On the power of conditional independence testing under model-X

Understand

For testing conditional independence (CI) of a response Y and a predictor X given covariates Z, the recently introduced model-X (MX) framework has been the subject of active methodological research, especially in the context of MX knockoffs and their successful application to genome-wide association studies.

• In this paper, we study the power of MX CI tests, yielding quantitative insights into the role of machine learning and providing evidence in favor of using likelihood-based statistics in practice.
• Focusing on the conditional randomization test (CRT), we find that its conditional mode of inference allows us to reformulate it as testing a point null hypothesis involving the conditional distribution of X.
• The Neyman-Pearson lemma then implies that a likelihood-based statistic yields the most powerful CRT against a point alternative.