Bayesian local false discovery rate for sparse count data with application to the discovery of hotspots in protein domains

Abstract

In cancer research at the molecular level, it is critical to understand which somatic mutations play an important role in the initiation or progression of cancer. Recently, studying cancer somatic variants at the protein domain level is an important area for uncovering functionally related somatic mutations. The main issue is to find the protein domain hotspots which have significantly high frequency of mutations. Multiple testing procedures are commonly used to identify hotspots; however, when data is not large enough, existing methods produce unreliable results with failure in controlling a given type I error rate. We propose multiple testing procedures, based on Bayesian local false discovery rate, for sparse count data and apply it in the identification of clusters of somatic mutations across entire gene families using protein domain models. In multiple testing for count data, it is not clear what kind of the null distribution should be admitted. In our proposed algorithms, we implement the zero assumption in the context of Bayesian methods to identify the null distribution for count data rather than using any theoretical null distribution. Furthermore, we also address different types of modeling of alternative distributions. The proposed fully Bayesian models are efficient when the number of count data is small (50≤N<200) while the local false discovery rate procedures, based on the empirical Bayes, is desirable for a large number of data (N>800). We provide numerical studies to show that the proposed fully Bayesian methods can control a given level of false discovery rate for small number of positions while existing approaches based on nonparametric empirical Bayes fail in controlling a false discovery rate. In addition, we present real data examples of protein domain data to select hotspots in protein domain data.