| ObjectiveWith the development of modern computing techniques,Bayesian statistics are applied to solve problems in clinical trials by providing new tools gradually.Clinical trial research in the medical device field has demonstrated that Bayesian statistics can play a key role in the design and analysis of clinical trials.It has gradually become a hotspot of research.However,the application of Bayesian statistics in clinical trials in China is still in its infancy.Therefore,in this study,we will explore the application of Bayesian statistics in sample size estimation in clinical trials and compare different Bayesian methods through simulation studies,develop an interactive program(The Bayesian Sample Size Estimation Program,Bayes SSE)for Bayesian sample size estimation based on theoretical research to promote the use of Bayesian statistics in clinical trials.Methods(1)Based on the simulation study,different Bayesian methods in the fixed sample size design are compared.The results of the sample size estimation are compared with the frequency statistical method,and the effects of the prior distribution and the main parameters on the different methods are also discussed.(2)Based on the simulation study,we explore the application of Bayesian methods for sample size estimation in adaptive design,including Bayesian interim analysis and sample size re-estimation,compare the results with the frequency statistical method,and discuss the influence of the prior distribution and main parameters on different methods.(3)Based on the theoretical research,an interactive Bayesian sample size estimation program(Bayes SSE)is constructed,the basic principles and usage methods are explained.Clinical trial cases are used to explore the feasibility of the procedure in Bayesian statistical sample size estimation.Results(1)In the fixed sample size design,the Posterior Credible Interval Approach(PCIA)is used when estimating the sample size,the different integral methods of PCIA will have different results.The sample size of the Average Coverage Criterion(ACC)method and the Average Length Criterion(ALC)method were less than the Worst Outcome Criterion(WOC)method.When using the Hybrid Classical-Bayesian Approach(HCBA)to estimate the sample size,if the parameters of the clinical trial have the same useful information as the frequency statistics method,the results are close to those of the frequency statistical method.With the same probability of making a type Ⅰ error and the same sample size,the average power of HCBA is usually less than that of the frequency statistical method and it has an upper limit,which is related to the prior distribution.Using the Hybrid Bayesian Approach(HBA)and Bayesian Factor Approach(BFA)when the same probability of making a type Ⅰ error and the sample size,their powers are greater than the frequency statistical methods.The results of all four Bayesian methods are influenced by prior information.(2)In the adaptive design,for the single-arm test of the Bayesian interim analysis,the results of Fleming method in frequency statistics is similar to the Predictive Sample Size Selection Design(PSSD)in that when estimating the sample size under specific conditions,there is a simple functional relationship between the Bayesian probability thresholds and type Ⅰ and type Ⅱ error in frequency statistics;For two-arm trials,the results of the Whitehead method of Bayesian approach are influenced by probability thresholds and prior information.For sample size re-estimation,the results of the Bayesian method with predicted probability and predicted power method in sample size estimation are almost the same when the analysis prior is non-informative prior.(3)Bayesian sample size estimation program(Bayes SSE)was built with the help of R package Shiny,which provides different Bayesian methods for sample size estimation in fixed sample size design and the adaptive design.It simplifies the Bayesian sample size calculation by dynamically displaying the graphs related to the sample size results in real-time according to the user’s parameter adjustment.Conclusion(1)Using Bayesian methods for estimating sample size,if the information used for the parameters of the clinical trial is the same as that used for frequency statistics,in most cases,the results of sample size estimation of the Bayesian method are close to those of the frequency statistics method.The Bayesian method can be used as an adjunct to the frequency statistics method.The advantage of the Bayesian method is that the sample size can be reduced by using enthusiastic prior.(2)In the fixed sample size design,different Bayesian methods have their advantages and disadvantages.The PCIA considers the precision of the parameter estimation,while for HCBA,HBA,and BFA,the power of hypothesis testing is considered.The use of prior information has a large impact on the Bayesian sample size estimation method.(3)In the adaptive design,for Bayesian interim analysis,if non-information prior is used in analysis phase,there is a simple functional relationship between the Bayesian probability threshold and the operating characteristics of frequency statistics(type Ⅰ error,power).The Fleming method can be regarded as a special case of the Bayesian PSSD method.For the reestimation of the sample size,the prediction probability method and the prediction power method in the Bayesian method can be substituted for each other when the analysis prior is noninformative prior.The sample size estimation of the Bayesian method is easily affected by prior information and the probability threshold.Therefore,although enthusiastic prior and reducing the probability threshold can reduce the sample size,we should pay attention to the expansion of type I error.(4)An interactive program for Bayesian sample size estimation(Bayes SSE)can simplify calculations and improve research efficiency,and it can be used to exploring the sample size estimation of Bayesian methods in clinical trials,which provides a simple tool for conducting similar studies in China and facilitates Bayesian extension of methods in national clinical trials. |
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