A basic introduction to fixed and random effects models for meta-analysis

Research Synthesis Methods 04/2010; 1(2):97 - 111. DOI: 10.1002/jrsm.12


There are two popular statistical models for meta-analysis, the fixed-effect model and the random-effects model. The fact that these two models employ similar sets of formulas to compute statistics, and sometimes yield similar estimates for the various parameters, may lead people to believe that the models are interchangeable. In fact, though, the models represent fundamentally different assumptions about the data. The selection of the appropriate model is important to ensure that the various statistics are estimated correctly. Additionally, and more fundamentally, the model serves to place the analysis in context. It provides a framework for the goals of the analysis as well as for the interpretation of the statistics. In this paper we explain the key assumptions of each model, and then outline the differences between the models. We conclude with a discussion of factors to consider when choosing between the two models. Copyright © 2010 John Wiley & Sons, Ltd.
Copyright © 2010 John Wiley & Sons, Ltd.

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    • "In this calculation, a positive score referred to a benefit from the therapy and a negative one to worsened performance after therapy. The calculations were based upon a random effects model, for which the T ES were supposed to vary between studies [48]. The statistical significance level for T ES was set at p < 0.05 in our analyses. "
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    • "In meta-analytic practice, it is often of interest to perform model selection (e.g., Sutton, 2000, Section 11.7.3). For example, model selection is used in meta-analysis to choose between the fixed-effects and randomeffects model (Borenstein et al. 2010), or to select important predictors of the effect-size in a regression setting (Higgins & Thompson, 2004). After M meta-analytic models are fit to a data set, D n , the predictive performance of each Bayesian model m ∈ {1, . . . "
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    ABSTRACT: In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal effect-size population distribution, conditionally on parameters and covariates. For estimating the mean overall effect size, such models may be adequate, but for prediction, they surely are not if the effect-size distribution exhibits non-normal behavior. To address this issue, we propose a Bayesian nonparametric meta-analysis model, which can describe a wider range of effect-size distributions, including unimodal symmetric distributions, as well as skewed and more multimodal distributions. We demonstrate our model through the analysis of real meta-analytic data arising from behavioral-genetic research. We compare the predictive performance of the Bayesian nonparametric model against various conventional and more modern normal fixed-effects and random-effects models. Copyright © 2014 John Wiley & Sons, Ltd. Copyright © 2014 John Wiley & Sons, Ltd.
    Full-text · Article · Mar 2015 · Research Synthesis Methods
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    • "The metaanalyses were performed using a random effects model to account for the heterogeneity between the trials included. The random effects model allowed for a distribution of true effect size (see, e.g., Borenstein et al., 2010). Our goal was to estimate the mean of this distribution. "
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    ABSTRACT: Aims: We investigate the effect of motivational interviewing (MI), delivered in a brief intervention during an emergency care contact, on the alcohol consumption of young people who screen positively for present or previous risky alcohol consumption. Methods: MEDLINE, CINAHL, EMBASE, PsycARTICLES, PsycINFO, PSYNDEX and Scopus were searched for randomized controlled trials with adolescents or young adults that compared MI in an emergency care setting to control conditions and measured drinking outcomes. Results: Six trials with 1433 participants, aged 13-25 years, were included in the systematic review and meta-analysis. MI was never less efficacious than a control intervention. Two trials found significantly more reduction in one or more measures of alcohol consumption in the MI intervention group. One trial indicated that MI may be used most effectively in young people with high-volume alcohol consumption. Separate random effects meta-analyses were performed based on the highest impact that MI added on reducing the drinking frequency and the drinking quantity at any point in time during the different study periods. Their results were expressed as standardized mean differences (SMDs). The frequency of drinking alcohol decreased significantly more after MI than after control interventions (SMD ≤ -0.17, P ≤ 0.03). In addition, MI reduced the drinking quantity further than control interventions in a meta-analysis of the subset of trials that were implemented in the USA (SMD = -0.12, P = 0.04). Meta-analyses of the smallest mean differences between MI and control groups detected no differences in alcohol use (SMD ≤ 0.02, P ≥ 0.38). Conclusion: MI appears at least as effective and may possibly be more effective than other brief interventions in emergency care to reduce alcohol consumption in young people.
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