Joint testing and false discovery rate control in high-dimensional multivariate regression

Heterogeneous associations between interleukin-6 receptor variants and phenotypes across ancestries and implications for therapy

The Phenome-Wide Association Study (PheWAS) is increasingly used to broadly screen for potential treatment effects, e.g., IL6R variant as a proxy for IL6R antagonists. This approach offers an opportunity to address the limited power in clinical trials to study differential treatment effects across patient subgroups. However, limited methods exist to efficiently test for differences across subgroups in the thousands of multiple comparisons generated as part of a PheWAS. In this study, we developed an approach that maximizes the power to test for heterogeneous genotype-phenotype associations and applied this approach to an IL6R PheWAS among individuals of African (AFR) and European (EUR) ancestries. We identified 29 traits with differences in IL6R variant-phenotype associations, including a lower risk of type 2 diabetes in AFR (OR 0.96) vs EUR (OR 1.0, p-value for heterogeneity = 8.5 × 10-3), and higher white blood cell count (p-value for heterogeneity = 8.5 × 10-131). These data suggest a more salutary effect of IL6R blockade for T2D among individuals of AFR vs EUR ancestry and provide data to inform ongoing clinical trials targeting IL6 for an expanding number of conditions. Moreover, the method to test for heterogeneity of associations can be applied broadly to other large-scale genotype-phenotype screens in diverse populations.

Global and Simultaneous Hypothesis Testing for High-Dimensional Logistic Regression Models

High-dimensional logistic regression is widely used in analyzing data with binary outcomes. In this paper, global testing and large-scale multiple testing for the regression coefficients are considered in both single- and two-regression settings. A test statistic for testing the global null hypothesis is constructed using a generalized low-dimensional projection for bias correction and its asymptotic null distribution is derived. A lower bound for the global testing is established, which shows that the proposed test is asymptotically minimax optimal over some sparsity range. For testing the individual coefficients simultaneously, multiple testing procedures are proposed and shown to control the false discovery rate (FDR) and falsely discovered variables (FDV) asymptotically. Simulation studies are carried out to examine the numerical performance of the proposed tests and their superiority over existing methods. The testing procedures are also illustrated by analyzing a data set of a metabolomics study that investigates the association between fecal metabolites and pediatric Crohn's disease and the effects of treatment on such associations.