Statistical test of structured continuous trees based on discordance matrix.

Abstract

Cell fate determination is a continuous process in which one cell type diversifies to other cell types following a hierarchical path. Advancements in single-cell technologies provide the opportunity to reveal the continuum of cell progression which forms a structured continuous tree (SCTree). Computational algorithms, which are usually based on a priori assumptions on the hidden structures, have previously been proposed as a means of recovering pseudo trajectory along cell differentiation process. However, there still lack of statistical framework on the assessments of intrinsic structure embedded in high-dimensional gene expression profile. Inherit noise and cell-to-cell variation underlie the single-cell data, however, pose grand challenges to testing even basic structures, such as linear versus bifurcation. In this study, we propose an adaptive statistical framework, termed SCTree, to test the intrinsic structure of a high-dimensional single-cell dataset. SCTree test is conducted based on the tools derived from metric geometry and random matrix theory. In brief, by extending the Gromov-Farris transform and utilizing semicircular law, we formulate the continuous tree structure testing problem into a signal matrix detection problem. We show that the SCTree test is most powerful when the signal-to-noise ratio exceeds a moderate value. We also demonstrate that SCTree is able to robustly detect linear, single and multiple branching events with simulated datasets and real scRNA-seq datasets. Overall, the SCTree test provides a unified statistical assessment of the significance of the hidden structure of single-cell data. SCTree software is available at https://github.com/XQBai/SCTree-test. Supplementary data are available at Bioinformatics online.