Some Problems Of Exact Statistical Inference In Clinical Trials

In Phase ? clinical trials for cancer study,the main goal is to minimize the sample size due to ethics and costs.To reduce the sample size,a multi-stage design,especially a two-stage one,is commonly used.When establishing an effective treatment with binary data in a two-stage design,one-sided tests for a proportion p are employed.Researchers typically use the parameter configuration at the boundary of the null hypothesis space to determine a rejection region and an optimal design.However,it is unclear whether the maximum Type ? error rate is achieved at the boundary especially when the sample size in the second stage is varied(Type ? adaptive design).In Chapter 2,we first prove that this is true for a large family of tests in adaptive two-stage designs by showing that any test in the family has a nondecreasing power function in p.Secondly,we propose an optimization algorithm for searching the optimal Type ? adaptive two-stage designs,and similar results are established for m-stage designs with m>2.Due to the limited sample sizes in adaptive multi-stage designs,it is necessary to derive exact intervals with a guaranteed confidence level.Since a large value of the response rate p for the treatment is wanted,one-sided confidence intervals for p are of interest.In Chapter 3,we first construct a rank function that is based on the Clopper-Pearson(1934)lower confidence limit and the smallest exact confidence interval under this rank.When the sample size in second stage is a constant(Type? adaptive two-stage design),two kinds of smallest intervals are constructed with or without using the sufficiency principle.Secondly,the proposed exact confidence intervals outperform the existing exact intervals and are recommended for practice due to their small expected interval lengths.Thirdly,the smallest exact one-sided confidence interval is also proposed in a Type ? adaptive two-stage designWhen establishing a treatment,it is important to evaluate both efficacy and safety.In Chapter 4,exact tests on the response rate and safety rate will be developed.However,existing tests use certain parameter configurations at the boundaries of null and alternative spaces to calculate the maximum Type ? error rate and minimum power,respectively,and determine the rejection regions without showing that it is true.In this chapter,we first show that the power function for each test in a large family of tests is nondecreasing in both response rate and safety rate.Then,we identify the parameter configurations at which the maximum Type? error rate and minimum power are achieved and derive level-?tests.Finally,we provide the optimal two-stage designs and the optimization algorithm,and extend the results to the case of m>2In Chapter 5,for consideration of the correlation between the efficacy and safety,a new set of hypotheses and exact tests are proposed.We prove that the power function is nondecreasing in the response rate and safety rate,respectively,using the conditional expectation.The Type ? error rate achieves its maximum at two points in the null space and the power achieves its minimum on a line in the alternative space.With control of maximum Type ? error rate and minimum power,the optimal two-stage designs are derived to minimize the expected total sample size.Additionally,since the new alternative space is a subset of original that,an optimal two-stage design for the original alternative space is also a two-stage design for the new alternative space.