Fig. 3: Comparison of batch effects correction methods in the simulation study.

a Comparison of the magnitude of cell type effects and batch effects in the simulation study and two real applications. The subpanel for the simulation study jitters around the assumed values for β and ν. The boxplots show the distributions of the estimated cell type effects \(\widehat{{\boldsymbol{\beta }}}\) and batch effects \(\widehat{{\boldsymbol{\nu }}}\) by BUSseq in the two real studies. The magnitude of the batch effects and cell type effects in the simulation study were chosen to mimic the real data scenarios. b The boxplots of silhouette coefficients for all compared methods. In these boxplots, the central line denotes the median; the upper and lower bounds represent the first and third quartiles; and the whiskers extend to a maximum of 1.5 times the interquartile (IQR) beyond the box, where the IQR is the difference between the third and the first quartiles. c T-distributed Stochastic Neighbor Embedding (t-SNE) plots colored by batch for each compared method. d t-SNE plots colored by true cell type labels for each compared method. BUSseq successfully corrects the batch effects and perfectly clusters cells into different cell types in the simulation study, whose batch effects and cell type effects are at the same scale as those of the two real datasets.