QINGYUAN ZHAO – UNIVERSITY OF CAMBRIDGE

ABSTRACT

Negative control is a common technique in scientific investigations and broadly refers to the situation where a null effect (“negative result”) is expected. Motivated by a real proteomic dataset and an ad hoc procedure shared with us by collaborators, I will present three promising and closely connected methods of using negative controls to assist simultaneous hypothesis testing. The first method uses negative controls to construct a permutation p-value for every hypothesis under investigation, and we give several sufficient conditions for such p-values to be valid and positive regression dependent on the set (PRDS) of true nulls. The second method uses negative controls to construct an estimate of the false discovery rate (FDR), and we give a sufficient condition under which the step-up procedure based on this estimate controls the FDR. The third method, derived from the original ad hoc algorithm given by our collaborators, uses negative controls to construct a nonparametric estimator of the local false discovery rate. I will conclude the talk with a dramatic twist in this story. This talk is based on joint work with Zijun Gao: https://arxiv.org/abs/2303.01552.