Assays can be so expensive that interesting hypotheses become impractical to study epidemiologically. One need not, however, perform an assay for everyone providing a biological specimen. We propose pooling equal-volume aliquots from randomly grouped sets of cases and randomly grouped sets of controls, and then assaying the smaller number of pooled samples. If an effect modifier is of concern, the pooling can be done within strata defined by that variable. For covariates assessed on individuals (e.g., questionnaire data), set-based counterparts are calculated by adding the values for the individuals in each set. The pooling set then becomes the unit of statistical analysis. We show that, with appropriate specification of a set-based logistic model, standard software yields a valid estimated exposure odds ratio, provided the multiplicative formulation is correct. Pooling minimizes the depletion of irreplaceable biological specimens and can enable additional exposures to be studied economically. Statistical power suffers very little compared with the usual, individual-based analysis. In settings where high assay costs constrain the number of people an investigator can afford to study, specimen pooling can make it possible to study more people and hence improve the study's statistical power with no increase in cost.