Propensity score methods, first introduced by Rosenbaum and Rubin, are increasingly being used in medical research to handle confounding. Observational studies potentially suffer from confounding. When effect modification is present, default settings of imputation methods may yield biased results even if data are missing at random. The optimal way to handle missing values in covariates of propensity score models depends on the missing data structure and the presence of effect modification. Here, combining multiple imputation and the missing indicator method reduced the bias as the missing indicator variable can be a proxy for unobserved confounding. Multiple imputation may fail when data are missing not at random. In the presence of effect modification, more complex imputation models than default options of commonly used statistical software were required. Multiple imputation worked well if the data were missing (completely) at random, and if the imputation model was correctly specified.

In some situations, complete case analysis was also able to partially correct for unmeasured confounding. When no effect modification existed, complete case analysis yielded valid causal treatment effects even when data were missing not at random.

Additionally, we demonstrated how missingness graphs help clarifying the missing structure. Simulated scenarios varied regarding missing mechanism, presence of effect modification or unmeasured confounding. Concurrently, we aimed to provide guidance in choosing the optimal strategy. These methods include: complete case analysis, missing indicator method, multiple imputation and combining multiple imputation and missing indicator method. In this simulation study, we compared four strategies of handling missing covariate values in propensity matching and propensity weighting. Several strategies for handling missing values exist, but guidance in choosing the best method is needed. A challenge in propensity methods is missing values in confounders. Propensity score analysis is a popular method to control for confounding in observational studies.

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