Covariate Shift Corrected Conditional Randomization Test

Conditional independence tests are crucial across various disciplines in determining the independence of an outcome variable Y from a treatment variable X, conditioning on a set of confounders Z . The Conditional Randomization Test (CRT) offers a powerful framework for such testing by assuming known distributions of X \mid Z; it controls the Type-I error exactly, allowing for the use of flexible, black-box test statistics. In practice, testing for conditional independence often involves using data from a source population to draw conclusions about a target population. This can be challenging due to covariate shift---differences in the distribution of X, Z, and surrogate variables, which can affect the conditional distribution of Y \mid X, Z ---rendering traditional CRT approaches invalid. To address this issue, we propose a novel Covariate Shift Corrected Pearson Chi-squared Conditional Randomization (csPCR) test.