On Construction of Exact Confidence Interval for the Proportion in Two-Stage Designs
In Phase Ⅱ clinical trials,when the efficacy of a drug is uncertain,the number of participants is often expected to be as small as possible.The commonly used confidence intervals of the single pro-portion of binomial distribution are the results of the large sample theory.However,for small samples,due to the inapplicability of large samples,we prefer to give exact confidence intervals of the parameter,that is,the minimum coverage probability is not less than 1-α.In this paper,the rank function on the original sample space is constructed based on the Clopper-Pearson interval and inverse search methods,and an optimal exact confidence interval is derived under this order in two-stage designs.By depicting the coverage probability graph on the whole parameter space,it can be seen that the confidence coeffi-cient of the interval is not less than 1-α.Further,taking the expected interval length as the evaluation standard,we compare three exact intervals,and the expected length of the new interval is the shortest in general.Finally,the data of olaparib(2018.03-2020.01),a breast cancer drug,is used to derive the optimal exact lower one-sided confidence interval for the efficacy rate of olaparib.