[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Evidence-based medicine](https://durgical.com/en/epidemiology/areas/ebm/) › Meta-analysis

# Meta-analysis

- Study design

Meta-analysis combines the results of several studies statistically into one effect, giving more weight to the more precise ones.

Updated Nov 5, 2026

## Key points

- Inverse-variance weight: w = 1 / SE²; the study with the smallest standard error weighs most.
- Pooled effect = Σ(w × effect) / Σw; its standard error = 1 / √Σw.
- Fixed effect: one true effect, differences are chance; random effects: different effects that follow a distribution.
- With heterogeneity, the random-effects model gives a wider CI and spreads the weight more evenly.
- Ratios (RR, OR) are combined on the log scale.
- A meta-analysis is no better than the studies it combines.

On this page

- The basics Key points
- What it is
- How it is built
- Worked example
- Fixed effect versus random effects
- Markers
- When to use it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## 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.

## Memory aid

Whoever measures better weighs more: the most precise study pulls hardest on the pooled effect.

## 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.

[Add to my cards (3)](https://durgical.app/estudiar/?add=/en/epidemiology/meta-analysis/)

## Connections

## Related 6

- [Systematic review](https://durgical.com/en/epidemiology/systematic-review/)
- [Forest plot](https://durgical.com/en/epidemiology/forest-plot/)
- [Heterogeneity (I²)](https://durgical.com/en/epidemiology/heterogeneity/)
- [Publication bias and the funnel plot](https://durgical.com/en/epidemiology/publication-bias-and-the-funnel-plot/)
- [Confidence interval](https://durgical.com/en/epidemiology/confidence-interval/)
- [Standard error](https://durgical.com/en/epidemiology/standard-error/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

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](https://www.cochrane.org/authors/handbooks-and-manuals/handbook/current/chapter-10) (Cochrane, 2026).

## **Spotted a mistake?** We are always improving for the community. Tell us what is wrong and our team will review it. Report a mistake

Representative model, for educational purposes only.

---
Source: https://durgical.com/en/epidemiology/meta-analysis/
License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/meta-analysis/