A simulation study was conducted to compare estimates from a naïve estimator, using standard conditional regression, and an IPTW (Inverse Probability of Treatment Weighted) estimator, to true causal parameters for a given MSM (Marginal Structural Model). The study was extracted from a larger epidemiological study (Longitudinal Study of Effects of Physical Activity and Body Composition on Functional Limitation in the Elderly, by Tager et. al [accepted, Epidemiology, September 2003]), which examined the causal effects of physical activity and body composition on functional limitation. The simulation emulated the larger study in terms of the exposure and outcome variables of interest-- physical activity (LTPA), body composition (LNFAT), and physical limitation (PF), but used one time-dependent confounder (HEALTH) to illustrate the effects of estimating causal effects in the presence of time-dependent confounding. In addition to being a time-dependent confounder (i.e. predictor of exposure and outcome over time), HEALTH was also affected by past treatment. Under these conditions, naïve estimates are known to give biased estimates of the causal effects of interest (Robins, 2000). The true causal parameters for LNFAT (-0.61) and LTPA (-0.70) were obtained by assessing the log-odds of functional limitation for a 1-unit increase in LNFAT and participation in vigorous exercise in an ideal experiment in which the counterfactual outcomes were known for every possible combination of LNFAT and LTPA for each subject. Under conditions of moderate confounding, the IPTW estimates for LNFAT and LTPA were -0.62 and -0.94, respectively, versus the naïve estimates of -0.78 and -0.80. For increased levels of confounding of the LNFAT and LTPA variables, the IPTW estimates were -0.60 and -1.28, respectively, and the naïve estimates were -0.85 and -0.87. The bias of the IPTW estimates, particularly under increased levels of confounding, was explored and linked to violation of particular assumptions regarding the IPTW estimation of causal parameters for the MSM.
