MOTIVATION: The false discovery rate (fdr) is a key tool for statistical assessment of differential expression (DE) in microarray studies. Overall control of the fdr alone, however, is not sufficient to address the problem of genes with small variance, which generally suffer from a disproportionally high rate of false positives. It is desirable to have an fdr-controlling procedure that automatically accounts for gene variability. METHODS: We generalize the local fdr as a function of multiple statistics, combining a common test statistic for assessing DE with its standard error information. We use a non-parametric mixture model for DE and non-DE genes to describe the observed multi-dimensional statistics, and estimate the distribution for non-DE genes via the permutation method. We demonstrate this fdr2d approach for simulated and real microarray data. RESULTS: The fdr2d allows objective assessment of DE as a function of gene variability. We also show that the fdr2d performs better than commonly used modified test statistics. AVAILABILITY: An R-package OCplus containing functions for computing fdr2d() and other operating characteristics of microarray data is available at http://www.meb.ki.se/~yudpaw.