Selection of Sufficient Adjustment Sets for Causal Inference : A Comparison of Algorithms and Evaluation Metrics for Structure Learning

Abstract: Causal graphs are essential tools to find sufficient adjustment sets in observational studies. Subject matter experts can sometimes specify these graphs, but often the dependence structure of the variables, and thus the graph, is unknown even to them. In such cases, structure learning algorithms can be used to learn the graph. Early structure learning algorithms were implemented for either exclusively discrete or continuous variables. Recently, methods have been developed for structure learning on mixed data, including both continuous and discrete variables. In this thesis, three structure learning algorithms for mixed data are evaluated through a simulation study. The evaluation is based on graph recovery metrics and the ability to find a sufficient adjustment set for the average treatment effect (ATE). Depending on the intended purpose of the learned graph, the different evaluation metrics should be given varying attention. It is also concluded that the pcalg+micd algorithm learns graphs such that it is possible to find a sufficient adjustment set for the ATE in more than 99% of the cases. Moreover, the learned graphs from pcalg+micd are the most accurate compared to the true graph using the largest sample size.