Sequential allocation in clinical trials comparing two exponential survival curves

The problem of comparing two medical treatments with respect to survival is considered. Treatment outcome is assumed to follow an exponential distribution. The ratio of expected survivals associated with the two treatments is the clinical parameter of interest. A nuisance parameter is present, but it is removed by an invariance reduction and a sequential probability ratio test is applied to the invariant likelihood ratio. A class of data-dependent treatment assignment rules is identified over which the probability of correct treatment selection at the termination of the trial is approximately constant. A cost function, the weighted sum of total patients in the trial and the number assigned to the inferior treatment is introduced, and a treatment allocation rule conjectured to minimize the expected cost is constructed. Both analytic and simulation results show that it is an improvement over rules previously proposed. The methodology contained herein can be used to construct near-optimal rules in other testing contexts.