Predictive distributions were developed for the extent of heterogeneity in meta-analyses of continuous outcome data

Abstract

Objectives: Estimation of between-study heterogeneity is problematic in small meta-analyses. Bayesian meta-analysis is beneficial because it allows incorporation of external evidence on heterogeneity. To facilitate this, we provide empirical evidence on the likely heterogeneity between studies in meta-analyses relating to specific research settings.

Study design and setting: Our analyses included 6,492 continuous-outcome meta-analyses within the Cochrane Database of Systematic Reviews. We investigated the influence of meta-analysis settings on heterogeneity by modeling study data from all meta-analyses on the standardized mean difference scale. Meta-analysis setting was described according to outcome type, intervention comparison type, and medical area. Predictive distributions for between-study variance expected in future meta-analyses were obtained, which can be used directly as informative priors.

Results: Among outcome types, heterogeneity was found to be lowest in meta-analyses of obstetric outcomes. Among intervention comparison types, heterogeneity was lowest in meta-analyses comparing two pharmacologic interventions. Predictive distributions are reported for different settings. In two example meta-analyses, incorporating external evidence led to a more precise heterogeneity estimate.

Conclusion: Heterogeneity was influenced by meta-analysis characteristics. Informative priors for between-study variance were derived for each specific setting. Our analyses thus assist the incorporation of realistic prior information into meta-analyses including few studies.

Keywords: Bayesian analysis; Continuous data; Heterogeneity; Intervention studies; Meta-analysis; Standardized mean difference.

Fig. 1

Examples of predictive t distributions for the between-study heterogeneity variance (plotted on the log scale). A vertical line highlights the probability of the variance being greater than 1. (A) Pharmacologic vs. placebo/control meta-analyses measuring an obstetric outcome. (B) Nonpharmacologic meta-analyses measuring resource use.

Fig. 2

Conventional and Bayesian random-effects meta-analyses combining standardized mean differences (SMDs); 95% confidence intervals (CIs) are shown for each study. (A) Example 1: four studies comparing exercise vs. control (no exercise or placebo exercise) with respect to depression in adults with chronic kidney disease. (B) Example 2: five studies to compare budesonide at different doses for chronic asthma.