Optimal Test Statistics for Minimising not Cured Proportion in Adaptive Clinical Trial

In last several decades adaptive sequential binary design has been used with a goal to increase performance in estimation, testing of parameters and to reduce expected number of non-cured patients in the context of clinical trials.The procedures have been studied theoretically and also using simulation techniques in many papers. As for example play the winner rule, randomised play the winner rule, adaptive randomised play the winner rule have been studied extensively. Rosenberger et al. (Biometrics 57, 3, 909–913, 2001) considered different types of difference function of \( \hat {p_{A}}\) and \(\hat {p_{B}}\) as the test statistic in adaptive sequential design for the purpose of better inference along with decreasing number of non-cured patients. In this paper we considered how to choose the optimal function to achieve the goals with better performance. Using extensive simulation studies we have supported our claim and have shown that our methods perform better than existing methods. Also in the methods given by us we have a choice on the proportion of non-cured patients which we can vary with the inferential goal in mind. This is a new approach in adaptive sequential design.