Many real datasets contain values missing not at random (MNAR). In this scenario, investigators often perform list-wise deletion, or delete samples with any missing values, before applying causal discovery algorithms. List-wise deletion is a sound and general strategy when paired with algorithms such as FCI and RFCI, but the deletion procedure also eliminates otherwise good samples that contain only a few missing values. In this report, we show that we can more efficiently utilize the observed values with test-wise deletion while still maintaining algorithmic soundness. Here, test-wise deletion refers to the process of list-wise deleting samples only among the variables required for each conditional independence (CI) test used in constraint-based searches. Test-wise deletion therefore often saves more samples than list-wise deletion for each CI test, especially when we have a sparse underlying graph. Our theoretical results show that test-wise deletion is sound under the justifiable assumption that none of the missingness mechanisms causally affect each other in the underlying causal graph. We also find that FCI and RFCI with test-wise deletion outperform their list-wise deletion and imputation counterparts on average when MNAR holds in both synthetic and real data. Keywords Causal inference · Missing values · Missing not at random · MNAR Many real observational datasets contain missing values, but modern constraint-based causal discovery (CCD) algorithms require complete data. These facts force many investigators to either perform list-wise deletion or imputation on their datasets. The first strategy can unfortunately result in the loss of many good samples just because of a few missing values. On the other hand, the second strategy can corrupt the joint distribution when the corresponding assumptions do not hold. Both of these approaches therefore can (and often do) degrade the performance of CCD algorithms. We thus seek a practical method which allows CCD algorithms to efficiently utilize the measured values while placing few assumptions on the missingness mechanism(s).
Fast causal inference (FCI) by test-wise deletion REF is exploited to handle missing data.
Fast causal inference with non-random missingness by test-wise deletion
International Journal of Data Science and Analytics
International Journal of Data Science and Analytics
Medicine Mathematics Computer Science