  The advent of single-cell sequencing opens new avenues for personalized
treatment. In this paper, we address a two-level clustering problem of
simultaneous subject subgroup discovery (subject level) and cell type detection
(cell level) for single-cell expression data from multiple subjects. However,
current statistical approaches either cluster cells without considering the
subject heterogeneity or group subjects without using the single-cell
information. To bridge the gap between cell clustering and subject grouping, we
develop a nonparametric Bayesian model, Subject and Cell clustering for
Single-Cell expression data (SCSC) model, to achieve subject and cell grouping
simultaneously. SCSC does not need to prespecify the subject subgroup number or
the cell type number. It automatically induces subject subgroup structures and
matches cell types across subjects. Moreover, it directly models the
single-cell raw count data by deliberately considering the data's dropouts,
library sizes, and over-dispersion. A blocked Gibbs sampler is proposed for the
posterior inference. Simulation studies and the application to a multi-subject
iPSC scRNA-seq dataset validate the ability of SCSC to simultaneously cluster
subjects and cells.
