## KEY TERMS

Meta-analysis

Meta-analysis is the statistical method for combining both qualitative and quantitative outcomes from multiple studies to draw statistically stronger conclusions. Researchers may want to use meta-analysis because of the greater statistical power it creates by means of having a larger number of subjects and results than any individual study. Meta-analysis also provides estimates of treatment effects, which can identify any asymmetries in the studies, such as publication bias and heterogeneity.

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Univariate vs. Multivariate meta-analysis

Univariate meta-analysis (UMA): Univariate meta-analysis is the process of aggregating multiple studies to better understand the effect of one outcome.

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Multivariate meta-analysis (MMA): Multivariate meta-analysis aggregates multiple studies to better understand the effect of multiple outcomes.

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Fixed effects vs. random effects meta-analysis model

Fixed effects meta-analysis model: The fixed-effect meta-analysis model is one of the two main methods of meta-analysis. This model assumes that the studies included in the meta-analysis come from a single homogeneous population and the observed heterogeneity is due to within-study variations. Under these assumptions, an overall estimate of the effect(s) can be calculated by simply averaging the studies’ estimates.

Random-effects meta-analysis model: The random-effects meta-analysis model is the other main method of meta-analysis. This model relies on the assumption that study effect estimates are often more variable than assumed in the fixed effects model, where observed heterogeneity is attributed to both within-study and between-study variation. This variability is captured by a normally distributed random variable with mean 0 and variance as the between-study heterogeneity.

Issues with meta-analysis

Heterogeneity in meta-analysis: There are two main types of heterogeneity that may occur in meta-analysis: clinical heterogeneity and statistical heterogeneity. Clinical heterogeneity arises from the way the study was conducted or designed, such as differences in patients, type of treatment intervention(s), and outcome definition(s). Statistical heterogeneity results from differences in the methods used to analyze the results of the studies. Heterogeneity may contribute to biased estimates and it may be identified using the forest plot visualization or statistical tests for heterogeneity such as Cochran’s Q test or the Index I .

Small study effect: The small study effect arises from the bias toward publishing studies with positive outcomes. This increased likelihood that small studies are published if their results are significant may skew the conclusions drawn from meta-analysis as the studies being pooled largely represent studies selected for their favorable results and larger effects.

Publication bias: Publication bias (PB) is the phenomenon that occurs when the outcome of a study influences the decision to publish it or not; typically, studies having favorable results are more likely to be published or submitted for approval than those with unfavorable results. The implications of PB in meta-analysis include drawing biased inferences from pooling potentially biased studies together, which may lead to observing an effect that does not reflect the true effect. Publication bias may be identified using the funnel plot visualization tool, the Trim and Fill method, and other techniques such as the Copas selection model and sensitivity analysis.

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