Paper. Tang, W., Bertaux, F., Thomas, P., Stefanelli, C., Saint, M., Marguerat, S., & Shahrezaei, V. (2020). bayNorm: Bayesian gene expression recovery, imputation and normalization for single-cell RNA-sequencing data. Bioinformatics, 36(4), 1174–1181. https://doi.org/10.1093/bioinformatics/btz726 (original), licensed CC BY 4.0. Below is a short summary in our own words; the full text is reproduced under the paper's licence.
bayNorm: Bayesian gene expression recovery, imputation and normalization for single-cell RNA-sequencing data¶
What this covers¶
How to turn raw single-cell RNA-sequencing (scRNA-seq) counts, which are dominated by technical dropout and capture noise, into estimates of the true number of transcripts per gene per cell — a problem at the intersection of computational biology and Bayesian statistics.
The question¶
scRNA-seq only captures a small, cell-varying fraction of the RNA actually present in a cell, so raw count matrices are sparse, noisy, and subject to batch-to-batch shifts in that capture fraction. Existing methods treated normalization (removing cell-size/capture differences), imputation (filling in dropouts) and batch correction as three separate problems, and several relied on explicit zero-inflation models to explain dropouts. The authors wanted a single, minimally-assumption approach that recovers true counts, handles dropouts, and corrects batch effects together, and that could also be tested for whether dropout really needs a special zero-inflation mechanism at all.
The approach¶
bayNorm treats observed counts as a Binomial sample of the true transcript count for each gene in each cell, with a cell-specific "capture efficiency" probability \(\beta_j\) standing in for the usual scaling factor. The true (unobserved) count is given a Negative Binomial prior, with gene-specific mean and dispersion parameters estimated empirically by pooling expression values across cells (an empirical Bayes approach), either across all cells ("global" priors) or within defined cell groups/batches ("local" priors). Combining the Binomial likelihood with the Negative Binomial prior gives, via Bayes' rule, a closed-form posterior distribution of the true count for every gene/cell pair; the paper derives this posterior (itself a shifted Negative Binomial) and its mean and variance analytically. The output is either point estimates (mean or MAP) of true counts, or samples drawn from the full posterior, both usable in downstream analyses such as differential expression (DE) testing and clustering. Choosing global versus local priors, and estimating the mean capture efficiency \(\bar\beta\), are the method's key tuning decisions.
What it found¶
Simulated data generated from the binomial-capture assumption reproduced the mean-variance and mean-dropout relationships, and the per-gene and per-cell dropout-rate distributions, of several real UMI-based scRNA-seq datasets more closely than the existing Gamma-Poisson-based Splatter simulator — support for treating dropout as a consequence of binomial sampling rather than requiring a separate zero-inflation mechanism. A simple constant rescaling made the same binomial model fit non-UMI data reasonably well too. Against datasets with matched single-molecule FISH (smFISH) ground truth, bayNorm recovered mean expression as well as competing methods but matched the FISH-measured noise (coefficient of variation) and dispersion (Gini coefficient) more closely than scaling normalization or other recent imputation methods (scImpute, MAGIC, SAVER, DCA). In differential expression benchmarks (using MAST, benchmarked against matched bulk RNA-seq DE gene lists), bayNorm with local (group-specific) priors matched or exceeded other methods' sensitivity (AUC), while with global priors it produced almost no spurious DE genes between groups selected only by differing capture efficiency — demonstrating that it is specifically controlling for the capture-efficiency bias rather than just performing well on average. Using within-individual local priors across batches, bayNorm reduced batch-driven false-positive DE rates (tested on data with three individuals x three batches each) while preserving true biological differences between individuals, outperforming the global-prior and within-batch-prior alternatives on that trade-off. Global priors preserved unsupervised cell-type clustering (by t-SNE/Jaccard index against scaling normalization) about as well as scaling-based normalization. The method was also shown not to be very sensitive to a 2-fold misestimate of mean capture efficiency.
Limits and context¶
The prior assumes no correlation between genes, so bayNorm's gene-specific priors were shown to underestimate gene-gene correlation on data with matched smFISH measurements (in the opposite direction to SAVER's pooling-across-genes approach, which tended to overestimate it). Accurate estimation of cell-specific capture efficiency remains central to the method and is not always easy to obtain, since calibration approaches such as smFISH are uncommon and spike-in-based estimates have known shortcomings; the paper found that neither spike-ins nor housekeeping-gene estimates improved recovery of per-cell dropout statistics in its tests. Local-prior estimation loses robustness when a comparison group has very few cells. The authors note that clustering could potentially be improved further by iterating the prior estimation together with clustering, as in the BISCUIT method, and suggest combining bayNorm's framework with deep-learning-based approaches as future work rather than presenting that combination here.
Citation¶
Tang, W., Bertaux, F., Thomas, P., Stefanelli, C., Saint, M., Marguerat, S., & Shahrezaei, V. (2020). bayNorm: Bayesian gene expression recovery, imputation and normalization for single-cell RNA-sequencing data. Bioinformatics, 36(4), 1174–1181. https://doi.org/10.1093/bioinformatics/btz726