Controlling the Average False Discovery in Large-scale Multiple Testing

 

M.S. Srivastava (2010). Controlling the Average False Discovery in Large-scale Multiple Testing. Journal of Statistical Research, Vol. 44, No. 1, pp.  85-102.

 

Abstract

In this paper, we consider multiple testing procedures in which we simultaneously test a large number $ m $ of null hypotheses $ H_1,\ldots,H_m $ using the test statistics $ T_1,\ldots,T_m $. The currently used procedure of controlling the false discovery rate (FDR) at a specified level requires that the statistics $ T_1,\ldots,T_m $ be either independently distributed or positively related. In practice $ T_i $'s are rarely independent and it is not known how to ascertain the positive relationship between $ T_i $'s. In this paper, we propose to control the expected value of the Average False Discovery (AFD) at some specified level. This AFD procedure controls its level at the specified value independent of how $ T_i $'s are related. This specified value can be chosen to control $ k $-FWER or $ \gamma $FWER and even FDR at their respective specified levels. Using simulation, we compare our proposed AFD procedure with the FDR procedure. In terms of power and stability, the proposed AFD procedure has an edge over the FDR procedure, as well as over $ k $-FWER procedure. Two illustrative examples are given to compare the number of differentially expressed genes obtained by the two methods.

 

Fulltext PDF not available for this article.