Curtailed procedures for binomial random-sized subset selection

Randomized subset selection procedures are important statistical tools in clinical trials involving multiple treatments. However, traditional methods lack built-in early stopping criteria, leading to potential inefficiencies and unnecessary patient exposure. Inspired by Gupta and Sobel's (1960) foundational subset selection approach and Bechhofer and Kulkarni's (1982) idea of curtailment, this paper introduces a curtailed subset selection procedure for binomial populations under a frequentist framework. Specifically, our method includes a mathematically driven stopping rule that terminates sampling as soon as non-leading treatments can no longer statistically surpass the current leader. We derive explicit formulas for calculating the probability of correct selection and the expected sample size, and we also introduce an optional randomization extension to precisely achieve pre-specified accuracy targets. Simulation studies confirm that the proposed curtailed procedure maintains comparable accuracy levels while substantially reducing expected sample sizes compared to existing procedures. Illustrative examples from clinical trial scenarios demonstrate the practical benefits and ease of implementation. This approach provides researchers and practitioners with an efficient, statistically rigorous tool for optimizing subset selection in biopharmaceutical research.