Accurate error control in high‐dimensional association testing using conditional false discovery rates

Abstract

High‐dimensional hypothesis testing is ubiquitous in the biomedical sciences, and informative covariates may be employed to improve power. The conditional false discovery rate (cFDR) is a widely used approach suited to the setting where the covariate is a set of p‐values for the equivalent hypotheses for a second trait. Although related to the Benjamini–Hochberg procedure, it does not permit any easy control of type‐1 error rate and existing methods are over‐conservative. We propose a new method for type‐1 error rate control based on identifying mappings from the unit square to the unit interval defined by the estimated cFDR and splitting observations so that each map is independent of the observations it is used to test. We also propose an adjustment to the existing cFDR estimator which further improves power. We show by simulation that the new method more than doubles potential improvement in power over unconditional analyses compared to existing methods. We demonstrate our method on transcriptome‐wide association studies and show that the method can be used in an iterative way, enabling the use of multiple covariates successively. Our methods substantially improve the power and applicability of cFDR analysis.

Leveraging auxiliary data from arbitrary distributions to boost GWAS discovery with Flexible cFDR

“…Given the assumptions in property (2), we can also approximate , noting that this is an equality if p is correctly calibrated. The estimated cFDR is therefore: and existing methods use empirical cumulative distribution functions (CDFs) to estimate and Pr ( P ≤ p, Q ≤ q ) 38,41 .…”

“…Yet unlike the BH procedure, this rejection rule does not control frequentist FDR at α 47 . Liley and Wallace 41 described a method to control the frequentist FDR, but it is currently only suited to instances where the auxiliary data may be modelled using a mixture of centered normal distributions (for example by transforming auxiliary p -values to Z scores; .…”

“…These sparse data regions are likely to be found more often in unbounded auxiliary data from arbitrary distributions (for example near the extreme observations) than auxiliary data that are p -values from related traits, and thus bounded by [0, 1]. Moreover, the method used to control the frequentist FDR 41 requires normally distributed auxiliary data. We describe a new, more versatile cFDR framework for data pairs consisting of p -values for the principal trait ( p ) and continuous covariates from more general distributions ( q ).…”

“…Hard thresholding is used to approximate the distribution of by Q | P > 1 / 2 in the earlier cFDR methods 38,41 . Instead, in Flexible cFDR we empirically evaluate the influence of specific p -value quantities on the null hypothesis by utilising the local FDR framework, which estimates 45 .…”

“…We were interested to see whether a more general form of cFDR could address the same covariate-informed multiple testing problems as the range of methods listed above. Here, we describe “Flexible cFDR”, a new cFDR framework 41 that enjoys all of the benefits of the conventional approach but now supports continuous auxiliary data from arbitrary distributions, thus enabling broader applicability. Specifically, our computationally efficient approach extends the usage of cFDR beyond only GWAS to the accelerating field of functional genomics and can be applied iteratively to incorporate additional layers of data.…”