| With the development of medical research,more and more new drugs are emerging.New drugs often have advantages that are not available in current standard drugs,such as fewer side effects and lower prices.In order to evaluate the therapeutic effect of a new drug,biopharmaceutical testing is the first step.Non-inferiority testing is one of the commonly used methods for testing biopharmaceuticals.The non-inferiority test is to prove that a new drug is not inferior to the standard drug under the pre-specified non-inferiority margin.In the traditional two-arm non-inferiority trial that does not include a placebo group,there are many problems in the design,analysis and evaluation of the test,especially the assay sensitivity cannot be test,which may lead to poor drug efficacy.Therefore,a three-arm noninferiority test involving a placebo group is usually used when ethically warranted.The three-arm non-inferiority trial includes an experimental drug(new drug)group,a traditional drug(standard drug)group and a placebo group,which can not only compare whether the new drug is non-inferior to the traditional standard drug,but also compare whether the new drug is better than the placebo,so it overcomes the disadvantage of a two-arm non-inferiority trial.However,many of the current studies on three-arm non-inferiority tests do not fully use the assay sensitivity,due to a poor efficiency of non-inferiority tests.This paper considers the three-arm non-inferiority test including assay sensitivity information,and constructs a more flexible semi-parametric Bayesian test,Fiducial confidence interval and empirical likelihood test,so as to establish a more reliable statistical theory and method.Specifically,the main work of this paper include:(1)Aiming at the three-arm non-inferiority trial with normal data,a semi-parametric Bayesian method to test the three-arm non-inferiority hypothesis is proposed from the Bayesian perspective.First,it is assumed that the outcomes of the experimental drug E,the standard drug R and the placebo P follow a normal distribution,but the prior distribution of their location parameters is unknown.Secondly,the unknown prior distribution of the location parameters is approximated by the Dirichlet process,then based on the posterior estimators of the location parameters,the test statistic for testing the three-arm non-inferiority hypothesis is constructed.The sample size are given by the test statistic,that is,the Bayesian power calculation method based on classical hypothesis testing,and compares the frequentist method and parametric Bayesian methods.The simulation results show that the semiparametric Bayesian test method has similar effects to the frequency method and the Bayesian method of strong prior distribution,and is better than the uninformative prior distribution Bayesian method,misinformation prior distribution Bayesian method and power prior distribution Bayesian method.(2)Aiming at the three-arm non-inferiority trial with normal data,a simultaneous confidence region method for testing the three-arm non-inferiority hypothesis is proposed from the Fiducial confidence interval.When the sample size is small,the test statistic or confidence interval constructed by the traditional large sample theory is not very well,which often cannot well control the Type 1 error and the power is low or the coverage probability of the confidence interval cannot reach the pre-specified confidence level.To overcome the disadvantages,this paper develops a new simultaneous confidence region for testing the three-arm non-inferiority hypothesis from the small sample size.Based on Fiducial generalized pivotal quantity and Method of variance estimates recovery,a simultaneous confidence region for non-inferiority and assay sensitivity is constructed.The simultaneous confidence region not only has a concise expression and is convenient to calculate,but also provides a proof of its asymptotic properties and a method of determining the sample size.Simultaneous confidence regions for non-inferiority and assay sensitivity are also proposed based on Wald-type statistics and parametric Bootstrap-based methods.Simulation results show that the simultaneous confidence region constructed by the Fiducial method is more effective than the classical method.(3)Aiming at the three-arm non-inferiority trial with data following unknown distribution,the empirical likelihood ratio test statistic for testing the hypothesis of three-arm non-inferiority were derived.When the outcomes of the three-arm non-inferiority trial follow unknown distribution,the method developed to test the three-arm non-inferiority hypothesis based on the normal data is not useful.However,in applications,the outcomes of the three-arm non-inferiority trial follow unknown distribution in many field.To overcome this disadvantage,this paper tests the three-arm non-inferiority hypothesis based on the nonparametric empirical likelihood method.First,to determine a non-inferiority margin,assuming the unknown distribution of the outcome of historical trial,the empirical likelihood ratio statistic of the difference between location parameters in historical trial is constructed.Then,the empirical likelihood ratio test statistic is constructed to simultaneously test non-inferiority and assay sensitivity,and the proof of the asymptotic property of the test statistic is given.Simulation results show that nonparametric empirical likelihood methods can effectively control the Type 1 error.This paper comprehensively and systematically studies the three-arm non-inferiority test.It proposes a semi-parametric Bayesian method to test the three-arm non-inferiority hypothesis,construct the simultaneous confidence region for non-inferiority and assay sensitivity based on the Fiduical method and the MOVER method,construct the simultaneous confidence region for non-inferiority and assay sensitivity based on Wald-type statistics and Bootstrap method and develop the empirical likelihood methods for testing non-inferiority and assay sensitivity when the outcome distribution of the three-arm non-inferiority is unknown.The simulation results show the validity of this methods.The study not only considers hypothesis testing and confidence interval methods,but also uses the empirical likelihood method to derive new test statistics.This study not only has important theoretical significance,but also can be provide method for drug efficacy testing in new drug development. |
