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Meta-analysis: proportion

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For a short overview of meta-analysis in MedCalc, see Meta-analysis: introduction.

MedCalc uses a Freeman-Tukey transformation (arcsine square root transformation; Freeman and Tukey, 1950) to calculate the weighted summary Proportion under the fixed and random effects model (DerSimonian & Laird, 1986).

How to enter data

The data of different studies can be entered as follows in the spreadsheet:

Meta-analysis for proportions - how to enter data

Required input

The dialog box for "Meta-analysis: proportion" can then be completed as follows:

Meta-analysis for proportions - dialog box

Studies: a variable containing an identification of the different studies.


Total number of cases: a variable containing the total number of cases in the different studies.

Number of positive cases: a variable containing the number of positive cases in the different studies.


A filter to include only a selected subgroup of studies in the meta-analysis.

Filter: a filter to include only a selected subgroup of cases in the graph.



Meta-analysis for proportions - results

The program lists the proportions (expressed as a percentage), with their 95% CI, found in the individual studies included in the meta-analysis.

The pooled proportion with 95% CI is given both for the Fixed effects model and the Random effects model.

The random effects model will tend to give a more conservative estimate (i.e. with wider confidence interval), but the results from the two models usually agree where there is no heterogeneity. See Meta-analysis: introduction for interpretation of the heterogeneity statistics Cohran's Q and I2. When heterogeneity is present the random effects model should be the preferred model.

See Meta-analysis: introduction for interpretation of the different publication bias tests.

Forest plot

The results of the different studies, with 95% CI, and the pooled proportions with 95% CI are shown in a forest plot:

Meta-analysis for proportions - forest plot


See also

Recommended book

Introduction to Meta-Analysis
Michael Borenstein, Larry V. Hedges, Julian P. T. Higgins, Hannah R. Rothstein

Buy from Amazon US - CA - UK - DE - FR - ES - IT

This book provides a clear and thorough introduction to meta-analysis, the process of synthesizing data from a series of separate studies. Meta-analysis has become a critically important tool in fields as diverse as medicine, pharmacology, epidemiology, education, psychology, business, and ecology.