  The standard pipeline to analyse single-cell RNA sequencing (scRNA-seq) often
involves two steps : clustering and Differential Expression Analysis (DEA) to
annotate cell populations based on gene expression. However, using clustering
results for data-driven hypothesis formulation compromises statistical
properties, especially Type I error control. Data fission was introduced to
split the information contained in each observation into two independent parts
that can be used for clustering and testing. However, data fission was
originally designed for non-mixture distributions, and adapting it for mixtures
requires knowledge of the unknown clustering structure to estimate
component-specific scale parameters. As components are typically unavailable in
practice, scale parameter estimators often exhibit bias. We explicitly quantify
how this bias affects subsequent post-clustering differential analysis Type I
error rate despite employing data fission. In response, we propose a novel
approach that involves modeling each observation as a realization of its
distribution, with scale parameters estimated non-parametrically. Simulations
study showcase the efficacy of our method when component are clearly separated.
However, the level of separability required to reach good performance presents
complexities in its application to real scRNA-seq data.
