How to interpret meta-analysis models: fixed effect and random effects meta-analyses

2014 ◽  
Vol 17 (2) ◽  
pp. 64-64 ◽  
Author(s):  
Adriani Nikolakopoulou ◽  
Dimitris Mavridis ◽  
Georgia Salanti
Keyword(s):  
Random Effects ◽  
Meta Analysis ◽  
Fixed Effect ◽  
Meta Analyses ◽  
Analysis Models

Meta-Analysis of Meta-Analyses in Communication: Comparing Fixed Effects and Random Effects Analysis Models

2010 ◽  
Vol 58 (3) ◽  
pp. 257-278 ◽  
Author(s):  
Ashley Anker ◽  
Amber Marie Reinhart ◽  
Thomas Hugh Feeley
Keyword(s):  
Random Effects ◽  
Fixed Effects ◽  
Meta Analysis ◽  
Meta Analyses ◽  
Analysis Models

scholarly journals A Primer on Bayesian Model-Averaged Meta-Analysis

2020 ◽  
Author(s):  
Quentin Frederik Gronau ◽  
Daniel W. Heck ◽  
Sophie Wilhelmina Berkhout ◽  
Julia M. Haaf ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Random Effects ◽  
Null Hypothesis ◽  
Bayesian Model ◽  
Alternative Hypothesis ◽  
Meta Analysis ◽  
Fixed Effect ◽  
Random Effects Model ◽  
Psychological Science ◽  
Analysis Models ◽  
Key Questions

Meta-analysis is the predominant approach for quantitatively synthesizing a set of studies. If the studies themselves are of high quality, meta-analysis can provide valuable insights into the current scientific state of knowledge about a particular phenomenon. In psychological science, the most common approach is to conduct frequentist meta-analysis. In this primer, we discuss an alternative method, Bayesian model-averaged meta-analysis. This procedure combines the results of four Bayesian meta-analysis models: (1) fixed-effect null hypothesis, (2) fixed-effect alternative hypothesis, (3) random-effects null hypothesis, and (4) random-effects alternative hypothesis. These models are combined according to their plausibilities in light of the observed data to address the two key questions "Is the overall effect non-zero?" and "Is there between-study variability in effect size?". Bayesian model-averaged meta-analysis therefore avoids the need to select either a fixed-effect or random-effects model and instead takes into account model uncertainty in a principled manner.

scholarly journals metamicrobiomeR: an R package for analysis of microbiome relative abundance data using zero-inflated beta GAMLSS and meta-analysis across studies using random effect models

2018 ◽  
Author(s):  
Nhan Thi Ho ◽  
Fan Li
Keyword(s):  
Random Effects ◽  
High Throughput ◽  
Relative Abundance ◽  
High Throughput Sequencing ◽  
Meta Analysis ◽  
R Package ◽  
Standard Errors ◽  
Relative Abundances ◽  
Meta Analyses ◽  
Analysis Models

ABSTRACTBackgroundThe rapid growth of high-throughput sequencing-based microbiome profiling has yielded tremendous insights into human health and physiology. Data generated from high-throughput sequencing of 16S rRNA gene amplicons are often preprocessed into composition or relative abundance. However, reproducibility has been lacking due to the myriad of different experimental and computational approaches taken in these studies. Microbiome studies may report varying results on the same topic, therefore, meta-analyses examining different microbiome studies to provide robust results are important. So far, there is still a lack of implemented methods to properly examine differential relative abundances of microbial taxonomies and to perform meta-analysis examining the heterogeneity and overall effects across microbiome studies.ResultsWe developed an R package ‘metamicrobiomeR’ that applies Generalized Additive Models for Location, Scale and Shape (GAMLSS) with a zero-inflated beta (BEZI) family (GAMLSS-BEZI) for analysis of microbiome relative abundance datasets. Both simulation studies and application to real microbiome data demonstrate that GAMLSS-BEZI well performs in testing differential relative abundances of microbial taxonomies. Importantly, the estimates from GAMLSS-BEZI are log(odds ratio) of relative abundances between groups and thus are comparable between microbiome studies. As such, we also apply random effects meta-analysis models to pool estimates and their standard errors across microbiome studies. We demonstrate the meta-analysis workflow and highlight the utility of our package on four studies comparing gut microbiomes between male and female infants in the first six months of life.ConclusionsGAMLSS-BEZI allows proper examination of microbiome relative abundance data. Random effects meta-analysis models can be directly applied to pool comparable estimates and their standard errors to evaluate the heterogeneity and overall effects across microbiome studies. The examples and workflow using our metamicrobiomeR package are reproducible and applicable for the analyses and meta-analyses of other microbiome studies.

scholarly journals Metaanalyse

2013 ◽  
Vol 23 (2) ◽  
Author(s):  
Geir Smedslund
Keyword(s):  
Random Effects ◽  
Effect Size ◽  
Meta Analysis ◽  
Large Body ◽  
Fixed Effect Model ◽  
English Summary ◽  
Fixed Effect ◽  
Effect Estimate ◽  
Study Results ◽  
Meta Analyses

<p>Metaanalyse er en kvantitativ metode for å oppsummere resultatene av flere enkeltstudier. I en metaanalyse forsøker man å tallfeste behandlingseffekten, og man gir store studier større vekt enn små studier. En mye brukt metode for å vekte er invers variansmetoden. Dersom alle studiene har målt resultatene på samme måte kan resultatene brukes direkte i metaanalysen, men dersom det samme utfallet er målt på ulike måter, må man bruke standardiserte effektstørrelser hvor alle resultatene er omregnet til en felles skala. Dersom man tror at effekten av behandlingen vil være lik for alle, bortsett fra tilfeldige variasjoner, benytter man en fixed-effect modell. Tror man derimot at det vil være systematiske forskjeller i effekt når behandlingen gis i ulike kontekster, legges dette inn i en såkalt random-effects modell. Metaanalyser blir ofte fremstilt grafisk i form av forest plots. Hver linje representerer da én studie, med effektestimatet markert som et punkt, mens ytterpunktene av linjen representerer konfidensintervallet. Metaanalysen blir fremstilt som en diamant hvor bredden viser usikkerheten i estimatet. Dersom resultatene fra alle studiene trekker i samme retning er metaanalysen ”homogen”. Men dersom studiene spriker når det gjelder effektstørrelse og retning på effekt, er det ”heterogenitet”. Styrken ved metaanalyse er at den kan sammenfatte en stor mengde informasjon i ett tall. Samtidig er dette også svakheten ved metoden. Et enkelt tall kan ikke beskrive variasjonen på tvers av flere studier.</p><p>Smedslund G. <strong>Meta-analysis.</strong> <em>Nor J Epidemiol</em> 2013; <strong>23 </strong>(2): 147-149.</p><p><strong>ENGLISH SUMMARY </strong></p><p>Meta-analysis is a quantitative method for summarizing single studies. In a meta-analysis, one tries to quantify the treatment effect, assigning more weight to large studies than to small studies. A much used method for weighting is the inverse variance method. If all studies have measured the results in the same way, the results can be used directly in the meta-analysis, but if the same outcome is measured in different ways across different studies, one has to use a standardized effect size where results are converted to a common scale. If it is believed that the effect is consistent across various populations and settings, one can employ a fixed-effect model. If systematic differences in effect can be expected, a random-effects model is used. Meta-analyses are often depicted as forest plots. Each line represents one study where the effect estimate is marked as a point on a line, with each end of the line representing the confidence interval around it. The meta-analysis is shown as a diamond where the width illustrates the uncertainty around the estimate. If all study results point in the same direction, the meta-analysis is considered “homogeneous”. But if the studies vary in their effect size and direction, the findings are “heterogeneous”. The strength of meta-analysis is that it can be used to summarize a large body of information in one number. This is also its limitation. One number cannot describe the variation that exists across different studies.</p>

scholarly journals Meta-analysis: How to quantify and explain heterogeneity?

2020 ◽  
Vol 19 (7) ◽  
pp. 646-652
Author(s):  
Todd Ruppar
Keyword(s):  
Random Effects ◽  
Systematic Reviews ◽  
Allied Health ◽  
Meta Analysis ◽  
Fixed Effect ◽  
Analysis Model ◽  
The Common ◽  
Meta Analyses

The number of systematic reviews and meta-analyses submitted to nursing and allied health journals continues to grow. Well-conducted and reported syntheses of research are valuable to advancing science. One of the common critiques identified in these manuscripts involves how the authors addressed heterogeneity among the studies in their meta-analyses. Methodologically inappropriate approaches regarding heterogeneity introduce error and bias into analyses and may lead to incorrect findings and conclusions. This article will discuss some of the approaches to take as well as avoid when addressing heterogeneity in meta-analyses, including suggestions for how to choose a fixed-effect or random-effects meta-analysis model and steps to follow to address heterogeneity in meta-analysis results.

Abstract P343: Comparison of Two-stage and One-stage Meta-analyses: An Example of eGFR-Cardiovascular Mortality Association (for CKD-PC collaborators)

Circulation ◽  
2012 ◽  
Vol 125 (suppl_10) ◽  
Author(s):  
Yingying Sang ◽  
Kunihiro Matsushita ◽  
Bakhtawar K Mahmoodi ◽  
Brad C Astor ◽  
Josef Coresh ◽  
...  
Keyword(s):  
Random Effects ◽  
Cardiovascular Mortality ◽  
Cox Model ◽  
Meta Analysis ◽  
Fixed Effect ◽  
Two Stage ◽  
Statistical Estimates ◽  
One Stage ◽  
Individual Participant ◽  
Meta Analyses

Purpose: Individual participant data (IPD) meta-analysis provides precise statistical estimates. Two approaches to meta-analyze IPD are currently used. The 1-stage approach fits a regression model to a pooled dataset including all studies. The 2-stage approach fits models in individual studies and meta-analyzes the estimates. However, their comparability has not been well described. We compare these methods for eGFR-cardiovascular mortality association in the CKD Prognosis Consortium (CKD-PC). Methods: For the 1-stage method, we fitted a Cox stratified model, allowing each study to have a unique baseline hazard but assuming a common hazard ratio (HR) for eGFR across studies. For the 2-stage method, we first fitted a Cox model in each study, and then meta-analyzed HRs using a fixed-effect (assuming one true HR for eGFR across studies) and a random-effects (allowing some variance of true HR) model. eGFR was fitted as linear splines in all models. Results: In a sample of 18 of 46 cohorts joining CKD-PC (191,276 participants and 8,732 cardiovascular deaths [CHD, stroke, or heart failure]), these methods gave nearly identical estimates except for the width of the confidence intervals ( Figure ). The 95% CIs were wider as methods made fewer assumptions - narrowest for 1-stage method, slightly wider for the fixed-effect 2-stage and wider for the random-effects 2-stage method. Conclusion: The two-stage and one-stage meta-analyses provided nearly identical estimates for the eGFR-cardiovascular mortality relationship. The random-effects 2-stage method will provide conservative estimates with wider 95% CIs but this is necessary in the presence of heterogeneity.

scholarly journals A Primer on Bayesian Model-Averaged Meta-Analysis

2021 ◽  
Vol 4 (3) ◽  
pp. 251524592110312
Author(s):  
Quentin F. Gronau ◽  
Daniel W. Heck ◽  
Sophie W. Berkhout ◽  
Julia M. Haaf ◽  
Eric-Jan Wagenmakers
Keyword(s):  
Random Effects ◽  
Null Hypothesis ◽  
Bayesian Model ◽  
Alternative Hypothesis ◽  
Meta Analysis ◽  
Fixed Effect ◽  
Random Effects Model ◽  
Psychological Science ◽  
Analysis Models ◽  
Key Questions

Meta-analysis is the predominant approach for quantitatively synthesizing a set of studies. If the studies themselves are of high quality, meta-analysis can provide valuable insights into the current scientific state of knowledge about a particular phenomenon. In psychological science, the most common approach is to conduct frequentist meta-analysis. In this primer, we discuss an alternative method, Bayesian model-averaged meta-analysis. This procedure combines the results of four Bayesian meta-analysis models: (a) fixed-effect null hypothesis, (b) fixed-effect alternative hypothesis, (c) random-effects null hypothesis, and (d) random-effects alternative hypothesis. These models are combined according to their plausibilities given the observed data to address the two key questions “Is the overall effect nonzero?” and “Is there between-study variability in effect size?” Bayesian model-averaged meta-analysis therefore avoids the need to select either a fixed-effect or random-effects model and instead takes into account model uncertainty in a principled manner.

Meta-analysis of effect sizes reported at multiple time points: A multivariate approach

2012 ◽  
Vol 9 (5) ◽  
pp. 610-620 ◽  
Author(s):  
Thomas A Trikalinos ◽  
Ingram Olkin
Keyword(s):  
Random Effects ◽  
Treatment Effects ◽  
Multivariate Analyses ◽  
Meta Analysis ◽  
Effect Sizes ◽  
Multiple Time ◽  
Time Points ◽  
Fixed And Random Effects ◽  
Multiple Time Points ◽  
Meta Analyses

Background Many comparative studies report results at multiple time points. Such data are correlated because they pertain to the same patients, but are typically meta-analyzed as separate quantitative syntheses at each time point, ignoring the correlations between time points. Purpose To develop a meta-analytic approach that estimates treatment effects at successive time points and takes account of the stochastic dependencies of those effects. Methods We present both fixed and random effects methods for multivariate meta-analysis of effect sizes reported at multiple time points. We provide formulas for calculating the covariance (and correlations) of the effect sizes at successive time points for four common metrics (log odds ratio, log risk ratio, risk difference, and arcsine difference) based on data reported in the primary studies. We work through an example of a meta-analysis of 17 randomized trials of radiotherapy and chemotherapy versus radiotherapy alone for the postoperative treatment of patients with malignant gliomas, where in each trial survival is assessed at 6, 12, 18, and 24 months post randomization. We also provide software code for the main analyses described in the article. Results We discuss the estimation of fixed and random effects models and explore five options for the structure of the covariance matrix of the random effects. In the example, we compare separate (univariate) meta-analyses at each of the four time points with joint analyses across all four time points using the proposed methods. Although results of univariate and multivariate analyses are generally similar in the example, there are small differences in the magnitude of the effect sizes and the corresponding standard errors. We also discuss conditional multivariate analyses where one compares treatment effects at later time points given observed data at earlier time points. Limitations Simulation and empirical studies are needed to clarify the gains of multivariate analyses compared with separate meta-analyses under a variety of conditions. Conclusions Data reported at multiple time points are multivariate in nature and are efficiently analyzed using multivariate methods. The latter are an attractive alternative or complement to performing separate meta-analyses.

Alternative Tendon Coaptations to the Pulvertaft Weave Technique: A Systematic Review and Meta-Analysis of Biomechanical Studies

Hand ◽  
2021 ◽  
pp. 155894472110432
Author(s):  
Emily M. Graham ◽  
Jeremie D. Oliver ◽  
Russell Hendrycks ◽  
Dino Maglic ◽  
Shaun D. Mendenhall
Keyword(s):  
Systematic Review ◽  
Yield Strength ◽  
Random Effects ◽  
Meta Analysis ◽  
Dichotomous Data ◽  
Inverse Variance ◽  
Significant Difference ◽  
Alternative Techniques ◽  
Meta Analyses

Background The Pulvertaft weave technique (PT) is frequently used during tendon repairs and transfers. However, this technique is associated with limitations. In this systematic review and meta-analysis, quantitative and qualitative analyses were performed on in vitro, biomechanical studies that compared the PT with alternative techniques. Methods Articles included for qualitative and/or qualitative analysis were identified following Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. Studies included in the meta-analysis were analyzed either as continuous data with inverse variance and random effects or as dichotomous data using a Mantel-Haenszel analysis assuming random effects to calculate an odds ratio. Results A comprehensive electronic search yielded 8 studies meeting inclusion criteria for meta-analysis. Two studies with a total of 65 tendon coaptations demonstrated no significant difference in strength between the PT and traditional side-to-side (STS) techniques ( P = .92). Two studies with a total of 43 tendon coaptations showed that the STS with 1 weave has a higher yield strength than the PT ( P = .03). Two studies with a total of 62 tendon repairs demonstrated no significant difference in strength between the PT and the step-cut (SC) techniques ( P = .70). The final 2 studies included 46 tendon repairs and demonstrated that the wrap around (WA) technique has a higher yield strength than the PT ( P < .001). Conclusions The STS, SC, and WA techniques are preferred for improving tendon form. The STS and WA techniques have superior yield strengths than the PT, and the SC technique withstands similar stress to failure as the PT.

scholarly journals Interval estimation of the overall treatment effect in random-effects meta-analyses: Recommendations from a simulation study comparing frequentist, Bayesian, and bootstrap methods

2020 ◽  
Author(s):  
Frank Weber ◽  
Guido Knapp ◽  
Anne Glass ◽  
Günther Kundt ◽  
Katja Ickstadt
Keyword(s):  
Literature Review ◽  
Random Effects ◽  
Simulation Study ◽  
Treatment Effect ◽  
Profile Likelihood ◽  
Meta Analysis ◽  
Artery Bypass ◽  
Interval Length ◽  
Interval Estimators ◽  
Meta Analyses

There exists a variety of interval estimators for the overall treatment effect in a random-effects meta-analysis. A recent literature review summarizing existing methods suggested that in most situations, the Hartung-Knapp/Sidik-Jonkman (HKSJ) method was preferable. However, a quantitative comparison of those methods in a common simulation study is still lacking. Thus, we conduct such a simulation study for continuous and binary outcomes, focusing on the medical field for application.Based on the literature review and some new theoretical considerations, a practicable number of interval estimators is selected for this comparison: the classical normal-approximation interval using the DerSimonian-Laird heterogeneity estimator, the HKSJ interval using either the Paule-Mandel or the Sidik-Jonkman heterogeneity estimator, the Skovgaard higher-order profile likelihood interval, a parametric bootstrap interval, and a Bayesian interval using different priors. We evaluate the performance measures (coverage and interval length) at specific points in the parameter space, i.e. not averaging over a prior distribution. In this sense, our study is conducted from a frequentist point of view.We confirm the main finding of the literature review, the general recommendation of the HKSJ method (here with the Sidik-Jonkman heterogeneity estimator). For meta-analyses including only 2 studies, the high length of the HKSJ interval limits its practical usage. In this case, the Bayesian interval using a weakly informative prior for the heterogeneity may help. Our recommendations are illustrated using a real-world meta-analysis dealing with the efficacy of an intramyocardial bone marrow stem cell transplantation during coronary artery bypass grafting.

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