Pool prevalence rates, complication rates, and single-group proportions across studies using Freeman-Tukey, logit, arcsine, or raw transformations with fixed or random-effects models.
Drag & drop a file or
CSV, TSV, Excel (.xlsx/.xls) - max 500 rows
Enter events and totals for at least 2 studies to see results. Each study needs an event count between 0 and the total sample size.
For each study, input the study label, the number of events (cases with the outcome), and the total sample size. You can also import data from a CSV or Excel file, or paste rows directly from a spreadsheet application.
Select how proportions are transformed before pooling. The Freeman-Tukey double arcsine is recommended for most applications because it stabilizes variance and handles zero events without continuity corrections. Logit works well for moderate proportions.
Choose between a fixed-effect model (assumes one true proportion across all studies) or a random-effects model with DerSimonian-Laird estimation (allows the true proportion to vary across populations). Random-effects is standard for prevalence studies.
The D3.js forest plot displays each study's proportion with its confidence interval, study weights as percentages, and the pooled diamond. Back-transformed proportions appear on the natural (0 to 1) scale for direct interpretation.
Examine I-squared, Cochran's Q, and tau-squared below the forest plot. For prevalence meta-analyses, I-squared above 75% is common and expected. Focus on the prediction interval, which shows the range of proportions expected in a new study setting.
Download the forest plot as PNG or PDF, copy the auto-generated methods paragraph for your manuscript, export the reproducible R code for the metafor package, or save the results table as CSV for further analysis in Excel or Stata.
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Get a Free QuoteRaw proportions are bounded between 0 and 1, violating normality assumptions. Transformations stabilize variance, prevent confidence intervals from exceeding logical bounds, and produce valid pooled estimates even when individual studies report extreme proportions near 0% or 100%.
The Freeman-Tukey transformation (Freeman and Tukey, 1950) is the most robust option for proportion meta-analysis. It stabilizes variance across the full range of proportions and handles zero-event studies without requiring ad hoc continuity corrections that distort estimates.
Studies with zero events pose problems for logit and raw proportion methods. The Freeman-Tukey and arcsine transformations handle zeros naturally. If using logit, a 0.5 continuity correction is added automatically, but this can bias results when sample sizes are small or highly unequal.
Unlike comparative meta-analyses where I-squared above 75% signals concern, prevalence studies routinely show I-squared above 90% because disease rates genuinely vary across populations, geographic regions, time periods, and clinical settings. This does not indicate an analytic error.
The prediction interval describes where the true proportion in a new study would likely fall, incorporating both estimation uncertainty and between-study variance. For prevalence meta-analyses with high heterogeneity, the prediction interval is more informative than the confidence interval alone.
Report the transformation method used, the model (fixed or random), the pooled proportion with confidence interval, the prediction interval, heterogeneity statistics (I-squared, tau-squared, Q), and the number of studies. Follow the PRISMA guidelines and specify the R package or software used.
Proportion meta-analysis pools single-group rates (disease prevalence, complication rates, mortality, treatment response) across independent studies. Unlike standard comparative meta-analysis that estimates a treatment effect between two groups, single-arm meta-analysis estimates a summary proportion from studies that each report the number of events out of a total sample size. Raw proportions violate the normality assumption of inverse-variance meta-analysis because they are bounded between 0 and 1. The Freeman-Tukey double arcsine transformation (Freeman and Tukey, 1950) stabilizes variance across all proportion values and handles zero events without continuity corrections. Barendregt et al. (2013) demonstrated its superiority in simulation studies, particularly for extreme proportions or widely varying sample sizes.
The choice of transformation method has practical consequences for the pooled estimate and its interpretation. The logit transformation converts proportions to log-odds, which are unbounded and approximately normally distributed for moderate proportions. However, logit requires a continuity correction (typically adding 0.5 to both numerator and denominator) when any study reports zero events or 100% event rates, and this correction can introduce bias with small samples. The arcsine square root transformation is computationally simple but can produce biased back-transformed estimates when sample sizes vary widely across studies. Barendregt et al. (2013) showed through extensive simulations that the Freeman-Tukey method consistently produced coverage probabilities closest to the nominal 95% level across all scenarios tested.
Heterogeneity in prevalence pooling is typically high because rates naturally vary across populations, geographic regions, and time periods. An I-squared above 75% is common and does not necessarily signal analytic problems. The prediction interval captures this variation and should be reported alongside the confidence interval (Viechtbauer, 2010). When heterogeneity is substantial, focus on understanding why rates differ through subgroup analysis or meta-regression rather than seeking a single universal estimate.
The metaprop function in R (and the equivalent metafor approach using rma() with proportion-specific measures) has become the standard software implementation for proportion meta-analysis. This tool generates R code compatible with the metafor package, using the measure argument PLO for logit, PFT for Freeman-Tukey, PAS for arcsine, and PR for raw proportions. The generated code includes the escalc() function for computing transformed proportions and their sampling variances, followed by the rma() function for fitting the random-effects model with back-transformation to the proportion scale.
Reporting standards for proportion meta-analysis follow the PRISMA 2020 guidelines with additional considerations specific to prevalence pooling. Authors should report the transformation method used, justification for model choice (fixed or random), the pooled proportion with its confidence interval and prediction interval, all heterogeneity statistics (I-squared, tau-squared, Cochran Q with degrees of freedom), and the number of studies contributing to the estimate. Subgroup analyses should be pre-specified in the protocol, and sensitivity analyses comparing results across different transformation methods provide evidence of robustness.
For comparative meta-analyses that estimate treatment effects between two groups, use our forest plot generator. Assess publication bias with the funnel plot and publication bias tool. Compute effect sizes from summary statistics using the effect size calculator, and evaluate between-study variability with the heterogeneity calculator. When pooling diagnostic accuracy measures rather than proportions, consider our diagnostic test accuracy meta-analysis tool.
A proportion meta-analysis pools single-group proportions, such as disease prevalence, complication rates, mortality rates, or treatment response rates, across multiple studies. Unlike a standard meta-analysis that compares two groups (for example, treatment versus control), a proportion meta-analysis estimates a single pooled rate from studies that each report the number of events out of a total sample size. The result is a summary proportion with a confidence interval that accounts for between-study variability.
Raw proportions are bounded between 0 and 1, which violates the normality assumption underlying standard inverse-variance meta-analysis. When proportions are very low (near 0%) or very high (near 100%), the sampling distribution becomes skewed, confidence intervals can extend beyond 0 or 1, and variance estimates become unreliable. Transformations such as the logit (log-odds), Freeman-Tukey double arcsine, and arcsine square root stabilize the variance and improve the normality of the sampling distribution. The pooled result is then back-transformed to the proportion scale for interpretation.
The Freeman-Tukey double arcsine transformation is the most commonly recommended for proportion meta-analysis because it stabilizes variance across all proportion values and handles zero events without requiring continuity corrections. The logit transformation (log-odds) is widely used in epidemiology and works well for moderate proportions but requires a continuity correction for 0% or 100% proportions. The arcsine square root transformation is simpler but can produce biased pooled estimates with unequal sample sizes. The raw proportion method is the most intuitive but performs poorly when proportions are near the boundaries. For most applications, the Freeman-Tukey or logit transformation is recommended.
Heterogeneity in proportion meta-analysis is typically high because prevalence and rates naturally vary across populations, settings, and time periods. An I-squared value above 75% is common in prevalence meta-analyses and does not necessarily indicate a problem with the analysis. The Q statistic tests whether observed variation exceeds sampling error, while tau-squared quantifies the absolute amount of between-study variance. The prediction interval shows the range within which the true proportion in a new study would be expected to fall. When heterogeneity is high, focus on the prediction interval rather than the confidence interval, and consider subgroup analysis or meta-regression to explore sources of variation.
The confidence interval quantifies uncertainty about the pooled (average) proportion. The prediction interval is wider and describes the range within which the true proportion in a new, similar study would be expected to fall. For example, if the pooled prevalence is 15% with a 95% confidence interval of 12% to 18%, the prediction interval might be 5% to 28%. The prediction interval incorporates both the uncertainty in the pooled estimate and the between-study variance (tau-squared). In proportion meta-analyses with high heterogeneity, the prediction interval provides a more realistic picture of how the proportion varies across settings.
Yes. After running the analysis, click the R Code button to generate a ready-to-run script that uses the metafor package (Viechtbauer, 2010). The generated code includes your study data, runs the meta-analysis with the same transformation method and model you selected, produces a forest plot, and creates a funnel plot. The measure argument in the rma() function corresponds to your chosen transformation: PLO for logit, PFT for Freeman-Tukey, PAS for arcsine, and PR for raw proportion. You can paste the code directly into RStudio for full reproducibility.
Generate publication-ready forest plots for comparative meta-analyses using our forest plot generator for meta-analysis. Detect publication bias with our funnel plot and publication bias tool. Compute individual study effect sizes with our effect size calculator for SMD, OR, and RR. Assess between-study variability with our heterogeneity calculator for I-squared and tau-squared.
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Dr. Sarah Mitchell holds a PhD in Biostatistics from Johns Hopkins Bloomberg School of Public Health and has over 15 years of experience in systematic review methodology and meta-analysis. She has authored or co-authored 40+ peer-reviewed publications in journals including the Journal of Clinical Epidemiology, BMC Medical Research Methodology, and Research Synthesis Methods. A former Cochrane Review Group statistician and current editorial board member of Systematic Reviews, Dr. Mitchell has supervised 200+ evidence synthesis projects across clinical medicine, public health, and social sciences. She reviews all Research Gold tools to ensure statistical accuracy and compliance with Cochrane Handbook and PRISMA 2020 standards.
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