Bias in the estimation of false discovery rate in microarray studies

Motivation: The false discovery rate (FDR) provides a key statistical assessment for microarray studies. Its value depends on the proportion π₀ of non-differentially expressed (non-DE) genes. In most microarray studies, many genes have small effects not easily separable from non-DE genes. As a result, current methods often overestimate π₀ and FDR, leading to unnecessary loss of power in the overall analysis. Methods: For the common two-sample comparison we derive a natural mixture model of the test statistic and an explicit bias formula in the standard estimation of π₀. We suggest an improved estimation of π₀ based on the mixture model and describe a practical likelihood-based procedure for this purpose. Results: The analysis shows that a large bias occurs when π₀ is far from 1 and when the non-centrality parameters of the distribution of the test statistic are near zero. The theoretical result also explains substantial discrepancies between non-parametric and model-based estimates of π₀. Simulation studies indicate mixture-model estimates are less biased than standard estimates. The method is applied to breast cancer and lymphoma data examples.