Association testing for binary trees—A Markov branching process approach

We propose a new approach to test associations between binary trees and covariates. In this approach, binary‐tree structured data are treated as sample paths of binary fission Markov branching processes (bMBP). We propose a generalized linear regression model and developed inference procedures for association testing, including variable selection and estimation of covariate effects. Simulation studies show that these procedures are able to accurately identify covariates that are associated with the binary tree structure by impacting the rate parameter of the bMBP. The problem of association testing on binary trees is motivated by modeling hierarchical clustering dendrograms of pixel intensities in biomedical images. By using semi‐synthetic data generated from a real brain‐tumor image, our simulation studies show that the bMBP model is able to capture the characteristics of dendrogram trees in brain‐tumor images. Our final analysis of the glioblastoma multiforme brain‐tumor data from The Cancer Imaging Archive identified multiple clinical and genetic variables that are potentially associated with brain‐tumor heterogeneity.