Distribution-Free Multisample Tests Based on Optimal Matchings With Applications to Single Cell Genomics

• Published in: Journal of the American Statistical Association Vol. 117; no. 538; pp. 627 - 638
• Main Authors: Mukherjee, Somabha, Agarwal, Divyansh, Zhang, Nancy R., Bhattacharya, Bhaswar B.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.04.2022; Taylor & Francis Ltd
• Subjects: Biological pathways; blood; Blood cancer; Cancer; Closeness; Data points; Distribution-free tests; Equality; Genomics; Graph-based methods; hepatoma; humans; Immune system; Liver cancer; Lung cancer; lung neoplasms; Matching; Multivariate analysis; Optimal matching; probability; Regression analysis; Research subjects; Simulation; Statistical analysis; Statistical methods; Statistics; transcriptomics; Tumors
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2020.1791131

In this article, we propose a nonparametric graphical test based on optimal matching, for assessing the equality of multiple unknown multivariate probability distributions. Our procedure pools the data from the different classes to create a graph based on the minimum non-bipartite matching, and then utilizes the number of edges connecting data points from different classes to examine the closeness between the distributions. The proposed test is exactly distribution-free (the null distribution does not depend on the distribution of the data) and can be efficiently applied to multivariate as well as non-Euclidean data, whenever the inter-point distances are well-defined. We show that the test is universally consistent, and prove a distributional limit theorem for the test statistic under general alternatives. Through simulation studies, we demonstrate its superior performance against other common and well-known multisample tests. The method is applied to single cell transcriptomics data obtained from the peripheral blood, cancer tissue, and tumor-adjacent normal tissue of human subjects with hepatocellular carcinoma and non-small-cell lung cancer. Our method unveils patterns in how biochemical metabolic pathways are altered across immune cells in a cancer setting, depending on the tissue location. All of the methods described herein are implemented in the R package multicross. Supplementary materials for this article are available online.