Construction And Application Of A Trivariate Network Meta-analysis Model For Diagnostic Tests Based On Beta Distribution

Objective: Network Meta-analysis can be seen as an extension of traditional Meta-analysis methods.It improve the evaluation process by sharing information among studies resulting in more accurate evaluation results,especially for diagnostic tests with a smaller number of studies.However,regardless of traditional methods or network structures,the clinical effects of diagnostic tests also maybe depend on the proportion of diseases in addition to sensitivity and specificity.If it is different that the distribution of continuous variables which distinguish disease states in groups or studies,the proportion of diseases between studies may affect the integration sensitivity and specificity in Meta-analysis.In addition,the normal assumptions of the generalized linear mixed model are difficult to verify which is commonly used in network Meta-analysis.Therefore,choosing a more appropriate hypothesis of distribution may make Meta-analysis results more accurate.Considering the characteristic of the beta distribution and the possible correlation between sensitivity and specificity with the prevalence of disease in diagnostic tests,we intends to use beta distribution and Copula function,taking into account the correlation between studies without any conversion of variables,to establish a trivariate network Meta-analysis model combined with the three variables of sensitivity,specificity,and disease prevalence in the study.At the same time,taking the actual disease as an example,considering the different choices of Copula function,the prior distributions of model and the number of iterations and repeated chains of the Markov chain,we adjust the constructed model of trivariate network Meta-analysis in diagnostic test,and compare the most ideal model with the original model of bivariate normal distribution hypothesis(ANOVA model)and the model of bivariate beta distribution to explore the advantages and shortcomings of them and to examine and evaluate the results of the new model under the condition that the actual literature retrieval is not complete.We hope to establish a model with less requires,more raw data information and the model of trivariate network Meta-analysis is simple and reasonable in order to provide more choices for researchers to Meta-analysis,and contribute to the development of statistical method of network Meta-analysis.Methods: In this study,we retrieved the articles evaluating the effectiveness and accuracy of APRI,ARFI,FIB-4,Fibro Scan,Fibro Test,and Forns Index in the electronic database of pub Med,EMBASE,and Cochrane libraries(deadline in December 2019).Extract the author,publication year,design type,patient basic information,phase of patient fibrosis,number of patients at each stage of fibrosis,and the diagnostic test method used in the study and the rate of true positive,false positive,false negative and true negative at each cut-off point,then use the sensitivity,specificity and prevalence of each study to build a trivariate network Meta-analysis model.The model is constructed using the beta distribution hypothesis,using the Copula function and the multi-dimensional joint distribution theory,and is estimated the model parameters using the MCMC method based on the Frank function.The model was be adjusted by the Clayton function and Gumbel function which are the congeneric as the Frank function.In addition,we adjust the a priori distribution of parameters in the MCMC method,adjust the number of iterations to 1000,4000,and5000,and adjust the number of Markov chains to 1,3,and 4.Selecting the appropriate model is compared with the bivariate normal distribution model(ANOVA model)and the bivariate beta distribution model through the results of mate-analysis and Watanabe-Akaike Information Criterion.For example,we limited the literature screening to the same document data set as the previous ANOVA model and the two-variable beta model in order to facilitate comparison with the original model.In total,the accuracy of 11 tests for detecting cervical precancer was evaluated.They are HC2,conventional cytology DNA analysis(CC),liquid-based cytology(LBC),generic PCRs targeting hr HPV DNA(PCR)for hr HPV DNA,and commercially available PCR-based hr HPV DNA testing,Abbott RT PCR hr HPV,Linear Array and Coba-4800,HPV Proofer,APTIMA,and protein markers,p16 and p16/Ki67.And in the hepatitis B fibrosis database,we randomly extracted 90% of the corresponding data that imitate the literature retrieval is not comprehensive.A total of 100 repeated random sampling was analyzed by the trivariate network model and was calculated the absolute deviation,the root mean square error and average relative error of sensitivity,specificity and prevalence to evaluate of stability of the ideal model in practical application.Results: There were a total of 1859 relevant literatures in Chinese and English,and finally 124 articles were included.After the network Meta-analysis,when diagnosing fibrosis of hepatitis B,APRI estimated that the confidence interval of sensitivity was the narrowest(0.08),and FIB-4 has the narrowest confidence interval of specificity(0.09);And in cirrhosis of hepatitis B,APRI and Fibro Scan estimated that the confidence interval of sensitivity was the narrowest(0.11),Fibro Scan has the narrowest confidence interval of specificity(0.08).During the model adjustment phase,the results of the network Meta-analysis of the Copula function model were more different compared with other adjustment methods,but the Clayton function is relatively simple to construct,and it has significantly less running time,and the WAIC value of the Clayton function model is acceptable.The confidential interval of Clayton model is smaller than the other two Copula models.Adjusting the a priori distribution of the hyper-parameters,WAIC values are slightly reduced.When adjusting the number of Markov chain iterations,the model of 5000 iterations have the lowest WAIC value.The WAIC that repeats the Markov chain 3 times and 4 times is smaller than the original model.At the time of model evaluation,the WAIC of brivariate beta model in the fibrosis dataset was 88168.6 which is the biggest,and in the cirrhosis dataset,the WAIC of ANOVA model with a maximum value of 395682.6.In the example,a total of 107 documents were included in the trivariate network Meta-analysis.And HC2 has the narrowest confidence interval of sensitivity(0.04),the maximum width of the confidence interval of sensitivity was LBC(0.25);In addition,the narrowest confidence interval of specificity in HC2 is 0.09,and the maximum width of confidence interval of specificity is 0.44 in Abbott.The absolute deviation of sensitivity of Fibro Test was the largest(0.0176)and the absolute deviation of Forns Index was the largest(0.0135)in specificity under the conditions of the incomplete retrieval literature.The absolute deviation of APRI and FIB-4 are small in sensitivity,specificity,and the prevalence.And Fibro Test and Forns Index also have a large average square root error and an average relative error relatively,but the absolute deviation was no more than 0.02.Conclusion: 1.The trivariate Meta-analysis model based on beta distribution in diagnostic test,whether in the results of diagnosis of hepatitis B fibrosis or cirrhosis,the (?) value of the model is close to 1,which means that the convergence of the model is good and the estimated results are credible.2.Considering the model fitting effect and running cost,we finally chose the Clayton Copula function model,with4000 iterations and three chains of Markov chain.3.If the number of documents is small,the trivariate network Meta-analysis model provides more accurate confidence intervals and the result of proportions,and it has good extensionality,but the model has a longer running time.4.Under the condition that the literature retrieval is not comprehensive,the influence on the results of trivariate network Meta-analysis is small,but the difference of the results will be slightly larger because of the small number of articles in network Meta-analysis and the credible interval of the results will be larger.