Estimation of empirical null using a mixture of normals and its use in local false discovery rate

When high dimensional microarray data is given, it is of interest to select significant genes by controlling a given level of Type-I error. One popular way to control the level is the false discovery rate (FDR). This paper considers gene selection based on the local false discovery rate. In most of the previous studies, the null distribution of gene expression is commonly assumed to be a normal distribution. However, if the null distribution has heavier tail than that of normal, there may exist too many false discoveries leading to the failure of controlling the given level of FDR. We propose a novel procedure which enriches a class of null distribution based on a mixture of normals. We present simulation studies to show that our proposed procedure is less sensitive to variation of null distribution than local false discovery rate with a single normal for the null. We also provide real example of gene expression profiles of antigen-specific human CD8+ T-lymphocytes treated with cytokine Interleukin-2 (IL-2) and Interleukin-15 (IL-15) for comparison.