced onset of functional limitation (table 3, rows 24, column 6).
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DISCUSSION |
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The results suggest that L/F and LTPA affect functioning differently. L/F, which varied minimally with time, appeared to establish levels (strata) of functioning at an early stage of the disablement process that continued over time. For example, we observed that if the population's L/F was one unit greater, the result was a smaller proportion of subjects who experienced limitation at all four surveys and a larger proportion of those who were limitation free over the same period. By contrast, high, sustained levels of LTPA did not increase the proportion of subjects without limitation nor reduce the proportion with a limitation at all four surveys. In fact, in the latter case, the proportion of subjects who were functionally limited at all four surveys increased. However, we observed that high levels of LTPA reduced the risk of onset of functional limitation in subjects without past limitation and increased the probability of recovery of functioning for those who were previously limited. On the basis of these findings, we conclude that LTPA reduces the risk of future functional limitation conditional on the level of functioning conferred by L/F.
The data also suggest that the beneficial effects of LTPA with respect to functioning occur indirectly through an increase in L/F (i.e., a reduction in the amount of fat relative to lean mass). We did not investigate the potential role of past physical activity history on baseline levels of L/F. There was also a suggestion of a direct effect of LTPA possibly on some component of functioning (i.e., improved mobility/dexterity). For example, among women, higher levels of physical activity, even without an increase in L/F, reduced the onset of functional limitation (table 2, column 4 vs. column 7). A comparison of the effects in men suggested that the advantages conferred by LTPA occur indirectly through L/F. The results were consistent with a previous analysis that indicated that LTPA exerts its beneficial effects through reductions in fat mass relative to lean body mass (4).
One potential limitation of the study could have arisen from failure to satisfy the assumptions required to obtain unbiased MSM estimates. For example, we may not have controlled for all measurable confounders of LTPA and L/F and/or misspecified the treatment and censoring models that were used. We approximated these assumptions by thoroughly examining the potential confounders in our data and developing treatment/censoring models to control for the effects of confounding and selection bias. We assume that we met all other assumptions required to implement the MSM.
We chose to examine the causal effect of L/F with respect to functioning. However, to investigate causal effects, the counterfactual outcomes under different levels of the exposure variable must be well defined. Different processes could have given rise to the same L/F (e.g., exercise, diet), and these different processes could have different implications for the outcome that corresponds to the given L/F. For our purposes, we defined L/F as a summary endpoint of these different processes, which in itself has ramifications for functioning regardless of the processes that lead to L/F. Evaluation of the differential effects of L/F on functioning with respect to these different processes was possible but was not a goal of this analysis.
In summary, our data provide population-level estimates of the extent to which functional limitation can vary over time in the elderly and the potential causal roles of physical activity and body composition in this variation. These causal estimates go beyond what can be inferred from studies that have used more conventional methods of analysis. In addition, our observations point to the need to account for this temporal variation in functioning when evaluating any interventions designed to improve the functional status in the elderly. Failure to consider this inherent variability could lead to overestimation of the impacts of interventions and their likely public health significance.
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APPENDIX 1 |
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APPENDIX 2 |
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APPENDIX 3 |
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APPENDIX 4 |
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We estimate the marginal probability of functional limitation = 1 at t = 1
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We estimate the marginal probability of functional limitation = 1 at t = 2 within strata of past functional history as
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For t = 3, the marginal probability of functional limitation = 1 (marginal probability of functional limitation = 0 not shown) within strata of functional history is given by
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Equations to estimate the probability of functional limitation = 1 for t = 4 build on the pattern for t = 3, except eight equations are estimated for each of the eight strata of past functional history.
We can now construct the joint probability of functional limitation over time by using the cumulative product of computed probabilities from above,
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ACKNOWLEDGMENTS |
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The authors gratefully acknowledge Patti LeBlanc and her dedicated staff who collected the data, Elizabeth MacDonald for providing data management, Romain Neugebauer for his analytic assistance, Huaxia Qin for her programming support, and Yue Wang and Jingrong Yang for their analytic assistance and review of the manuscript.
Conflict of interest: none declared.
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NOTES |
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References |
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