Missing Confounding Data in Marginal Structural Models: a Comparison of Inverse Probability Weighting and Multiple Imputation

Standard statistical analyses of observational data often exclude valuable information from individuals with incomplete measurements. This may lead to biased estimates of the treatment effect and loss of precision. The issue of missing data for inverse probability of treatment weighted estimation of marginal structural models (MSMs) has often been addressed, though little has been done to compare different missing data techniques in this relatively new method of analysis. We propose a method for systematically dealing with missingness in MSMs by treating missingness as a cause for censoring and weighting subjects by the inverse probability of missingness. We developed a series of simulations to systematically compare the effect of using case deletion, our inverse weighting approach, and multiple imputation in a MSM when there is missing information on an important confounder. We found that multiple imputation was slightly less biased and considerably less variable than the inverse probability approach. Thus, the lower variability achieved through multiple imputation makes it desirable in most practical cases where the missing data are strongly predicted by the available data. Inverse probability weighting is, however, a superior alternative to naive approaches such as complete-case analysis.