Comparison of the Inverse Probability of Treatment Weighted (IPTW) Estimator With a Naïve Estimator in the Analysis of Longitudinal Data With Time-Dependent Confounding: A Simulation Study
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.
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ABSTRACT: Cardiovascular disease and obstructive lung disease are leading global causes of death. Despite this, the impact of secondhand smoke (SHS) exposure on pulmonary function and cardiovascular disease remains uncertain. Our goal was to elucidate the association between baseline SHS exposure and the risk of lung function decline and cardiovascular mortality over a period of nearly a decade.
We used data from a longitudinal cohort study of 1,057 older adults to study the association between baseline SHS exposure and the risk of lung function decline and cardiovascular mortality. The effect of SHS exposure on cardiovascular mortality may be mediated by its influence on FEV1 and biological processes captured by measurement of FEV1. Alternatively, the effect of SHS may be mediated by baseline cardiovascular disease status, which reflects the combined effects of traditional cardiovascular risk factors. To correctly estimate the effect of SHS and FEV1 on cardiovascular mortality, we used marginal structural models (MSMs) that took into account the mediating effects of FEV1 and baseline cardiovascular disease in the causal pathway.
In longitudinal multivariate analyses, lifetime cumulative home and work SHS exposure were associated with a greater decline of FEV1 (-15 mL/s; 95% CI, -29 to -1.3 mL/s and -41 mL/s; 95% CI, -55 to -28 mL/s per 10-year cumulative exposure, respectively). Lifetime home SHS exposure was associated with a greater risk of cardiovascular mortality in both conventional multivariate analysis (HR, 1.10 per 10 years of exposure; 95% CI, 0.99 to 1.24) and the MSM for FEV1 (HR, 1.06; 95% CI, 0.95 to 1.19) and baseline cardiovascular disease (HR for subjects with no baseline cardiovascular disease, 1.39; 95% CI, 1.17 to 1.66).
Lifetime SHS exposure appears to result in a greater decline in lung function and risk of cardiovascular mortality, taking into account confounders and the mediating effect of FEV1 and baseline cardiovascular disease.
Available from: Shuying Shen
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ABSTRACT: We used agent-based simulation to examine the problem of time-varying confounding when estimating the effect of an adverse event on hospital length of stay. Conventional analytic methods were compared with inverse probability weighting (IPW).
A cohort of hospitalized patients, at risk for experiencing an adverse event, was simulated. Synthetic individuals were assigned a severity of illness score on admission. The score varied during hospitalization according to an autoregressive equation. A linear relationship between severity of illness and the logarithm of the discharge rate was assumed. Depending on the model conditions, adverse event status was influenced by prior severity of illness and, in turn, influenced subsequent severity. Conditions were varied to represent different levels of confounding and categories of effect. The simulation output was analyzed by Cox proportional hazards regression and by a weighted regression analysis, using the method of IPW. The magnitude of bias was calculated for each method of analysis.
Estimates of the population causal hazard ratio based on IPW were consistently unbiased across a range of conditions. In contrast, hazard ratio estimates generated by Cox proportional hazards regression demonstrated substantial bias when severity of illness was both a time-varying confounder and intermediate variable. The direction and magnitude of bias depended on how severity of illness was incorporated into the Cox regression model.
In this simulation study, IPW exhibited less bias than conventional regression methods when used to analyze the impact of adverse event status on hospital length of stay.
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