Significance Many studies use measurements of gene expression in human postmortem and ex vivo tissues like brain and blood to characterize genomic correlates of illness. However, molecular analyses of these tissues can be susceptible to a wide range of confounders that may be difficult to measure and remove. In this article, we describe an analysis framework for identifying and removing previously uncharacterized quality biases in measurements of RNA. Our paper critically highlights the shortcomings of standard RNA quality correction approaches, such as statistically adjusting for RNA integrity numbers. We show that the our framework removes residual confounding by RNA quality and greatly improves replication of significant differentially expressed genes across independent datasets by more than threefold compared with previous approaches.