Empirical Null Estimation using Discrete Mixture Distributions and its Application to Protein Domain Data

In recent mutation studies, analyses based on protein domain positions are gaining popularity over gene-centric approaches since the latter have limitations in considering the functional context that the position of the mutation provides. This presents a large-scale simultaneous inference problem, with hundreds of hypothesis tests to consider at the same time. This paper aims to select significant mutation counts while controlling a given level of Type I error via False Discovery Rate (FDR) procedures. One main assumption is that there exists a cut-off value such that smaller counts than this value are generated from the null distribution. We present several data-dependent methods to determine the cut-off value. We also consider a two-stage procedure based on screening process so that the number of mutations exceeding a certain value should be considered as significant mutations. Simulated and protein domain data sets are used to illustrate this procedure in estimation of the empirical null using a mixture of discrete distributions.