Selection-model-based Meta-analysis With Publication Bias Correction

Meta analysis is commonly-used to synthesize multiple results from individual studies,and quantitatively analyzes the results of scientific research.The rationality and credibility of meta analysis results may often be affected by publication bias.Therefore,it is necessary and important to detect and correct publication bias in a meta-analysis with published scientific research.The contribution of this paper to the meta-analysis study is threefold.First,we study the one-dimensional summary data and use the Copas selection model to describe the publication mechanism,so as to achieve the goal of correcting publication bias.In the literature,Copas selection model is widely used to correct publication bias.Under the Copas selection model,the existing statistical inference methods are based on conditional likelihood,which makes efficiency loss.Moreover,the coverage rate of the Wald confidence interval based on conditional likelihood may be lower than the nominal level,and the lower limit of the interval may have unreasonable values.Motivated the weaknesses of conditional likelihood method under Copas selection model,we propose a full likelihood method for meta analysis by integrating the conditional likelihood and a marginal semi-parametric likelihood.This method can not only make full use of data information,but also make up for the disadvantages of conditional likelihood method.In addition,We show that the proposed MLEs of all the underlying parameters have a jointly normal limiting distribution,and the full likelihood ratio follows an asymptotic central chisquare distribution.Our simulation results indicate that the full maximum likelihood estimators have smaller mean squared errors than the conditional-likelihood-based estimators.Also the full likelihood ratio confidence intervals for the effect size and the total number of studies have more accurate coverage probabilities than the Wald intervals under the conditional likelihood.Furthermore,we conducted a study on two-dimensional aggregated data,that is,focusing on diagnostic test meta analysis.The accuracy of diagnostic test is generally measured by a pair of measurement results,such as sensitivity and specificity,and these results is also affected by the publication bias.Diagnostic test meta analysis based on the Copas selection model in the literature also rely on conditional likelihood to make statistical inferences.However,the disadvantages of low coverage rate and unreasonable lower limit of Wald confidence interval based on conditional likelihood also exist in two-dimensional diagnostic test data.In this paper,we extend the full likelihood method to diagnostic meta analysis which involves bivariate outcomes.Besides,we not only proves the asymptotic limit distribution of maximum likelihood estimation in theory,but also further shows that the full likelihood method has better performance in point estimation and interval estimation than the conditional likelihood method through simulation results.In reality,it is difficult to obtain the information of the selection mechanism from the data in advance,which leads to the complexity of the structure and parameters of the Copas selection model,as well as the difficulty in calculation.Therefore,the third contribution of this paper is to consider a simple,convenient and more applicable p-value selection model,with the purpose of using this selection model to correct the influence of publication bias on the total effect size.We consider using the conditional likelihood method to make statistical inference under the p-value selection model,and compare the results with the commonly used inverse variance weighted estimation results.At the same time,we also uses the likelihood ratio test to measure whether publication bias exists.In addition,we also prove that the likelihood ratio follows an exponential distribution.It is worth noting that this theoretical property is different from the common chi-square distribution.Finally,simulations show that when publication bias exists,the proposed method has significant advantages over the inverse variance weighting method in both the bias and the root mean square error,and the coverage of the corresponding confidence intervals is closer to the nominal level.