Adjusting SPRT for an Efficient Procedure with Finite Number of Applications of Less Effective Treatment

Abstract

We propose an adaptive Sequential Probability Ratio Test (SPRT) which allocates a finite number of applications to the less effective treatment. In the classical SPRT framework, patients are assigned to the two competing treatments one by one until the stopping criterion, based on breaching the boundary values which are pre-determined using the Type-I and Type-II error probabilities, is met. This ensures the control of errors at the cost of ethical efficiency as the exposure to the less effective treatment is large. We begin with proposing an adaptive sequential framework for testing two simple hypotheses that analytically ensures finite exposure to the less effective treatment. Our proposed procedure employs a likelihood ratio driven adaptive allocation rule, dynamically concentrating sampling effort on the superior population while preserving asymptotic efficiency (in terms of average sample number), comparable to the classical SPRT. We derive an explicit closed-form expression for the expected number of allocations to the inferior treatment. Extensive simulation studies and real data analyses substantiate the theoretical results, evincing a significant reduction in inferior allocations compared to the classical SPRT. The proposed design thus offers a balanced method between statistical precision and ethical responsibility, aligning inferential reliability with patient safety.