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Abstract:
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Inferring a causal relationship is an important task in both social science and health research. In an observational study, unlike a randomized experiment, treatment assignment is likely to be confounded with many factors. Under the potential outcome framework, propensity score based matching, stratification, and weighting approaches are commonly used to estimate the average treatment effect. The propensity score aids the inference substantially as a dimension reduction tool under the ignorable treatment assignment assumption. We propose a nonparametric Bayesian approach to estimating the potential outcome response surfaces, which is both less model dependent and natural to incorporate heterogeneous treatment effects from the posterior distribution. Also, we show the popular propensity score matching estimator is a special case for our approach as a limit of prior distributions. A sensitivity analysis strategy is proposed to assess the impact due to potential unmeasured confounders. We apply our method to investigate the impact of college attendance on women fertility, which is known to suffer from the potential heterogeneous effects.
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