An Optimal FDR Control Method Under The Three-group Model

The development of biomedical technology has enabled people to measure the expression levels of thousands of genes at the same time.We can measure the gene expression levels of normal people and patients.An important statistical problem when analyzing these gene expression data is how to find abnormally expressed genes,these abnormally expressed genes are likely to be disease-causing genes.The commonly used two-group model only describe the mixed distribution of the test statistics corresponding to normal genes and abnormally expressed genes,and do not further divide abnormally expressed genes into over-expressed genes and under-expressed genes.Therefore,the multiple models under the two models The test cannot guarantee the error rate of over-expressed and under-expressed genes in the abnormally expressed genes.In order to solve this problem,we expand the two-group model into three-group model,and convert the multiple testing problem under the three-group model into constraints optimization problem.Under certain conditions,the nature of the optimal solution can be used to solve the constrained optimization problem,and theoretically obtain the optimal decision criterion that can control the two FDRs.Based on this,we designed the corresponding algorithm and compared it with the other two existing control methods that can control the two FDRs in the numerical simulation.Finally,we used the above three methods to analyze the two sets of gene expression data.