Stratifying on propensity score in observational studies of treatment is a common technique used to control for bias in treatment assignment; however, there have been few studies of the relative efficiency of the various ways of forming those strata. The standard method is to use the quintiles of propensity score to create subclasses, but this choice is not based on any measure of performance either observed or theoretical. In this paper, we investigate the optimal subclassification of propensity scores for estimating treatment effect with respect to mean squared error of the estimate. We consider the optimal formation of subclasses within formation schemes that require either equal frequency of observations within each subclass or equal variance of the effect estimate within each subclass. Under these restrictions, choosing the partition is reduced to choosing the number of subclasses. We also consider an overalll optimal partition that produces an effect estimate with minimum MSE among all partitions considered. To create this stratification, the investigator must choose both the number of subclasses and their placement. Finally, we present a stratified propensity score analysis of data concerning insurance plan choice and its relation to satisfaction with asthma care.


Statistical Methodology | Statistical Theory