Testing for dependence on tree structures

Tree structures, showing hierarchical relationships and the latent structures between samples, are ubiquitous in genomic and biomedical sciences. A common question in many studies is whether there is an association between a response variable measured on each sample and the latent group structure represented by some given tree. Currently this is addressed on an ad hoc basis, usually requiring the user to decide on an appropriate number of clusters to prune out of the tree to be tested against the response variable. Here we present a statistical method with statistical guarantees that tests for association between the response variable and a fixed tree structure across all levels of the tree hierarchy with high power, while accounting for the overall false positive error rate. This enhances the robustness and reproducibility of such findings.Significance StatementTree like structures are abundant in the empirical sciences as they can summarize high dimensional data and show latent structure among many samples in a single framework. Prominent examples include phylogenetic trees or hierarchical clustering derived from genetic data. Currently users employ ad hoc methods to test for association between a given tree and a response variable, which reduces reproducibility and robustness. In this paper, we introduce treeSeg, a simple to use and widely applicable methodology with high power for testing between all levels of hierarchy for a given tree and the response while accounting for the overall false positive rate. Our method allows for precise uncertainty quantification and therefore increases interpretability and reproducibility of such studies across many fields of science.