Analysis of treatment response data without the joint distribution of potential outcomes

In this paper we show how it is possible to develop a Bayesian framework for analyzing structural models for treatment response data without the joint distribution of the potential outcomes. That this is possible has not been noticed in the literature. We also discuss the computation of the model marginal likelihood and present recipes for finding relevant treatment effects, averaged over both parameters and covariates. As compared to an approach in which the counterfactuals are part of the prior-posterior analysis (as in the work to date), the approach we suggest is simpler in terms of the required prior inputs, computational burden and extensibility to more complex settings.