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# Learning Treatment Effects from Observational and Experimental Data

*Proceedings of The 26th International Conference on Artificial Intelligence and Statistics*, PMLR 206:7126-7146, 2023.

#### Abstract

Decision making often depends on causal effect estimation. For example, clinical decisions are often based on estimates of the probability of post-treatment outcomes. Experimental data from randomized controlled trials allow for unbiased estimation of these probabilities. However, such data are usually limited in the number of samples and the set of measured covariates. Observational data, such as electronic medical records, contain many more samples and a richer set of measured covariates, which can be used to estimate more personalized treatment effects; however, these estimates may be biased due to latent confounding. In this work, we propose a Bayesian method for combining observational and experimental data for unbiased conditional treatment effect estimation. Our method addresses the following question: Given observational data $D_o$ measuring a set of covariates $\mathbf V$, and experimental data $D_e$ measuring a possibly smaller set of covariates $\mathbf{V_b}\subseteq \mathbf{V}$, which set of covariates $\mathbf{Z}$ leads to the optimal, unbiased prediction of the post-intervention outcome $P(Y |do(X), \mathbf{Z})$, and when can we use observational data for this estimation? In simulated data, we show that our method improves the prediction of post-intervention outcomes.