Testing Non-inferiority Of A New Treatment In Three-arm Clinical Trials With Binary Endpoints

Two-arm non-inferiority trials without a placebo are usually used to show that the experimental treatment is not worse than the reference treatment by a small pre-specified non-inferiority margin because of ethical concerns. There are often problems in design, analysis and interpretation for two-arm non-inferiority trials, such as the selection of the non-inferiority margin and the establishment of assay sensitivity etc. If ethically justifiable, it may be advisable to use a three-arm non-inferiority clinical trial with placebo to assess the assay sensitivity and internal validation purpose. A three-arm trial consists of a placebo, a reference control and an experimental treatment, and can not only tests the superiority of the experimental treatment over the placebo, but also tests the non-inferiority of the experimental treatment to an active control.Consequently, many large sample approaches have been developed to assess superiority and non-inferiority of a new treatment in a three-arm trial over the years. Unfortunately, these methods behave poor when sample sizes in three arms are small. The objective is to develop some effective approaches to test three-arm non-inferiority when sample sizes are small. The main tasks and results of our study are listed as follows:1. Based on the rate difference, Saddlepoint approximation, exact and approximate unconditional, and bootstrap-resampling methods are developed to calculate p-values of the Wald-type test, score test and likelihood ratio test for the first time. Simulation studies are conducted to compare their performance in terms of the type I error rate and power. The results show that:both approximate unconditional and bootstrap-resampling test procedures with the score test statistic are recommended for hypothesis testing. 2. For the test of three-arm non-inferiority clinical trial, we also construct confidence intervals for the interested parameter φ. We provide saddlepoint approximation and Edgeworth expansion based confidence intervals, comparison with existing four confidence intervals (wald-type, score-type, bootstrap-resampling and MOVER-type). Comparative studies among these confidence intervals through Monte Carlo simulation results indicate that:when sample sizes are small, the saddlepoint approximation and Edgeworth expansion based confidence intervals and bootstrap-resampling confidence interval are generally more appealing.3. To the Bayesian inference for the three-arm non-inferiority clinical trial, we calculate the posterior probability of the hypothesis H1. And based on the least Bayes posterior risk criterion, we have determined the sample size when we estimate φ. Our simulation suggest that:(1) The computation process of Bayes test is more easier than the classical hypothesis test which yield almost the same result.(2) Under the quadratic loss function, the Bayes posterior risk of φ is its posterior variance. It is very easy to use our method to obtain the sample size with less risk.In conclusion, we have systematically studied the test of three-arm non-inferiority clinical trial, construction of confidence intervals and the sample size determination. Based on existing three statistics, we have proposed several new test methods and provide good methods via simulation study. The question which we are interested in comes from the needs of practical application. We consider it necessary to combine theory with practice during our study, and support our idea and methods with empirical analysis.