Causal Discovery in the Presence of Missing Data

Abstract: Missing data are ubiquitous in many domains including healthcare. When these data entries are not missing completely at random, the (conditional) independence relations in the observed data may be different from those in the complete data generated by the underlying causal process. Consequently, simply applying existing causal discovery methods to the observed data may lead to wrong conclusions. In this paper, we aim at developing a causal discovery method to recover the underlying causal structure from observed data that follow different missingness mechanisms, including missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). With missingness mechanisms represented by missingness graphs, we analyse conditions under which additional correction is needed to derive conditional independence/dependence relations in the complete data. Based on our analysis, we propose the Missing Value PC (MVPC) algorithm for both continuous and binary variables, which extends the PC algorithm to incorporate additional corrections. Our proposed MVPC is shown in theory to give asymptotically correct results even on data that are MAR or MNAR. Experimental results on synthetic data show that the proposed algorithm is able to find correct causal relations even in the general case of MNAR. Moreover, we create a neuropathic pain diagnostic simulator for evaluating causal discovery methods. Evaluated on such simulated neuropathic pain diagnosis records and the other two real world applications, MVPC outperforms the other benchmark methods.