A robust statistical modelling framework for random effects meta-analysis

Abstract text

In meta-analysis, heterogeneity is the norm rather than the exception. The most common modelling approach to dealing with heterogeneity is to adopt random effects models where random effects are typically assumed to have normal distributions. However, outliers often occur that may influence estimation of the heterogeneity parameter under a normality assumption, which in turn might distort statistical inference for parameters of interest.


To apply a robust modelling framework for the heterogeneity parameter in random effects meta-analysis.


We applied a robust alternative to the Gaussian model and used the Laplace (double exponential) distribution, which has heavier tails than the normal distribution, thus robust to outliers. We estimated model parameters using an Empirical Fisher Scoring (EFS) algorithm. We compared results from the robust modelling approach with that of the restricted maximum likelihood (REML) method. The methods were applied to two illustrative meta-analytic data sets.


We applied our method to the following two published systematic reviews: 1) Intravenous immunoglobulin (IVIG) for preventing infection in preterm and/or low-birth-weight infants for which estimates of treatment effects for 16 randomized clinical trials were available for analysis, 2) Overweight and obesity in mothers and risk of preterm birth and low birth weight infants which included 39 cohort studies. For both data sets, the robust model led to larger estimated effect estimates, smaller standard errors for the estimated treatment effects and smaller p values. For the cohort study, for example, the combined log(Relative Risk), its standard error and corresponding p-value using REML were 0.06, 0.07, 0.39, respectively, compared to 0.09, 0.05, 0.08, respectively, for the robust method.


When normality assumption is violated, inference about an overall effect in random effects meta-analysis model can be improved using a robust approach. A simulation study is underway to better understand the performance of the proposed method.
Beyene J1, Liu X1, Hamid JS1
1 Department of Clinical Epidemiology and Biostatistics, McMaster University, Canada
Presenting author and contact person
Presenting author: 
Joseph Beyene
Contact person Affiliation Country
Joseph Beyene (Contact this person) Faculty of Health Sciences, McMaster University Canada
Date and Location
Oral session C16O2
Wednesday 3 October 2012 - 11:20 - 11:40