Sample size calculation for a regularized tt-statistic in microarray experiments

The regularized tt-statistic, wherein, a regularization term is added to the denominator in order to improve the identifiability of differentially expressed genes, outperforms an ordinary tt-statistic. Most methods of sample size calculation in the literature, however, calculate the sample size based on the ordinary one. We derive an approximate formula for the distribution of regularized tt-statistics and develop a formula of sample size calculation for regularized tt-statistics. The sample size is determined based on sensitivity under certain conditions to maintain a certain false discovery rate using a mixture model. The usefulness of the proposed method is demonstrated by numerical studies that compare the sample sizes of regularized and ordinary tt-statistics and simulation studies for examining the robustness of the proposed method based on real data.