  In many applications, a large number of features are collected with the goal
to identify a few important ones. Sometimes, these features lie in a metric
space with a known distance matrix, which partially reflects their
co-importance pattern. Proper use of the distance matrix will boost the power
of identifying important features. Hence, we develop a new multiple testing
framework named the Distance Assisted Recursive Testing (DART). DART has two
stages. In stage 1, we transform the distance matrix into an aggregation tree,
where each node represents a set of features. In stage 2, based on the
aggregation tree, we set up dynamic node hypotheses and perform multiple
testing on the tree. All rejections are mapped back to the features. Under mild
assumptions, the false discovery proportion of DART converges to the desired
level in high probability converging to one. We illustrate by theory and
simulations that DART has superior performance under various models compared to
the existing methods. We applied DART to a clinical trial in the allogeneic
stem cell transplantation study to identify the gut microbiota whose abundance
will be impacted by the after-transplant care.

Methodology