The problem of multiple inference in identifying point-source environmental hazards.

Point-source environmental hazards are often identified by examination of unusual clusters of disease cases. The very large number of potential clusters give rise to the statistical problem of "multiple inference," i.e., the more clusters examined, the greater the risk of "false-positive" associations emerging by chance alone. This paper first distinguishes the situation of clusters identified by anecdotal observation from those that emerge from systematic searches. The latter may or may not include a systematic enumeration of potential causal factors associated with each potential disease cluster. If exposure information is not systematically available, empirical Bayes procedures are suggested as a basis for ranking the observed clusters in order of priority for further investigation. If exposure information is systematically available, empirical Bayes procedures can be used to select associations to report or to rank them in order of priority for confirmation. In addition, procedures are described for testing the global null hypothesis of no exposure-disease associations and for estimating the number of true-positive associations. These approaches are advocated in preference to classical frequentist approaches of multiplying p values by the number of tests performed.