A class comparison method with filtering‐enhanced variable selection for high‐dimensional data sets

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 highdimensional 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 noninformative "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 instead of 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 with an example from the literature that FEVS can be useful for gaining sensitivity for the detection of truly differentially expressed variables.

Independent filtering increases detection power for high-throughput experiments

“…In the microarray literature, several authors have suggested filtering to reduce the impact that multiple testing adjustment has on detection power (7)(8)(9)(10)(11)(12). Conceptually similar screening approaches have also been proposed for variable selection in high-dimensional regression models (13,14).…”

A robust variable screening procedure for ultra-high dimensional data

“…If we are to relate these high-dimensional features to some outcome variable in a regression set-up, we need to perform some sort of variable selection. 1–4…”

“…If we are to relate these high-dimensional features to some outcome variable in a regression set-up, we need to perform some sort of variable selection. [1][2][3][4] The most commonly used method for identifying important predictor variables in a high-dimensional regression model is to fit a penalized model. Consider the linear regression model with response variable Y and p explanatory variables (e.g.…”

Single-index modulated multiple testing

“…A comprehensive review of weighted hypothesis testing can be found in [27] and the references therein. A different approach, based on a two-stage approach mainly arising from the microarray literature [6,16,24,25,33,34], extracted the prior information to remove a subset of genes which seem to generate uninformative signals in the filtering stage, followed by applying some multiple testing procedure to the remaining genes which have passed the filter in the selection stage.…”