Optimal sequential designs of case-control studies

Fixed case-control studies separately collect a case sample and a control sample with the two sample sizes being fixed prior to studies and sometimes arbitrarily chosen. This often results in loss of efficiency of case-control designs in terms of cost-saving or time-saving of the studies. We study sequential case-control designs and, in connection with treatment allocation and stochastic approximation, derive a simple sampling rule that leads to optimal case-control designs. Some important issues such as fixed-width confidence intervals and sequential tests of hypotheses with possible early stopping to save time or costs, which cannot be answered with fixed case-control designs, are shown to be naturally solved with the derived optimal sequential case-control designs.