## Meta AnalysisJ. Sánchez-MecaF. Marín-Martínez, in International Encyclopedia of Education (Third Edition), 2010 - Meta Analysis
- Calculating an Average Effect Size
- Association Mapping in Crop Plants
- 6.4 Meta-analysis for GWAS
- Meta-analysis of Clinical Trials
- Evidence-Based Medicine
- SECONDARY STUDY DESIGN
- Meta-analysis
- Introduction
- External Validity
- Meta-Analysis
- Evidence and Hyperbaric Oxygen Therapy
- Meta-analysis
- A Worldwide Yearly Survey of New Data in Adverse Drug Reactions
- Arsenic-Related Keratotic Skin Lesions
- Video liên quan
## Calculating an Average Effect SizeThe statistical analyses in a meta-analysis are guided by a statistical model that must be previously assumed. The main task of the statistical model is to establish the properties of the effect-size population from which the individual effect-size estimates have been selected. To accomplish the first purpose in a meta-analysis, that is, to calculate an average effect size, two statistical models can be assumed: the fixed- and the random-effects models. Suppose there are k independent empirical studies about a given topic and Ti is the effect-size estimate obtained in the ith study (here Ti refers to any of the different effect-size indices presented above, both from the d and the r families.) In a fixed-effects model, it is assumed that all of the effect-size estimates come from a population with a common parametric effect size, θ, and as a consequence the only error source is that produced by sampling error, ei. Thus, the model can be formulated as Ti = θ + ei, the sampling errors, ei, being normally distributed with mean 0 and sampling variance σi2, ei N(0,σi2). Therefore, the effect-size estimates, Ti, are also normally distributed with mean θ and sampling variance σi2, Ti N(θ,σi2). In a random-effects model, it is assumed that the effect-size estimates, Ti, estimate different population effect sizes, θi, that is, Ti = θi + ei, and θi pertains to a distribution of parametric effect sizes with mean μ and variance τ2, usually called between-studies variance. The parametric effect sizes can be modeled as θi=μ+ϵi, ϵi being the errors of the parameters around its mean, μ. Therefore, the random-effects model is formulated as Ti = μ +εi + ei. Assuming normality, Ti has as mean μ and variance τ2+σi2,TiN(μ,τ2+σi2). Thus, the fixed-effects model can be considered a particular case of the random-effects model when the between-studies variance is zero (τ2=0) and, as a consequence, all the parametric effect sizes are equal (θ1 = θ2 = = θi = θ= μ). To calculate an average effect size from a set of studies, each effect-size estimate must be weighted by its precision. Both in a fixed- and a random-effects model, the uniformly minimum variance unbiased estimator (UMVUE) of the average effect size, μ, is that obtained by weighting each effect-size estimate by its inverse variance: [8]TUMVUE=i=1kwiTii=1kwi where wi is the optimal weight for the ith study and, depending on the statistical model assumed, it is defined as wiFE=1/σi2or as wiRE=1/(τ2+σi2), for the fixed- and the random-effects models, respectively. In practice, the optimal weights cannot be used, because the within-study sampling variances, σi2, and the between-studies variance, τ2, are unknown. For each effect-size index, formulas have been devised to estimate σi2and τ2. Thus, the estimated weights are defined as wˆiFE=1/σˆi2and wˆiRE=1/(τˆ2+σˆi2)for fixed- and random-effects models, respectively. (Another option consists of simply weighting each effect-size estimate by its sample size (Hunter and Schmidt, 2004).) Here σˆi2is the estimated within-study sampling variance for the ith study (e.g., eqn [4] for the d index), and τˆ2can be calculated by applying one of the different estimators of the between-studies variance proposed in the meta-analytic literature. The τ2 estimator most usually applied in meta-analysis is that based on the moments method: [9]τˆ2=Q(k1)c where k is the number of studies, Q is a heterogeneity statistic defined in eqn [17], and c is obtained by: [10]c=i=1kwˆiFEi=1k(wˆiFE)2i=1kwˆiFE When Q < (k 1), then τˆ2is negative and must be truncated to zero. Other τ2 estimators can be consulted in Viechtbauer (2005). With the respective estimated variances, the population effect size, μ, is then estimated by: [11]TFE=i=1kwˆiFETii=1kwˆiFE [12]TRE=i=1kwˆiRETii=1kwˆiRE for fixed- and random-effects models, respectively. When a fixed-effects model is assumed, TFE is approximately normally distributed and its sampling variance defined as: [13]V(TFE)=1/i=lkwˆiFE Thus, a confidence interval for the average effect size can be obtained by (cf. e.g., Cooper et al. 2009): [14]TFE±zα/2V(TFE) where zα/2 is the 100(α/2) percentile of the standard normal distribution and α is a significance level. Under a random-effects model, a better approach for obtaining a confidence interval for the overall effect size consists of assuming a Student t reference distribution with k 1 degrees of freedom, instead of the standard normal distribution: [15]TRE±tk1,α/2V(TRE) where tk-1,α/2 is the 100(α/2) percentile of the Student t distribution with k 1 degrees of freedom, and V(TRE) is an estimate of the sampling variance for TRE, which is obtained by (cf. Sánchez-Meca and Marín-Martínez, 2008) [16]V(TRE)=i=1kwˆiRE(TiTRE)2(k1)i=1kwˆiRE Alternative approaches to those presented in eqns [14] and [15] have been proposed (cf. e.g., Sánchez-Meca and Marín-Martínez, 2008). View chapterPurchase book Read full chapter URL:https://www.sciencedirect.com/science/article/pii/B9780080448947013452 ## Association Mapping in Crop PlantsPushpendra K. Gupta, ... Vandana Jaiswal, in Advances in Genetics, 2014 ## 6.4 Meta-analysis for GWASMeta-analysis combines information from multiple GWAS and can increase the chances of finding true positives among the identified associations (Cantor etal., 2010). Hundreds of studies involving GWAS meta-analysis have been published for humans (Evangelou & Ioannidis, 2013), but there seems to be no published report of meta-analysis for GWAS in plants. Therefore, it will be desirable to conduct meta-analysis using results of several GWAS involving the same trait in the same crop. While doing so, one should recognize that several factors may influence the results of GWAS meta-analysis. First, different studies may be based on heterogeneity in data, due to genetic and environmental factors, making interpretation of the results of meta-analysis difficult, although methods have been suggested to deal with this problem (Han & Eskin, 2012). Second, sample size and design may be different in different studies included in meta-analysis (Moonesinghe, Khoury, Liu, & Ioannidis, 2008; Spencer, Su, Donnelly, & Marchini, 2009). Third, some studies included in a meta-analysis may be based on imputed data, which should be taken into consideration (de Bakker etal., 2008). Fourth, meta-analysis for a complex trait involving rare variants may create some problems (Evangelou & Ioannidis, 2013). Some of these issues have also been addressed by Thompson, Attia, and Minelli (2011). View chapterPurchase book Read full chapter URL:https://www.sciencedirect.com/science/article/pii/B9780128002711000020 ## Meta-analysis of Clinical TrialsJunfeng Sun, ... Charles Natanson, in Principles and Practice of Clinical Research (Fourth Edition), 2018 ## AbstractMeta-analysis has become a popular approach for summarizing a large number of clinical trials and resolving discrepancies raised by these trials. In this chapter, we introduce the general procedures for meta-analysis: formulating the question, defining eligibility, identifying studies, abstracting data, statistical analysis, and reporting the results. One key issue determining whether studies can be combined is the extent of heterogeneity among individual studies. We review graphical and statistical tools for assessing heterogeneity, describing the fixed-effect and random-effect models commonly used in meta-analysis, and providing some general recommendations regarding when fixed-effect or random-effect approach is appropriate. Publication bias is an inherent issue with meta-analysis, since studies (especially smaller ones) with negative results are frequently unpublished. Funnel plot, Begg and Mazumdar's rank correlation, and Egger regression are useful tools for assessing publication bias. As an illustration of the concepts discussed, we apply meta-analysis techniques to studies examining the use of antiinflammatory therapies in sepsis. View chapterPurchase book Read full chapter URL:https://www.sciencedirect.com/science/article/pii/B9780128499054000228 ## Evidence-Based MedicineJohn V. White MD, Ginger Barthel RN, MA, FACHE, in Comprehensive Vascular and Endovascular Surgery (Second Edition), 2009 ## SECONDARY STUDY DESIGNMeta-analysis is an analytical tool that permits the evaluation of a diagnostic or therapeutic modality through the appropriate use of previously published smaller studies.21 Meta-analysis is not the simple pooling of data reported in numerous small studies, a notion that has often caused investigational errors. The simple pooling of data from multiple small studies often compounds biases and may further reduce the ability to detect important differences among study groups.22 A meta-analysis of available data is a rigorous, systematic, and quantitative review. To undertake a meta-analysis to address a research question or hypothesis, the investigator must first define the appropriate study population and methodology. The literature is then reviewed exhaustively for the identification of all relevant studies that meet the established criteria. These studies are then evaluated critically to determine and correct for possible bias in data collection. Reports in which data collection did not adhere to the established meta-analysis criteria, or in which an unquantified bias was introduced, are not included. The raw data from the selected studies are then combined and analyzed. This methodology permits the detection of statistically significant differences among study groups that may not have been possible in individual reports due to their small size. View chapterPurchase book Read full chapter URL:https://www.sciencedirect.com/science/article/pii/B9780323057264000056 ## Meta-analysisJulien I.E. Hoffman, in Biostatistics for Medical and Biomedical Practitioners, 2015 ## IntroductionMeta-analysis is a set of techniques used to combine the results of a number of different reports into one report to create a single, more precise estimate of an effect (Ferrer, 1998). The aims of meta-analysis are to increase statistical power; to deal with controversy when individual studies disagree; to improve estimates of size of effect, and to answer new questions not previously posed in component studies (Hunter and Schmidt, 1990). All definitions stress that there must be a valid reason to combine the studies. Egger etal. (2002) wrote Indeed, it is our impression that reviewers often find it hard to resist the temptation of combining studies when such meta-analysis is questionable or clearly inappropriate. Although the frequency at which meta-analysis is used isincreasing (Egger and Smith, 1997), meta-analysis has its detractors. In reality, if carefully performed, it yields useful information, but a meta-analysis of badly designed studies produces erroneous statistics and may be misleading. Ignoring heterogeneity and combining apples and oranges is a pervasive error in meta-analysis (Eysenck, 1995) and techniques exist to assess it (Ferrer, 1998; Tang and Liu, 2000). Other forms of bias also interfere with effective meta-analysis (Egger and Smith, 1998). There are several advantages to meta-analysis. It allows investigators to pool data from many trials that are too small by themselves to allow for secure conclusions. Although ideally any clinical trial should plan an adequate sample size, historically most trials have been underpowered. In 2002, a study of 5503 clinical trials (McDonald etal., 2002) identified 69% as having fewer than 100 subjects. Small trials make it more difficult to reject the null hypothesis because they lead to larger standard deviations and standard errors. There is also a risk of bias. A small trial that does not show a significant effect might not be submitted for publication, whereas the same sized trial that reached significance (whether warranted or not) will probably be published (Stern and Simes, 1997). Eggeretal. (2002) concluded that on average unpublished trials underestimate treatment effects by 10%. Furthermore, Stanbrook etal. (2006) found that clinical trials named with an acronym were more likely to be published in a major journal or to be cited than trials not named, independent of whether the results were positive or negative. View chapterPurchase book Read full chapter URL:https://www.sciencedirect.com/science/article/pii/B9780128023877000366 ## External ValidityG.E. Matt, ... M. Sklar, in International Encyclopedia of Education (Third Edition), 2010 ## Meta-AnalysisMeta-analysis combines findings from many different yet related studies to foster empirical knowledge about causal associations that are more trustworthy than those possible from any single study. This benefit arises for two main reasons. First, combining findings from parallel studies promises to increase statistical power and precision for estimating the magnitude of a causal association. More importantly, however, is the potential of meta-analysis to strengthen external validity by identifying the realm of application of a causal association that is, meta-analyses are most useful when they allow us to examine whether a causal association (1) holds with specific populations of persons, settings, times, and ways of varying the cause or measuring the effect; (2) holds across different populations of people, settings, times, and ways of operationalizing a cause and effect; and (3) can even be extrapolated to other populations of people, settings, times, causes, and effects than those that have been studied to date that is, meta-analyses offer opportunities to probe external validity questions 1, 2, and 3. In 1978, Glass and Smith published a noteworthy meta-analysis examining the relationship between class-size and academic achievement an issue that was previously surrounded by inconclusive research findings. This meta-analysis synthesized the results of 77 separate studies that included 725 comparisons of academic achievement in smaller versus larger classes. It received considerable attention because it was the first meta-analysis to find clear evidence that reduced student-to-instructor ratios significantly improved academic achievement (Cooper, 1989). Examples from this meta-analysis will be presented to illustrate how Cooks five principles justify generalization in the absence of formal sampling. View chapterPurchase book Read full chapter URL:https://www.sciencedirect.com/science/article/pii/B9780080448947017000 ## Evidence and Hyperbaric Oxygen TherapyMichael H. Bennett MBBS, MD, MM(Clin Epi), FANZCA, ... Herbert B. Newton MD, FAAN, in Physiology and Medicine of Hyperbaric Oxygen Therapy, 2008 ## Meta-analysisMeta-analysis is the quantitative analysis of the results included in an SR. In practice, this implies the combination of the results of several individual clinical trials using specialized statistical methodology. Such analyses are essentially observational, using trials as the unit of enrollment rather than individual patients. Although there is some room for dispute, most authorities agree that such analysis is likely to have high validity only if the individual trials are randomized controlled trials (RCTs). Although meta-analyses of cohort trials are not uncommon, the conclusions to be drawn from such reviews remain unclear.24 If the included trials are subject to bias, then any meta-analysis is similarly subject to bias. The strength of meta-analysis lies in the ability to summarize a large volume of literature in a single publication and to produce clinically relevant conclusions. Meta-analysis can generate sufficient power from a series of smaller trials to answer important clinical questions. In the absence of meta-analysis, the combination of a series of small trials with low individual power can lead to confusion about appropriate therapeutic decisions. Prior experience suggests that meta-analysis might not only make the evidence clear and unequivocal, but also avoid unnecessary and wasteful repetition of research performed in the belief that the truth is not yet evident. A good example is that described by Lau and colleagues5 concerning trials of the use of streptokinase for the prevention of myocardial infarction. Lau found 33 such trials executed between 1959 and 1988. The authors performed a cumulative meta-analysis, repeating analysis with each study chronologically by publication date, and found a consistent and significant reduction in mortality with the use of streptokinase had already been found by 1973 (odds ratio [OR], 0.74; 95% confidence interval [CI], 0.590.92). At that time only eight trials involving 2432 subjects were available for analysis. The results of the 25 subsequent trials, enrolling an additional 34,542 patients, through 1988 had little or no effect on the OR. All those trial subjects had contributed limited information concerning the efficacy of streptokinase. View chapterPurchase book Read full chapter URL:https://www.sciencedirect.com/science/article/pii/B9781416034063500263 ## A Worldwide Yearly Survey of New Data in Adverse Drug ReactionsDeepa Patel, ... Vicky V. Mody, in Side Effects of Drugs Annual, 2016 ## Arsenic-Related Keratotic Skin LesionsMeta-Analysis In this study the meta-analysis of 54913 participants in all included 14 trials, all double-blinded, with a mean age ranging from 52 to 68.9 years [19R]. All trials has combined intervention with B vitamins, except one study which had only folic acid as the intervention. In the study reporters noted a reduction in overall stroke events resulting from lowered homocysteine levels following B vitamin supplementation (RR, 0.93; 95% CI, 0.861.00; P=0.04). However, the findings showed that taking vitamin B supplements did not reduce the severity of strokes or the risk of death. The researchers found that a supplemental form of folate (vitamin B9), a vitamin frequently found in fortified cereals, actually reduced the effect of vitamin B on the risk of stroke. The effect of B vitamins supplementation is influenced by many factors such as status of absorption, response to vitamin supplementation, the existence of chronic kidney disease, or high blood pressure. The study revealed that patients with chronic kidney disease reported decreased glomerular filtration rate with B vitamin supplements. As for analyses specific to vitamin B12, the report did not find significant benefit for reduction of stroke events in subgroups according to intervention dose, reduction of homocysteine level, or baseline blood vitamin B12 concentration [19R]. View chapterPurchase book Read full chapter
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