Covariate Selection in Propensity Scores Using Outcome Proxies

This study examined the practical problem of covariate selection in propensity scores (PSs) given a predetermined set of covariates. Because the bias reduction capacity of a confounding covariate is proportional to the concurrent relationships it has with the outcome and treatment, particular focus is set on how we might approximate covariate-outcome relationships while retaining the PS as a design tool (i.e., without using the observed outcomes). To make this approach tractable, I examined the extent to which alternative measures of the outcome might inform covariate-outcome empirical relationships and corresponding covariate selection. Specifically, two such measures were examined: proximal pretreatment measures of the outcome and cross validation. Further, because the implications of covariate choice reach beyond the properties of the treatment effect estimator, I reason that the primary objective of PS covariate selection is to effectively and efficiently reduce bias while forming a scientific basis for inference through, for example, covariate balance. By using outcome proxies or cross validation, substantive knowledge is augmented with empirical evidence of covariates' bias reduction/amplification capacities to better inform covariate selection, improve estimation, and form an evidentiary basis for inference.