  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.
