Meta-analysis
- Study design
Meta-analysis combines the results of several studies statistically into one effect, giving more weight to the more precise ones.
What it is
Meta-analysis is the statistical combination of the results of two or more studies that answer the same question. Each study gets a weight, usually the inverse of its variance, so large and precise studies count more. The fixed-effect model assumes all studies estimate the same true effect; the random-effects model assumes different but related effects, gives relatively more weight to small studies and yields a wider confidence interval when there is heterogeneity.
How it is built
- It starts from a systematic review with studies similar enough (population, intervention, outcome).
- An effect measure (RR, OR, mean difference) and a model (fixed or random) are chosen.
- Each study's weight and the pooled effect with its CI are computed.
- Heterogeneity (I²) is examined, sensitivity analyses are run and publication bias is looked for.
Worked example
- Data (made up): 3 trials measure the difference in systolic pressure (mmHg): A −4 (SE 2), B −2 (SE 1), C −6 (SE 4).
- Weights (1 / SE²): A = 1/4 = 0.25; B = 1/1 = 1; C = 1/16 = 0.0625; sum = 1.3125.
- Weights as percentages: A ≈ 19 %, B ≈ 76 %, C ≈ 5 %.
- Weighted sum: (−4 × 0.25) + (−2 × 1) + (−6 × 0.0625) = −1 − 2 − 0.375 = −3.375.
- Pooled effect (fixed effect): −3.375 / 1.3125 ≈ −2.57 mmHg.
- Standard error: 1 / √1.3125 = 1 / 1.146 ≈ 0.873.
- 95 % CI: −2.57 ± 1.96 × 0.873 = −2.57 ± 1.71, that is, from −4.28 to −0.86 mmHg.
- Reading: pressure falls ≈ 2.6 mmHg on average; the CI excludes 0, and trial B, the most precise, dominates the result.
Fixed effect versus random effects
| Feature | Fixed effect | Random effects |
|---|---|---|
| Assumption | All studies estimate the same effect | Effects vary between studies |
| What it estimates | The common effect | The average effect of the distribution |
| Weights | Large studies dominate | More even; small studies gain relative weight |
| CI with heterogeneity | Narrower | Wider |
| When | Very homogeneous studies | Clinical or statistical heterogeneity expected |
Markers
- MA
- Fixed effect
- Random effects
- Inverse variance
When to use it
- A meta-analysis can show an effect no small trial detected alone, because it adds statistical power.
- Before trusting the pooled effect, look at the forest plot, the heterogeneity and the quality of the studies.
Common pitfalls
- Combining very different studies (different populations or interventions): the average represents none of them.
- Averaging the results without weights, as if every study counted the same.
- Believing the random-effects model fixes publication bias: it can make it worse by giving more weight to small studies.
Test yourself
Think of the answer, then tap the question to see it.
How is a study's weight computed in an inverse-variance meta-analysis?
As 1 divided by the square of its standard error: more precise studies weigh more.
What does the fixed-effect model assume?
That all studies estimate the same true effect and that differences between them are only chance.
What happens to the confidence interval in a random-effects model when there is heterogeneity?
It becomes wider than in the fixed-effect model, because it adds the variation between studies.
Connections
Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.
Sources: Chapter 10: Analysing data and undertaking meta-analyses (Cochrane, 2026).
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Representative model, for educational purposes only.