Individualized conditional independence testing under model-X with heterogeneous samples and interactions
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Model-X knockoffs and the conditional randomization test are methods that search for conditional associations in large data sets, controlling the type-I errors if the joint distribution of the predictors is known. However, they cannot test for interactions nor find whether an association is only significant within a latent subset of a heterogeneous population. We address this limitation by developing an extension of the knockoff filter that tests conditional associations within automatically detected subsets of individuals, provably controlling the false discovery rate for the selected hypotheses. Then, under the additional assumption of a partially linear model with a binary predictor, we extend the conditional randomization test as to make inferences about quantiles of individual effects that are robust to sample heterogeneity and interactions. The performances of these methods are investigated through simulations and with the analysis of data from a randomized blood donation experiment with several treatments.
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