Multilevel models are an improvement over fixed and random effects models, as they allow simultaneous estimation of the overall reliability and the between-study variability and do not assume the independency of the effect sizes or correlations.
We used the DerSimonian and Laird random-effects models to incorporate between-study variability and to report pooled effect estimates (22).
Subgroup analyses were conducted to identify potential sources of heterogeneity or between-study variability and to estimate the effect of EPA+DHA according to key study characteristics.
To test statistical heterogeneity across the study estimates, we estimated the variance corresponding to the between-study variability, and tested the null hypothesis that the between-study variability was absent.
Specifically, we used a two-stage inverse variance weighting approach to account for both between-study variability and within-study individual effect estimates that minimize uncertainties based on spatial and temporal data availability (Hubbell et al. 2005).
Random-effects models take into account both within- and between-study variability, and provide a more conservative estimate of effect sizes than can be obtained with the fixed-effect models.
Three main effects (experimental arm, cirrhosis, funding) and one interaction (funding*location of principal author) explained 31% of between study variability in a random-effect meta-regression.
33 Four sample sizes (N=10, N=20, N=50 and N=100), three sizes of the between-study variability (τ=0.02, τ=0.12 and τ=0.9), and three levels of publication bias were considered (RR=1, RR=4 and RR=10), resulting in 36 simulation scenarios.
Second, there was some between study variability in conservative treatment regimens that clearly had an impact on the findings.
