Optimal two-stage screening designs for survival comparisons

A two-stage design is presented which enables the screening, at the first stage, of several new experimental treatments for survival improvement over a standard regimen. Only promising treatments are carried forward to the second stage for definitive evaluation. Our procedure is to minimize the number of patients expected to be accrued to new regimens which do not offer a survival benefit over the standard regimen, subject to constraints of specified alpha-error, power, and a stopping rule which allows specification of the magnitude of the hazards ratio which would warrant accrual beyond the first stage. We explore the savings in patient accrual by comparing our design with a single-stage design for a variety of situations. Our design may offer a substantial saving when the hazard rate is large relative to the patient accrual rate, a situation often encountered in clinical trials in advanced cancer. Although computations are based on asymptotic results, simulations verify that the approximations are adequate for most trials of interest.