Learning Adjustment Sets from Observational and Limited Experimental Data

Abstract: Estimating causal effects from observational data is not always possible due to confounding. Identifying a set of appropriate covariates (adjustment set) and adjusting for their influence can remove confounding bias; however, such a set is typically not identifiable from observational data alone. Experimental data do not have confounding bias, but are typically limited in sample size and can therefore yield imprecise estimates. Furthermore, experimental data often include a limited set of covariates, and therefore provide limited insight into the causal structure of the underlying system. In this work we introduce a method that combines large observational and limited experimental data to identify adjustment sets and improve the estimation of causal effects. The method identifies an adjustment set (if possible) by calculating the marginal likelihood for the experimental data given observationally-derived prior probabilities of potential adjustmen sets. In this way, the method can make inferences that are not possible using only the conditional dependencies and independencies in all the observational and experimental data. We show that the method successfully identifies adjustment sets and improves causal effect estimation in simulated data, and it can sometimes make additional inferences when compared to state-of-the-art methods for combining experimental and observational data.