Application Of Bayesian Estimation Based On Weak Information Priori In Small Sample Meta-Analysis

Objective:This study aims at the problem of limited number of studies in valuable meta analysis.It describes the basic principles of four traditional frequency school meta analytic methods and three bayesian meta analytic methods,then simulates small sample size contingency tables close to the actual situation and performs a real example.Comparing the performance differences between traditional frequency school meta analysis and bayesian school meta analysis,and evaluating the merits and demerits of different methods about between-study heterogeneity bias?the mean square error?effect size interval width?coverage rate,etc.Provide advice on selecting the appropriate small sample size meta analytic method.Methods:Study the influence of different number of included studies and different between-study heterogeneity on each method,which was simulated in the case of small samples.A combination of each given number of included studies and between-study heterogeneity yielded 10,000 data sets.Data were generated according to Turner et al.'s study of the Cochrane systematic review database involving 14886 meta analyses which effect size was binary outcome.The seven methods involved in this paper were used to analyze and evaluate 280,000 data sets under different between-study variances(0,0.01,0.04,0.16,0.25,1,2)combination with different studies(2,3,4,5).Study the applicability and existing problems of seven methods in the case of small samples.A real example is the efficacy and safety evaluation of different doses of clazosentan in the treatment of cerebral vasospasm after aneurysmal subarachnoid hemorrhage.Study endpoints included the incidence of delayed ischemic neurological deficit and the use of rescue therapy.Further clarify the applicability and operability of the methods involved in this paper in practice.Results:The simulation results show that the bias and mean square error of frequency school and bayesian school methods are slightly different.Considering the coverage rate and interval width,in the frequency school methods,the PM+modified HKSJ method has the highest coverage rate,but at the cost of a wider confidence interval,the PM+HKSJ method performs relatively well,but when the heterogeneity is particularly large,the confidence interval is wide.The coverage rate of BB1 N and BBMP performs well when the heterogeneity is small,but when the heterogeneity 2t values are 1 and 2,the coverage rate shows a significant downward trend;In the bayesian methods,when the heterogeneity is small,the coverage rate of half Cauchy(0.05),half t(0.21,df=4),and half normal(0.3)priors maintained above 0.95,and the interval width is small,when the heterogeneity is large,the interval width of half normal(1.0)prior is the largest,but the coverage is still maintained at around 0.95.The real example results shows that different methods for different doses of clazosentan in the treatment of celebral vasospasm after aneurysmal subarachnoid hemorrhage to reduce the incidence of delayed ischemic neurological deficit are inconsistent,which needs a larger sample of clinical trial or increases the number of included studies for verification;different methods reached the same conclusion on the increased occurrence of rescue therapy in the treatment of cerebral vasospasm after aneurysmal subarachnoid hemorrhage with different doses of clazosentan,and all of these results indicated that there was no statistical difference in the incidence of rescue therapy between high dose group and low dose group.Conclusion:In the small sample meta analysis,the bayesian estimation uing weak information prior is superior to the traditional frequency school methods in small sample meta analysis.When meta analysis included small sample studies,the half Cauchy(0.05),half t(0.21,df=4),and half normal(0.3)priors should be preferred for the small between-study heterogeneity;and half normal(1.0)prior should be preferred for the large between-study heterogeneity.When the between-study heterogeneity is unknown,the above four priors can be used as sensitivity analysis to check the robustness of the combined results in small sample cases.