Bayesian Method And Its Application To Decision-making In Clinical Trials

Objective: Decision-making is a key component of clinical trials.Bayesian method can combine prior distributions,thus providing more information in decision analyses compared to frequency studies.Based on Bayesian method,the present study aimed to discusss how to use historical data or experts' subjective opinions to construct robust prior distributions,and to explore appropriate Bayesian decision-making methods to guide robust decision analyses in clinical trials.And then,to increasethe efficiency of trails and improve the probability of study success,which will provide methodological reference for the application of Bayesian methods in decision analysis of clinical trial.Method: 1.In the case of less historical studies were available,we used simulation studies and real cases to evaluate the accuracy and robustness of pooled effects estimation when using the Bayesian random-effects model and frequency systematic review method,separately.2.When historical data were available,the Bayesian random-effects model was used to analyze the historical information comprehensively to obtain the posterior estimation of the pooled effects.And then,the method of fitting mixed distributions was used to obtain the approximate analytical form of the complex posterior distribution.Based on the distribution of approximate mixtures of conjugate distributions,we considered to add a non-information heavy-tailed distribution component to construct a robust mixed prior distribution and investigate its ability of dealing with prior-data conflicts.3.When no historical information was available,the experts' opinions can be very usefull to construct the information prior distributions.We used the questionnaire to obtain the clinical experts' opinons on the therapeutic effect of Huaier granule on recurrence after curative resection of HCC.Then the subjective opinons were used to construt the information prior distribution,and then applied to the Bayesian decisionanalysis in a real clinical RCT.Sensitivity analyses considering different prior information were applied to evaluate the roubustness of Bayesian decision-analysis.4.Based on the survival-related outcomes,we discussed the construction of exponential Bayesian decision-making model under the exponential distribution and applied it to three critical decision scenarios on a real clinical trial to illustrate the specific steps of Bayesian method to guide the decision-making process in clinical trials.Result: 1.Bayesian random-effects model considers heterogeneity better than frequency method when there is less historical information.The confidence interval of pooled effects estimated by the approximate normal distribution method is narrow,and the probability of containing the true effect value is low.The confidence interval of pooled effects estimated by HKSJ and the adjusted HKSJ had high probabilities of containing the true effect value,but the confidence interval is too wide,lacking of certain estimation accuracy.However,the Bayesian method with appropriate prior distribution specified for the heterogeneity parameter can provide pooled effects with higher accuracy and reliability.2.After the Bayesian random-effects model,the analytical expression of the complex posterior distribution can be approximated by mixtures of conjugate distributions,which is???.The results of the case study suggest that the three-component mixtures of beta distribution can fit the posterior distribution of bladder tumor recurrence rate after pirarubicin perfusion perfectlyand the KL divergence is only 0.001.3.Based on the mixtures of distribution,further adding a non-information heavytailed distribution as a robust component,such as???.This new mixtures of distribution can be used as prior distribution in a new study.The case study proves that the fourcomponent mixtures of prior distribution deals well with the priori-data conflicts,which can provide more accurate estimation of parameter's posterior distribution.4.In a real clinical trial of Huaier granule,the method of expert consultation is used to obtain the subjective probability prior,and the prior distribution of 2-year RFS in the control group is Sc₂-Beta?37,60?CS Beta,as well as the prior distribution of 2-year RFS difference between experimental group and the control group is ?-N?0.12,0.07?.5.In the clinical trial design phase,using the Bayesian prediction power instead of power can effectively save sample size when the prior distribution is appropriate.6.In the interim analysis stage,the Bayesian prediction power can provide richer decision-making opinions.In an unblinded trial,the probability of success?POS?at the end of the trial can be calculated directly from the specific outcomes observed in the interim analysis.While,in a double-blind trial,the POS after the Go decision can be calculated based on the possible outcomes that may be observed during the interim analysis.In addition,the Bayesian prediction power can decrease rapidly with the outcomes tending to be invalid.And the probability of making early No-Go decision is increased and conclude the study could be failed.Moreover,with the accumulation of observed data in interim analysis,the POS calculated by Bayesian prediction power increases rapidly and providing more chance to make early No-Go decision and conclude the study is success.7.At the end of the POC study,even if the statistical significant result was obtained,the decision of whether to carry on the confirmatory study will be more robust if theBayesian decision-making method is considered.Combined with all available historical/present information,the Bayesian method could provide more robust and comprehensive evidence for decision making.Conclusion: Bayesian random-effects model can fully consider the heterogeneity between trials than traditional frequency methods,and can provide reliable and robust posterior estimation of the pooled effect based on the utilizing of less historical data.Then,the mixtures of conjugate distributions can be usd to desceibe the posterior and a heavy-tail distribution can optimize the mixed distributions,which can surve as the prior distribution in a new study.The optimized mixed prior distribution has a good property to deal with prior-data conflicts flexibly and can be applied to the Bayesian decision-making method to guide comprehensive decision making.