Propensity score analysis with partially observed covariates: Howshould multiple imputation be used?

摘要

Inverse probability of treatment weighting is a popular propensity score-based approach to estimate marginal treatment effects in observational studies at risk of confounding bias. A major issue when estimating the propensity score is the presence of partially observed covariates. Multiple imputation is a natural approach to handle missing data on covariates: covariates are imputed and a propensity score analysis is performed in each imputed dataset to estimate the treatment effect. The treatment effect estimates from each imputed dataset are then combined to obtain an overall estimate. We call this method MIte. However, an alternative approach has been proposed, in which the propensity scores are combined across the imputed datasets (MIps). Therefore, there are remaining uncertainties about how to implement multiple imputation for propensity score analysis: (a) should we apply Rubin’s rules to the inverse probability of treatment weighting treatment effect estimates or to the propensity score estimates themselves? (b) does the outcome have to be included in the imputation model? (c) how should we estimate the variance of the inverse probability of treatment weighting estimator after multiple imputation? We studied the consistency and balancing properties of the MIte and MIps estimators andperformed a simulation study to empirically assess their performance for theanalysis of a binary outcome. We also compared the performance of these methodsto complete case analysis and the missingness pattern approach, which uses adifferent propensity score model for each pattern of missingness, and a thirdmultiple imputation approach in which the propensity score parameters arecombined rather than the propensity scores themselves (MIpar). Under a missingat random mechanism, complete case and missingness pattern analyses were biasedin most cases for estimating the marginal treatment effect, whereas multipleimputation approaches were approximately unbiased as long as the outcome wasincluded in the imputation model. Only MIte was unbiased in all the studiedscenarios and Rubin’s rules provided good variance estimates for MIte. Thepropensity score estimated in the MIte approach showed good balancingproperties. In conclusion, when using multiple imputation in the inverseprobability of treatment weighting context, MIte with the outcome included inthe imputation model is the preferred approach.