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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