Utilizing stratified generalized propensity score matching to approximate blocked randomized designs with multiple treatment levels.

Conducting causal inference in settings with more than one treatment level can be challenging. Classical methods, such as propensity score matching (PSM), are restricted to only a binary treatment. To extend propensity score methods beyond a binary treatment, generalized propensity score methods have been proposed, with generalized propensity score matching (GPSM) standing as the multi-level treatment analog to PSM. One drawback of GPSM is it is only capable of emulating a completely randomized trial (CRT) design and not the more efficient blocked randomized trial design. Motivated by the desire to emulate the more efficient design, we expand on GPSM estimating literature and develop a new estimator incorporating relevant stratifying variables into the GPSM framework. We examine the variance estimation methods available for GPSM and demonstrate how to extend the estimator to one where stratifying variables are included. While it would be straightforward to include relevant stratifying variables as covariates in the propensity score estimation, our method provides for researchers to conduct retrospective analyses more consistently with the prospective experiment they would have designed if permitted. Namely, our method permits researchers to approximate a stratified randomized trial as opposed to the CRT otherwise obtainable by GPSM. We apply our proposed method to an analysis of how the number of children in a household affects systolic blood pressure in adults. We conduct a simulation study assessing how the relationship between response, treatment, and strata affect the performance of our method and compare the results to non-stratified GPSM.