Abstract
qPCR is still the gold standard for gene expression quantification. However, its accuracy is highly dependent on the normalization procedure. The conventional method involves using the geometric mean of multiple study-specific reference genes (RGs) expression for cross-sample normalization. While research on selecting stably expressed RGs is extensive, scant literature exists regarding the optimal approach for aggregating multiple RGs into a unified RG. In this paper, we introduce a family of scale-invariant functions as an alternative to the geometric mean aggregation. Our candidate method (weighted geometric mean minimizing standard deviation) demonstrated significantly better results compared to other proposed methods. We provide theoretical and experimental support for this finding using real data from solid tumors and liquid biopsies. Moreover, the closed form and regression-based solution enable efficient computation and straightforward adoption on various platforms. All the proposed methods have been implemented within an easy-to-use R package with graphics processing unit (GPU) acceleration.