TimelyScholarFree Tools › Meta-Analysis of Proportions
Pool prevalence, incidence or single-arm proportions across studies. Get the pooled proportion with its 95% CI and prediction interval, heterogeneity statistics and a forest plot.
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| Study | Events (cases) | Sample size | |
|---|---|---|---|
| Pooled proportion | 75.7% (95% CI 66.1% to 83.3%) |
|---|---|
| 95% prediction interval | 43.2% to 92.8%Where the proportion in a new setting is likely to lie |
| I² | 56.4%may represent substantial heterogeneity (50-90%) |
| Cochran's Q | 29.79 (df = 13, p = 0.005) |
| τ² | 0.3616On the logit scale |
| Total participants | 326 |
Number of events (cases) and the sample size.
Logit is recommended; Freeman-Tukey is also available.
With CI, prediction interval, I² and forest plot.
Proportions are transformed before pooling so that their sampling distribution is closer to normal and their variance does not depend on the proportion itself. The pooled value is then back-transformed to a percentage.
The logit transformation is widely used. The Freeman-Tukey double arcsine transformation handles proportions of 0% and 100% smoothly, but its back-transformation can give misleading pooled values when study sizes differ greatly (Schwarzer et al. 2019).
Prevalence meta-analyses usually show high heterogeneity, so the prediction interval is often more informative than the confidence interval.
Logit is a safe default. If you use Freeman-Tukey, check the back-transformed result against the logit analysis, especially when study sizes vary a lot.
Large studies give very precise proportions, so even small real differences between settings produce high I². Report the prediction interval and explore sources of heterogeneity.