  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.
