To Study Properties of a Known Procedure in Adaptive Sequential Sampling Design

Abstract: We consider the procedure proposed by Bhandari et al. (2009) in the context of two-treatment clinical trials, with the objective of minimizing the applications of the less effective drug to the least number of patients. Our focus is on an adaptive sequential procedure that is both simple and intuitive. Through a refined theoretical analysis, we establish that the number of applications of the less effective drug is a finite random variable whose all moments are also finite. In contrast, Bhandari et al. (2009) observed that this number increases logarithmically with the total sample size. We attribute this discrepancy to differences in their choice of the initial sample size and the method of analysis employed. We further extend the allocation rule to multi-treatment setup and derive analogous finiteness results, reinforcing the generalizability of our findings. Extensive simulation studies and real-data analyses support theoretical developments, showing stabilization in allocation and reduced patient exposure to inferior treatments as the total sample size grows. These results enhance the long-term ethical strength of the proposed adaptive allocation strategy.