In the last five years, adaptive multiple testing with covariates has gained much traction. It has been recognized that the side information provided by auxiliary covariates which are independent of the primary test statistics under the null can be used to devise more powerful testing procedures for controlling the false discovery rate (FDR). For example, in the differential expression analysis of RNA-sequencing data, the average read counts across samples provide useful side information alongside individual p-values, as the genetic markers with higher read counts should be more promising to display differential expression.
However, for two-sided hypotheses, the usual data processing step that transforms the primary test statistics, generally known as z-values, into p-values not only leads to a loss of information carried by the main statistics but can also undermine the ability of the covariates to assist with the FDR inference. Motivated by this and building upon recent theoretical advances, we develop ZAP, a z-value based covariate-adaptive methodology. It operates on the intact structural information encoded jointly by the z-values and covariates, to mimic an oracle testing procedure that is unattainable in practice; the power gain of ZAP can be substantial in comparison with p-value based methods, as demonstrated by our simulations and real data analyses.