We develop approximate methods to compare the efficiencies and to compute the power of alternative potential designs for sampling from a cohort before beginning to collect exposure data. Our methods require only that the cohort be assembled, meaning that the numbers of individuals Nkj at risk at pairs of event times tk and tj greater than or equal to tk are available. To compute Nkj, one needs to know the entry, follow-up, censoring, and event history, but not the exposure, for each individual. Our methods apply to any "unbiased control sampling design," in which cases are compared to a random sample of noncases at risk at the time of an event. We apply our methods to approximate the efficiencies of the nested case-control design, the case-cohort design, and an augmented case-cohort design, compared to the full cohort design, in an assembled cohort of 17,633 members of an insurance cooperative who were followed for mortality from prostatic cancer. The assumptions underlying the approximation are that exposure is unrelated both to the hazard of an event and to the hazard for censoring. The approximations performed well in simulations when both assumptions held and when the exposure was moderately related to censoring.