title: Optimal conditional error functions for the control of conditional power.
abstract: Ethical considerations and the competitive environment of clinical trials usually require that any given trial have sufficient power to detect a treatment advance. If at an interim analysis the available data are used to decide whether the trial is promising enough to be continued, investigators and sponsors often wish to have a high conditional power, which is the probability to reject the null hypothesis given the interim data and the alternative of interest. Under this requirement a design with interim sample size recalculation, which keeps the overall and conditional power at a prespecified value and preserves the overall type I error rate, is a reasonable alternative to a classical group sequential design, in which the conditional power is often too small. In this article two-stage designs with control of overall and conditional power are constructed that minimize the expected sample size, either for a simple point alternative or for a random mixture of alternatives given by a prior density for the efficacy parameter. The presented optimality result applies to trials with and without an interim hypothesis test; in addition, one can account for constraints such as a minimal sample size for the second stage. The optimal designs will be illustrated with an example, and will be compared to the frequently considered method of using the conditional type I error level of a group sequential design.
authors.affiliation: Department of Medical Statistics, Medical University of Vienna, Schwarzspaniesrstr. 17, Vienna, Austria. werner.brannath@meduniwien.ac.at
authors.forename: Werner
authors.initials: W
authors.lastname: Brannath
authors.forename: Peter
authors.initials: P
authors.lastname: Bauer
mesh_terms: D001699:Biometry; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D003627:Data Interpretation, Statistical; D015987:Effect Modifier, Epidemiologic; D006146:Guanidines / Q000627:therapeutic use; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009203:Myocardial Infarction / Q000188:drug therapy; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D018401:Sample Size; D013450:Sulfones / Q000627:therapeutic use
chemical_list: D006146:Guanidines; D013450:Sulfones; C118397:eniporide