  In the analysis of single-cell RNA sequencing data, researchers often
characterize the variation between cells by estimating a latent variable, such
as cell type or pseudotime, representing some aspect of the individual cell's
state. They then test each gene for association with the estimated latent
variable. If the same data are used for both of these steps, then standard
methods for computing p-values and confidence intervals in the second step will
fail to achieve statistical guarantees such as Type 1 error control.
Furthermore, approaches such as sample splitting that can be applied to solve
similar problems in other settings are not applicable in this context. In this
paper, we introduce count splitting, a flexible framework that allows us to
carry out valid inference in this setting, for virtually any latent variable
estimation technique and inference approach, under a Poisson assumption. We
demonstrate the Type 1 error control and power of count splitting in a
simulation study, and apply count splitting to a dataset of pluripotent stem
cells differentiating to cardiomyocytes.
