Discoveries at Risk

Nicolai Meinshausen and Peter Bühlmann

May 2003

Abstract

When testing multiple hypotheses simultaneously, the false discovery rate (FDR) measures the expected proportion of falsely rejected hypothesis. The true amount of false discoveries, however, is very often much larger than indicated by FDR. We propose the new Discoveries-at-Risk approach (DaR) to multiple hypotheses testing, a generalization of the family-wise error rate (FWER). FWER can still be controlled, if desired, but more powerful testing is possible by allowing a certain fraction of false discoveries. This is in common with the FDR-approach to multiple hypotheses testing. The risk of underestimating the true proportion of false discoveries is, however, tightly controlled in the Discoveries-at-Risk approach. Although DaR often pays a price in terms of power for such tighter control of underestimation compared to FDR, we present a surprising result saying that our new DaR approach offers both tighter control and more power than FDR when controlling at low error rates. The proposed method of DaR -control is applied to simulated and microarray data and compared to FWER - and FDR - controlling procedures.

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