Overcoming systematic errors caused by log-transformation of normalized single-cell RNA sequencing data

Applying a log-transformation to normalized expression values is one of the most common procedures in exploratory analyses of single-cell RNA sequencing (scRNA-seq) data. Normalization removes systematic biases in sequencing coverage between cells, while the log-transformation ensures that downstream computational procedures operate on relative rather than absolute differences in expression. We show that the log-transformation can introduce systematic errors when cells vary in sequencing coverage, leading to spurious non-zero differences in expression and artificial population structure in simulations. We observe similar effects in real scRNA-seq data where the difference in transformed values between groups of cells is not an accurate proxy for the log-fold change. We provide some practical recommendations to overcome this effect and analytically derive an expression for a larger pseudo-count that controls the transformation-induced error to a specified threshold.