FDR control for linear log-contrast models with high-dimensional compositional covariates

Linear log-contrast models have been widely used to describe the relationship between the response of interest and the compositional covariates, in which one central task is to identify the significant compositional covariates while controlling the false discovery rate (FDR) at a nominal level. To achieve this goal, a new FDR control method is proposed for linear log-contrast models with high-dimensional compositional covariates. An appealing feature of the proposed method is that it completely bypasses the traditional p-values and utilizes only the symmetry property of the test statistic for the unimportant compositional covariates to give an upper bound of the FDR. Under some regularity conditions, the FDR can be asymptotically controlled at the nominal level for the proposed method in theory, and the theoretical power is also proven to approach one as the sample size tends to infinity. The finite-sample performance of the proposed method is evaluated through extensive simulation studies, and applications to microbiome compositional datasets are also provided.