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Abstract:
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Classical multiple-comparison procedures tend to be underpowered in large-scale hypothesis testing problems. Procedures that control false discovery rate are more powerful, yet treat all hypothesis tests as exchangeable, ignoring any auxiliary covariates that may influence the distribution of the test statistics. The current work proposes a novel Bayesian semi-parametric two-group mixture model and develops a Markov chain Monte Carlo fitting routine for a covariate-modulated local false discovery rate (cmfdr). The probability of non-null status depends on the covariates via a logistic function and the non-null distribution is approximated as a linear combination of B-spline densities, where the weight of each B-spline density also depends on the covariates. We illustrate our proposed methods on a schizophrenia genome wide association study. In particular, we demonstrate that cmfdr dramatically improves power. We also show that the new approach fits the data closely, performing better than our previously proposed parametric gamma model for the non-null density.
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