Optimal two-stage screening designs for survival comparisons

SUMMARY 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 wlhich 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. In the development of treatments for advanced cancer, a standard regimen with limited survival benefit may be available, as well as several new promising regimens which have not been evaluated in a comparative trial to determine their possible survival benefit. We offer an efficient two-stage design which allows survival comparisons of the new regimens with a standard regimen, but which permits early termination of accrual onto those new regimens which do not demonstrate a minimum prespecified survival advantage over the standard regimen. In this way we hope to minimize the number of patients assigned to new regimens which are not promising. The design also permits early accrual termination if a new treatment offers an early substantial survival advantage over the standard regimen. 2. THE DESIGN We propose a two-stage screening design so that survival times of each of K experimental regimens will be compared to the survival of the standard treatment at possibly two time points, t1 and t2. Furthermore, we assume proportional hazards such that