Statistical Diagnostics In Meta-regression Model

Meta-analysis provides a quantitative method for combining and assessing results from separate studies with the same treatment or issue and allows the researchers to take into account the variation(heterogeneity)between studies.Meta-analysis has been widely used in different areas of scientific research such as in clinical trials,biology,ecology,management research and so on.There are a large number of literature concerning on this topic,for example review of recent development by Sutton and Higgins(2008)and the references therein.Among a number of methods,the random effects(or mixed effects)Meta-regression model has become a routinely used procedure in combining the results of a set of independent studies and assessing heterogeneity in effect sizes by considering the between-study variance(or heterogeneity),in which the estimation of betweenstudy variance is essential to give the estimator of overall effect size and find the confidence intervals of interesting parameters.As many statistical models,Meta-analysis is also sensitive to the appearance of outliers and influential observations(or studies)in the data set,even a random effects is assumed for individual study.Therefore it is very important to develop some methodologies to identify these special observations.For outlier detection problem in Meta-analysis,several authors have explored this issue.For detection of influential studies,there are few literatures.Viechtbauer and Cheung(2010)examined the potential impact of outliers and influential studies in Meta-analysis by extending standard diagnostic procedures developed for linear regression analyses to the Meta-analytic models.However they didn't give the updating formulae for diagnostics,and their method is time-consuming and has many limitations.This paper studies the influence diagnostics in random effect Meta-regression model including case deletion diagnostic and local influence analysis.We derive the subset deletion formulae for the estimation of regression coefficient and heterogeneity variance and obtain the corresponding influence measures.The generalized Cochran heterogeneity statistics and Likelihood-based(i.e.maximum likelihood estimation(ML)and restricted maximum likelihood estimation(REML))estimation methods in random effect Meta-regression are considered respectively to derive the results.The diagnostics such as residual,leverage measure and Cook's distance with internally and externally scaling are derived and discussed.The formulae under the generalized Cochran heterogeneity statistics estimation method are exact and that under ML and REML method employs one-step approximation.Two real examples are used to illustrate the proposed methodology and they show that the one-step approximation performs well in applications.We also use simulations to compare the performance of correct detection rate of influential observations and study the robustness of the methods proposed which based on different estimation framework.The local influence analysis based on case-weights perturbation scheme,responses perturbation scheme,covariate perturbation scheme and within-variance perturbation scheme are explored.We introduce a method by simultaneous perturbing responses,covariate and within-variance to obtain the local influence measure,which has an advantage of capable to compare the influence magnitude of influential studies from different perturbations.Two examples are used to illustrate the proposed methodology.