Meta-analysis

Single proportion (events / total)

Meta-analysis of a single proportion pools prevalence across studies, using the Freeman-Tukey double-arcsine transform to stabilise the variance.

What is Single proportion (events / total)?

Pooling raw proportions is tricky because their variance depends on the proportion itself (p(1-p)/n). The Freeman-Tukey transform y = arcsin(√(x/(n+1))) + arcsin(√((x+1)/(n+1))) makes the variance approximately constant (≈ 1/(n + 0.5)) so inverse-variance pooling works.

Back-transform via sin²(y/2) for reporting. The transform doesn't handle extreme rates (0 or 1) entirely cleanly; consider GLMM-based pooling for those cases.

When should I use Single proportion (events / total)?

  • Single-arm rate or prevalence meta-analyses (e.g. pooled prevalence of a condition across surveys).

What data does it need?

Two integer columns: events xᵢ and total nᵢ + optional labels.

What does it report?

Pooled transformed proportion + back-transformed pooled rate with CI.

What does it assume?

  • Studies are independent.
  • Within-study events follow a binomial distribution.

How do I interpret the result?

Back-transformed pooled rate is what you report; the transformed scale is only an intermediate step for variance stabilisation.

See also

References

  • Freeman & Tukey (1950). Transformations related to the angular and the square root. AoMS 21(4).