Abstract: Case-control study designs are popular in epidemiological research for their cost saving and time saving properties. The efficiency of the design depends on the choice of case-control ratio, which is often arbitrarily chosen, resulting in a loss of efficacy. We study sequential case-control designs where cases occur sequentially over time and propose a sampling rule and a simple Bayes stopping rule which lead to the optimal sequential case-control design. This sampling rule can be applied to ``case-control within cohort'' studies where controls are sampled from failure-free members of the cohort at each distinct failure time when a case occurs, the study design itself being intrinsically sequential in nature. The proposed stopping rule is shown to be first order asymptotically optimal. Simulation results indicate that finite sample performance of the stopping rule and the estimation rule is satisfactory for moderate sample sizes.
Key words and phrases: Asymptotically pointwise optimal (APO) rules, case-control ratio, cost effective, Laplace approximation, Nurse's health study, Synthetic case-control studies.