We analyze data collected as part of a prospective cohort study of elderly people living in and around Sonoma, CA, in order to estimate, for each round of interviews, the causal effect of leisure-time physical activity (LTPA) over the past year on the risk of mortality in the following two years. For each round of interviews, this effect is estimated separately for subpopulations defined based on past exercise habits, age, and whether subjects have had cardiac events in the past. This decomposition of the original longitudinal data structure into a series of point-treatment data structures corresponds to an application of history-adjusted marginal structural models as introduced by van der Laan et al. (2005). We propose five different estimators of the parameter of interest, based on various combinations of the usual G-computation, inverse-weighting, and double robust approaches for the two layers of missingness corresponding to the treatment mechanism and right-censoring by drop-out. The models for all nuisance parameters required by these different estimators are selected data-adaptively. For most subpopulations, our analyses suggest that high leisure-time physical activity reduces the subsequent two-year mortality risk by about 50%. Among populations of elderly people aged 75 years or older, these effect estimates are generally significant at the 0.05 level. Notably, our analyses also identify one subpopulation that is estimated to experience an increase in mortality risk when exercising at a higher level, namely subjects aged 75 years or older with previous cardiac events and no history of habitual exercise (RR: 2.33, 95% CI: 0.76-4.35).



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