Abstract: Many microarray experiments have factorial designs, but there are few statistical methods developed explicitly to handle the factorial analysis in these experiments. We propose a bootstrap-based non-parametric ANOVA (NANOVA) method and a gene classification algorithm to classify genes into different groups according to the factor effects. The proposed method encompasses one-way and two-way models, as well as balanced and unbalanced experimental designs. False discovery rate (FDR) estimation is embedded in the procedure, and the method is robust to outliers. The gene classification algorithm is based on a series of NANOVA tests. The false discovery rate of each test is carefully controlled. Gene expression pattern in each group is modeled by a different ANOVA structure. We demonstrate the performance of NANOVA using simulated and microarray data.
Key words and phrases: Bootstrap re-sampling, factorial design, false discovery rate estimation, gene classification, microarray, non-parametric ANOVA, robust test.