Bayesian Causal Models For Three-arm Non-inferiority Clinical Trials With Bias From Non-compliance

ObjectiveA three-arm non-inferiority clinical trial refers to a non-inferiority clinical trial including a test group,an active control group,and a placebo control group,which is recognized as the‘gold standard design’ of the non-inferiority clinical trial.The traditional methods of controlling non-compliance bias in non-inferiority trials have always been controversial and have become more challenged in the three-arm design.Therefore,further systematic research is needed for the evaluation of the three-arm non-inferiority clinical trial in the presence of non-compliance,establishing a more complete theoretical system to promote the development of the three-arm non-inferiority design.MethodsGiven the acceptance of the regulatory agency,the principal stratum strategy recommended by ICH E9(R1)was employed to construct the estimand of the three-arm non-inferiority design in the presence of non-compliance.We established a general Bayesian causal model and defined the certain stratum as the main stratum through certain model assumptions,where the total effect of the population was considered as the finite mixture distribution of the effects of the population from different principal strata.The Data Augmentation algorithms were programmed for estimating parameters of interest of the mixture distribution.The Bayesian decision rule was constructed to evaluate the non-inferiority of the test group.Different parameter combinations were simulated to evaluate the performance of the algorithm.The percentage bias and mean square error were used to evaluate the accuracy of the estimates,and the type I error rates and Power in the Bayesian hypothesis testing were computed by setting pre-specified cut-off point,RNI,to 0.50,0.70,0.90,0.95,0.975,respectively.It was the optimal RNI that controlled the type I error rate no more than 0.05 and obtained higher Power at the same time.Through quantitative analysis,the statistics of ITT analysis,PP analysis and AT analysis were compared with CACE estimators in the Bayesian causal model framework.Finally,a real example was given to testify for the proposed method.ResultsIn the three-principal-strata structure with the normal outcome,the percentage bias of the placebo control group,the active control group,and the test group were 7.8%,3.0%and 0.01%,respectively;The optimal RNI was 0.7,where the average type I error rate was 0.024 and the average Power was 0.921.In the three-principal-strata with the binary outcome,the percentage bias of the placebo control group,the active control group,and the test group were 13.6%,4.0%and-0.3%,respectively.The optimal RNI was 0.9,where the average type I error rate was 0.016 and the average Power was 0.600.Compared with results in the three-principal-strata structure,the parameter estimate in the four-principal-strata structure had a larger overall deviation;The optimal RNI changed to 0.975 when the outcome followed the normal distribution and remained unchanged when the outcome was the binary outcome.By the quantitative analysis,the statistics of ITT analysis,PP analysis,and AT analysis all have linear relationships with CACEs estimators,influenced by compliance ratios and compliance effects.In the case study,the proposed method had a better performance than other traditional analysis methods.ConclusionsThe accuracy of the DA algorithm depends on the principal strata structure,where the fewer principal strata structure tends to be more accurate.In the non-inferiority hypothesis testing,the type I error rate within a reasonable range and high Power can be gained by setting a reasonable RNI.The magnitude of bias between the estimates of ITT analysis,PP analysis and AT analysis and the true parameters depends on the size of the compliance effects and the principal strata structure.When compliance effects have obvious impacts on the treatment effect,it is recommended to use the proposed method in this study,which can obtain more accurate and valid conclusions.