Robust Meta-analysis Model Using T-distribution And Its Application

Many conventional models used for meta-analysis assume that both the random effects term and the within-study error term all have normal distribution,and the normal distribution is susceptible to outliers,leading to a model that is sensitive to outliers.In fact,outliers in the model may appear in the random effects term,the within-study error term,or both.In order to further improve the sensitivity of the model to outliers,some scholars have proposed a meta-analysis model in which the random effects term obeys the t distribution.This model is limited to the study of the distribution of random effects,which can deal with the problem of abnormal random effects but cannot handle the research.The problem of abnormal internal error.In order to enable the model to deal with two outliers at the same time,we established a robust meta-analysis model in which both the random effect term and the within-study error term obey the t distribution and consider the cases with and without covariates.The model without covariates is the robust random effect model with t distribution,and the model with covariates is the robust meta regression model with t distribution.By using the hierarchical form of the model,not only can the four EM-type algorithms be used naturally,but also statistical data for identifying and distinguishing outliers can be generated.The simulation and empirical studies show that: under AIC and BIC criteria,when there are outliers,the normal model(both random effects and research errors obey nor-mal distribution)always performs the worst? When only random effects are abnormal,there is no significant difference between the t- RE model(random effects obey the tdistribution,and the study internal error obey the normal distribution)and the tmodel(both random effects and study internal error obey the tdistribution)? The performance of the tmodel is optimal when only internal error anomalies or both are studied.In addition,the tmodel can not only effectively identify outliers,but also distinguish the types of outliers.In summary,compared to the Normal model and the t-RE model,the t model is the most robust and has a wider range of applications.