Workshop in Biostatistics

Medical School Office Building (MSOB)
Rm x303

DATE: October 5, 2017
TIME: 1:30 - 2:50 pm
TITLE: DAGGER: A sequential algorithm for FDR control on DAGs
Aaditya Ramdas
Postdoctoral Researcher
Statistics and EECS, UC Berkeley



We construct a top-down algorithm for multiple testing on directed acyclic graphs (DAGs), where nodes represent hypotheses and edges specify a partial ordering in which hypotheses must be tested, that rejects a sub-DAG with bounded false discovery rate (FDR) while satisfying the logical constraint that a rejected node’s parents must also be rejected. The algorithm is designed for sequential testing settings, when the DAG is known a priori but the p-values are obtained selectively (such as sequential conduction of experiments), but the algorithm is also applicable in non-sequential settings when all p-values can be calculated in advance (such as variable/model selection). We name our algorithm DAGGER, for Greedily Evolving Rejections on DAGs. We prove that DAGGER works on two different types of DAGs — (a) “intersection DAGs” where all nodes are intersection hypotheses, with parents being supersets of children, or (b) “general DAGs” where all nodes may be elementary hypotheses — under independence, positive or arbitrary dependence of the p-values. DAGGER has the appealing property that it specializes to known algorithms in the special cases of trees and line graphs, and simplifies to the classic Benjamini-Hochberg procedure when the DAG has no edges. We explore the empirical performance of DAGGER using simulations, as well as a real gene ontology DAG, on which it is shown to be faster and more powerful than existing algorithms that control the familywise error rate (FWER) on DAGs.

(Joint work with Jianbo Chen, Martin Wainwright, Michael Jordan)

Suggested reading:

A. Ramdas, J. Chen, M.J. Wainwright, M.I. Jordan.  DAGGER: A sequential algorithm for FDR control on DAGs.