Rejoinder: ‘Gene hunting with hidden Markov model knockoffs’

原文摘要

We are very grateful to the editors for the opportunity to expand and deepen the reflection on the possible advantages of a knockoff approach to genome-wide association studies. The discussants bring up a number of important points, related to either the knockoffs methodology in general or its specific application to genetic studies. In this rejoinder we offer some clarifications, mention relevant recent developments, and highlight a few remaining open problems. The model-X framework of knockoffs (Candès et al., 2018) addresses a general multiple testing problem in which the |$j$|th null hypothesis states that the response |$Y$| is independent of the explanatory variable |$X_j$| conditional on all other predictors |$X_{-j}$|⁠. In the very special case where the joint distribution of |$X$| and |$Y$| is multivariate Gaussian, this is equivalent to testing for the presence of conditional or partial correlations (Rosenblatt et al., 2019). In general, the nonnull variables in the model-X framework are those belonging to the Markov blanket of |$X$| on |$Y$| (Candès et al., 2018). There is little sense in arguing that, generally speaking, conditional or marginal hypotheses are the right ones to test: the choice between these two approaches will clearly depend on the problem at hand. For example, if |$Y$| describes the cancer status of a tissue sample and each |$X_j$| the expression level of gene |$j$|⁠, one might be interested in testing the hypotheses that |$Y\perp\!\!\!\perp X_j$|⁠. The rejections of these null hypotheses would describe all genes whose expression level changes with cancer status. Whenever we think of relating a response |$Y$| with a linear, or generalized linear, model in terms of |$X$|⁠, and test the hypotheses that the regression coefficients vanish, we are testing hypotheses that are of a conditional flavour. These hypotheses correspond exactly to the conditional ones in the case where the response follows a generalized linear model; see Candès et al. (2018).

摘要来源：OpenAlex 索引摘要（稿件版本未注明）