Generalized α-investing: Definitions, optimality results and application to public databases

The increasing prevalence and utility of large public databases necessitates the development of appropriate methods for controlling false discovery. Motivated by this challenge, we discuss the generic problem of testing a possibly infinite stream of null hypotheses. In this context, Foster and Stine suggested a novel method named α-investing for controlling a false discovery measure known as mFDR. We develop a more general procedure for controlling mFDR, of which α-investing is a special case. We show that, in common practical situations, the general procedure can be optimized to produce an expected reward optimal version, which is more powerful than α-investing. We then present the concept of quality preserving databases which was originally introduced by Aharoni and co-workers, which formalizes efficient public database management to save costs and to control false discovery simultaneously. We show how one variant of generalized α-investing can be used to control mFDR in a quality preserving database and to lead to significant reduction in costs compared with naive approaches for controlling the familywise error rate implemented by Aharoni and co-workers.