Three-Arm Non-Inferiority Statistical Inference Based On Poisson Response Endpoints

Based on the three-arm non-inferiority trial design of clinical endpoints of Poisson distribution,this thesis mainly constructs the hypothesis tests of risk difference,ratio and two types of odds ratio for drug effect measurements,and derives Wald,Score and conditional normal test statistics,as well as confidence Interval estimates which consisting of Wald-type(Sample Variance,Maximum Likelihood Estimation),Score-type(Restricated MLE),conditional-type(CONDI),variance recovery-type,Bootstrap-type and so on for statistical inference.The results of this thesis are mainly three-fold:(1)The conclusions of the numerical simulation and real data analysis of the hypothesis testing methods under the measurement of risk difference,ratio and odds ratio all show that the conditional test is the most powerful;the simulation results of different confidence interval estimates and conclusions of real data analysis all show that the hybrid confidence interval estimates are most effective and robust,especially the Agresti-Coull type confidence interval estimation;conclusions of real data analysis is consistent with the previous scholars.(2)Using the Delta method to approximate the variance estimation will cause the value of the test statistics to be overestimated,and the conditional test method can better control the probability of making the type one error rate under different measurement methods.This method is relatively robust.(3)During the assessment of three-arm non-inferiority trials based on Poisson distribution,if we choose the method of hypothesis test,then the conditional test is recommended to use,if we choose the method of confidence interval,then the method of hybrid confidence interval is recommended to use.We can adaptively choose different effect measurements by the purpose of practical conditions,if we could allow the cost of calculation and time,then the method of RMLE and the standard method of Bootstrap are suggested to use.In addition,it is recommended to use unbalanced trial design,which is beneficial to statistical reliability and save costs.