A Bottom-up Approach to Testing Hypotheses That Have a Branching Tree Dependence Structure, with Error Rate Control.

Modern statistical analyses often involve testing large numbers of hypotheses. In many situations, these hypotheses may have an underlying tree structure that both helps determine the order that tests should be conducted but also imposes a dependency between tests that must be accounted for. Our motivating example comes from testing the association between a trait of interest and groups of microbes that have been organized into operational taxonomic units (OTUs) or amplicon sequence variants (ASVs). Given p-values from association tests for each individual OTU or ASV, we would like to know if we can declare a certain species, genus, or higher taxonomic group to be associated with the trait. For this problem, a bottom-up testing algorithm that starts at the lowest level of the tree (OTUs or ASVs) and proceeds upward through successively higher taxonomic groupings (species, genus, family etc.) is required. We develop such a bottom-up testing algorithm that controls a novel error rate that we call the false selection rate. By simulation, we also show that our approach is better at finding driver taxa, the highest level taxa below which there are dense association signals. We illustrate our approach using data from a study of the microbiome among patients with ulcerative colitis and healthy controls.