The problem of multiple inference in studies designed to generate hypotheses.

Epidemiologic research often involves the simultaneous assessment of associations between many risk factors and several disease outcomes. In such situations, often designed to generate hypotheses, multiple univariate hypothesis-testing is not an appropriate basis for inference. The number of true positive associations in a collection of many associations can be estimated by comparing the observed distribution of p values for the positive associations to a theoretical uniform distribution, or to the observed distribution of negative associations, or to an empiric randomization distribution. None of these approaches, however, will distinguish the true from the false positive associations. Various criteria for selecting a subset of associations to report are considered by the authors, including Bonferoni adjustment of p values, splitting the sample for searching and testing, Bayesian inference, and decision theory. The authors prefer an approach in which all associations in the data are reported, whether significant or not, followed by a ranking in order of priority for investigation using empirical Bayes techniques. Methods are illustrated by application to preliminary data from a study aimed at identifying hitherto unsuspected occupational carcinogens.