MOTIVATION: Logistic regression is a standard method for building prediction models for a binary outcome and has been extended for disease classification with microarray data by many authors. A feature (gene) selection step, however, must be added to penalized logistic modeling due to a large number of genes and a small number of subjects. Model selection for this two-step approach requires new statistical tools because prediction error estimation ignoring the feature selection step can be severely downward biased. Generic methods such as cross-validation and non-parametric bootstrap can be very ineffective due to the big variability in the prediction error estimate. RESULTS: We propose a parametric bootstrap model for more accurate estimation of the prediction error that is tailored to the microarray data by borrowing from the extensive research in identifying differentially expressed genes, especially the local false discovery rate. The proposed method provides guidance on the two critical issues in model selection: the number of genes to include in the model and the optimal shrinkage for the penalized logistic regression. We show that selecting more than 20 genes usually helps little in further reducing the prediction error. Application to Golub's leukemia data and our own cervical cancer data leads to highly accurate prediction models. AVAILABILITY: R library GeneLogit at http://geocities.com/jg_liao

MOTIVATION: Statistical methods based on controlling the false discovery rate (FDR) or positive false discovery rate (pFDR) are now well established in identifying differentially expressed genes in DNA microarray. Several authors have recently raised the important issue that FDR or pFDR may give misleading inference when specific genes are of interest because they average the genes under consideration with genes that show stronger evidence for differential expression. The paper proposes a flexible and robust mixture model for estimating the local FDR which quantifies how plausible each specific gene expresses differentially. RESULTS: We develop a special mixture model tailored to multiple testing by requiring the P-value distribution for the differentially expressed genes to be stochastically smaller than the P-value distribution for the non-differentially expressed genes. A smoothing mechanism is built in. The proposed model gives robust estimation of local FDR for any reasonable underlying P-value distributions. It also provides a single framework for estimating the proportion of differentially expressed genes, pFDR, negative predictive values, sensitivity and specificity. A cervical cancer study shows that the local FDR gives more specific and relevant quantification of the evidence for differential expression that can be substantially different from pFDR. AVAILABILITY: An R function implementing the proposed model is available at http://www.geocities.com/jg_liao/software