Variable Selection for Estimating Optimal Sequential Treatment Decisions Using Bayesian Networks

Abstract: We propose a variable selection method for estimating decision rules of optimal sequential treatment assignments when the decision-relevant variables are unknown. Standard variable selection methods are insufficient in this setting since they choose covariates that are predictive of the outcome, not those that interact with the treatment on the outcome and are therefore relevant for decision-making. Furthermore, estimation of optimal treatment assignments requires predicting outcomes from alternative treatment decisions than those observed in the data. Since only causal models can reliably predict outcomes under interventions on the data, the idea is to choose the covariates that are causally related to the outcome and treatment. This is achieved by first using a causal discovery algorithm to estimate a graph of the causal structure of the data and then apply a criteria on the discovered graph to choose the relevant covariates. If the true causal structure is discovered, the method finds the minimal sufficient sets of covariates required for unbiased estimation of the optimal decision rules. The method is evaluated with simulations using existing estimators, algorithms and extensions thereof. The results suggest that the method successfully identifies the correct variables when the decisions are independent across stages and the treatment binary, or if it is continuous, when the sample size is also large. The method is demonstrated with an empirical study on optimal educational choice using real data on returns to schooling. The empirical findings are in agreement with recent empirical evidence from labor economics.