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Meta Analysis Essentials
Giorgio Alfredo Spedicato
Ph.D FCAS FSA CSPA CStat
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.
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,…
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
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;
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)
Possible outputs
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.

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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.