Considerations for Using Multiple Imputation in Propensity Score-Weighted Analysis - A Tutorial with Applied Example

Propensity score-weighting for confounder control and multiple imputation to counter missing data are both widely used methods in epidemiological research. Combination of the two is not trivial and requires a number of decisions to produce valid inference. In this tutorial, we outline the assumptions underlying each of the methods, present our considerations in combining the two, discuss the methodological and practical implications of our choices and briefly point to alternatives. Throughout we apply the theory to a research project about post-traumatic stress disorder in Syrian refugees.

We detail how we used logistic regression-based propensity scores to produce "standardized mortality ratio"-weights and Substantive Model Compatible-Full Conditional Specification for multiple imputation of missing data to get the estimate of association. Finally, a percentile confidence interval was produced by bootstrapping.

A simple propensity score model with weight truncation at 1st and 99th percentile obtained acceptable balance on all covariates and was chosen as our model. Due to computational issues in the multiple imputation, two levels of one of the substantive model covariates and two levels of one of the auxiliary covariates were collapsed. This slightly modified propensity score model was the substantive model in the SMC-FCS multiple imputation, and regression models were set up for all partially observed covariates. We set the number of imputations to 10 and number of iterations to 40. We produced 999 bootstrap estimates to compute the 95-percentile confidence interval.

Combining propensity score-weighting and multiple imputation is not a trivial task. We present considerations necessary to do so, realizing it is demanding in terms of both workload and computational time; however, we do not consider the former a drawback: it makes some of the underlying assumptions explicit and the latter may be a nuisance that will diminish with faster computers and better implementations.