Statistical test of structured continuous trees based on discordance matrix

Abstract

Motivation: 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.

Results: 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.

Availability and implementation: SCTree software is available at https://github.com/XQBai/SCTree-test.

Supplementary information: Supplementary data are available at Bioinformatics online.