Abstract
High-throughput molecular analysis technologies can produce thousands of measurements for each of the assayed samples. A common scientific question is to identify the variables whose distributions differ between some pre-specified classes (i.e. are differentially expressed). The statistical cost of examining thousands of variables is related to the risk of identifying many variables that truly are not differentially expressed, and many different multiple testing strategies have been used for the analysis of high-dimensional data sets to control the number of these false positives. An approach that is often used in practice to reduce the multiple comparisons problem is to lessen the number of comparisons being performed by filtering out variables that are considered non-informative 'before' the analysis. However, deciding which and how many variables should be filtered out can be highly arbitrary, and different filtering strategies can result in different variables being identified as differentially expressed. We propose the filtering-enhanced variable selection (FEVS) method, a new multiple testing strategy for identifying differentially expressed variables. This method identifies differentially expressed variables by combining the results obtained using a variety of filtering methods, instead of using a pre-specified filtering method or trying to identify an optimal filtering of the variables prior to class comparison analysis. We prove that the FEVS method probabilistically controls the number of false discoveries, and we show with a set of simulations and an example from the literature that FEVS can be useful for gaining sensitivity for the detection of truly differentially expressed variables.