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Causal discovery algorithms estimate causal graphs from observational data.This can provide a valuable complement to analyses focussing on the causalrelation between individual treatment-outcome pairs. Constraint-based causaldiscovery algorithms rely on conditional independence testing when building thegraph. Until recently, these algorithms have been unable to handle missingvalues. In this paper, we investigate two alternative solutions: Test-wisedeletion and multiple imputation. We establish necessary and sufficientconditions for the recoverability of causal structures under test-wisedeletion, and argue that multiple imputation is more challenging in the contextof causal discovery than for estimation. We conduct an extensive comparison bysimulating from benchmark causal graphs: As one might expect, we find thattest-wise deletion and multiple imputation both clearly outperform list-wisedeletion and single imputation. Crucially, our results further suggest thatmultiple imputation is especially useful in settings with a small number ofeither Gaussian or discrete variables, but when the dataset contains a mix ofboth neither method is uniformly best. The methods we compare include randomforest imputation and a hybrid procedure combining test-wise deletion andmultiple imputation. An application to data from the IDEFICS cohort study ondiet- and lifestyle-related diseases in European children serves as anillustrating example.

Multiple imputation and test-wise deletion for causal discovery with incomplete cohort data