Meta analysis essentials
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Meta Analysis Essentials provides an overview of meta-analysis techniques. Meta-analysis allows researchers to synthesize and aggregate results from different studies on the same topic to obtain more consistent statistics. It requires restructuring collected study materials. Meta-analyses typically compare one or two groups and estimate an effect size for each study. Estimates can be obtained using standard, random effects, or mixed effects models, with the latter two accounting for potential heterogeneity across studies. Conducting a meta-analysis requires input data on study details, measures, and results to estimate effect sizes and assess heterogeneity. Tools like R can be used to perform the analyses and generate outputs.
Meta analysis essentials
- 1. Meta Analysis Essentials Giorgio Alfredo Spedicato Ph.D FCAS FSA CSPA CStat
- 2. Intro • Technique to synthetize and aggregate different studies on the same topic(s). • Obtain more consistent statistics (𝜃𝑖, effect sizes) consolidating results from different samples. • Require tidily restructure of collected materials.
- 3. Possible θ Typically one or two groups are compared in each considered study i, where an effect size of 𝑦𝑖 = 𝜃𝑖 + ⋯ is observed: • Individual data: raw mean, proportions / probabilities, incidence ratios; • Correlation indices; • Pairwise data: pairwise mean difference, odds ratios,…
- 4. Possible approaches 1. Standard model: 𝑦𝑖 = 𝜃𝑖 + 𝜀𝑖 (no heterogeneity across studies) 2. Random effect model:𝜃𝑖 = 𝜇𝑖 + 𝑢𝑖, 𝑢𝑖~𝑁 0, 𝜏 3. Mixed effect model: 𝜃𝑖 = 𝑓(𝑥𝑖) + 𝑢𝑖
- 5. Possible approaches • Latter two models assume that structural heterogeneity exists either unexplicable or explicable adding covariates (xi), at least partially. • Testing for RANDOM EFFECT: • I2: percentage of variance due to structural heterogeneity across studies; • Q statistic (χ2) distributed • Testing for MIXED EFFECTS: • QM (moderators effect) and QE (residual heterogeneity) statistics;
- 6. Data requirements & Tools The input database should contain: 1. Paper id 2. Type of measure 3. Possible covariates 4. All data required for the θ of the study. E.g.: 1. Independent sample t-test: x, s and n for treatment and control groups 2. Raw means: x, s and n for the group 5. Possible tools: 1. Ad. Hoc software 2. R Statistical software specific packages (metafor)
- 8. References • Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. J Stat Softw, 36(3), 1-48. • Schoonjans, F. R. A. N. K., Zalata, A., Depuydt, C. E., & Comhaire, F. H. (1995). MedCalc: a new computer program for medical statistics. Computer methods and programs in biomedicine, 48(3), 257-262. • Higgins, J. P., & Green, S. (Eds.). (2011). Cochrane handbook for systematic reviews of interventions (Vol. 4). John Wiley & Sons.