Estimating propensity scores with missing covariate data using general location mixture models.

In many observational studies, analysts estimate causal effects using propensity scores, e.g. by matching, sub-classifying, or inverse probability weighting based on the scores. Estimation of propensity scores is complicated when some values of the covariates are missing. Analysts can use multiple imputation to create completed data sets from which propensity scores can be estimated. We propose a general location mixture model for imputations that assumes that the control units are a latent mixture of (i) units whose covariates are drawn from the same distributions as the treated units' covariates and (ii) units whose covariates are drawn from different distributions. This formulation reduces the influence of control units outside the treated units' region of the covariate space on the estimation of parameters in the imputation model, which can result in more plausible imputations. In turn, this can result in more reliable estimates of propensity scores and better balance in the true covariate distributions when matching or sub-classifying. We illustrate the benefits of the latent class modeling approach with simulations and with an observational study of the effect of breast feeding on children's cognitive abilities.