Missing data in the exposure of interest and marginal structural models: a simulation study based on the Framingham Heart Study

Abstract

Missing data are common in longitudinal studies and can occur in the exposure interest. There has been little work assessing the impact of missing data in marginal structural models (MSMs), which are used to estimate the effect of an exposure history on an outcome when time-dependent confounding is present. We design a series of simulations based on the Framingham Heart Study data set to investigate the impact of missing data in the primary exposure of interest in a complex, realistic setting. We use a standard application of MSMs to estimate the causal odds ratio of a specific activity history on outcome. We report and discuss the results of four missing data methods, under seven possible missing data structures, including scenarios in which an unmeasured variable predicts missing information. In all missing data structures, we found that a complete case analysis, where all subjects with missing exposure data are removed from the analysis, provided the least bias. An analysis that censored individuals at the first occasion of missing exposure and includes a censorship model as well as a propensity model when creating the inverse probability weights also performed well. The presence of an unmeasured predictor of missing data only slightly increased bias, except in the situation such that the exposure had a large impact on missing data and the unmeasured variable had a large impact on missing data and outcome. A discussion of the results is provided using causal diagrams, showing the usefulness of drawing such diagrams before conducting an analysis.