Meta-analysis
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IntroductionSee Major clinical studies & trial types and Systematic reviews A meta-analysis is a method used to pool the results of various clinical research studies quantitatively after the systematic reviews. A meta-analysis provides a precise estimate of treatment effect and gives weight to the different studies included. Its validity depends on the quality of the studies included in the review. Good meta-analyses strive to account for all relevant studies, look for heterogeneity and the robust nature of findings. Karl Pearson performed the first meta-analysis in 1904. Pearson wanted to overcome reduced statistical power in studies with small sample sizes. He analyzed the results from a group of studies and concluded that a new piece of research could be created to allow for more accuracy. Although meta-analysis is now widely used in medicine, its use did not come into effect until 1955. Sophisticated techniques were introduced in educational research in the 1970s. Uses in modern biomedicineThe results from different biomedical studies investigating different variables will be measured on different scales in the meta-analysis. The dependent variable is a standard measure of effect size; to describe the results of comparative experiments the effect size is the standard mean difference (d). This standard score is equivalent to the difference between means or an odds ratio if the outcome of the experiments is a dichotomous variable (success versus failure). A meta-analysis can be performed on studies that describe findings in correlation coefficients - for example, studies of the correlation between familial relationships and intelligence where the correlation is an indicator of effect size. Meta-analysis is not restricted to situations where one or more variables are defined as "dependent." For example, a meta-analysis can be performed on a pool of studies each of which estimates the incidence of left-handedness in various groups of people. Researchers should be aware that variations in sampling may introduce heterogeneity - or, the presence of more than one variation in the study. Where studies use 30mg of a drug and others 50mg, we might expect two clusters to be seen in the data each varying around the mean of one dosage or the other. This can be modelled using a "random effects model." Results from studies are combined using different approaches. One approach used is called 'inverse variance method'. The average effect size across all studies is computed as a weighted mean where weights are equal to the inverse variance of each studies' effect estimator. Larger studies and studies with less variation are given greater weight than smaller studies. Weighting, and effect sizesA recent method of studying the influence that weighting schemes have on results was proposed through a construct called gravity, which is a special case of combinatorial analysis. Modern meta-analysis goes beyond combining effect sizes of a set of studies. It tests if those studies' outcomes show more variation than what is expected due to sampling different research participants. If that is the case, study characteristics such as measurement instruments used, populations sampled or aspects of the studies' design are coded. These are then used as predictor variables to analyze the excess variation in effect sizes. Some of the methodological weaknesses of studies can be corrected statistically; for example, it is possible to correct effect sizes or correlations for the downward bias due to measurement error or restriction on score ranges. Meta-analysis leads to a shift of emphasis from single to multiple studies. It emphasizes the practical importance of the effect size instead of the statistical significance of individual studies. This shift in thinking has been termed meta-analytic thinking. The results of a meta-analysis are often shown using a forest plot. Trial qualityOne weakness of meta-analysis is that sources of bias are hard to control. A good meta-analysis of poorly-designed studies will still result in a set of unreliable numbers. Slavin has argued that methodologically sound studies are preferable for meta-analyses, a practice he calls 'best evidence meta-analysis'. However, other meta-analysts include weaker studies, adding a study-level predictor variable to reflect the quality of studies included. This is to examine the effect of study quality on effect size. A second weakness is the heavy reliance on published studies, which may increase effect. However, it is easier to publish studies that show significant results. Publication bias or "file-drawer effect" (where non-significant studies end up in desk drawers rather than in the public domain) must be considered in interpreting outcomes. Where publication bias is likely, some meta-analyses include a "failsafe N" statistic that calculates the number of studies with null results that needs to be added in order for the treatment effect to be unreliable. See also
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