# Is there an effect size for a single proportion?

I want to conduct a meta analysis of the incidence rate of the complications of a specific disease. Studies report these complications as 4 patients died or 2% died. And there are no comparable group.Is it possible to have an effect size for single proportions.Any suggestions or further readings are appreciated.

Let me take the title question ("Is there an effect size for a single proportion?") literally and set aside the meta analysis context.

There are effect sizes for single proportions, when a null proportion value is specified. Moreover, the effect sizes for single proportions are the same as for two observed proportions and work the same way. You could use:

1. The difference of proportions: prop - null
2. The ratio of proportions: prop/null
3. The odds ratio: [prop/(1-prop)] / [null/(1-null)]

Returning to the context of meta analysis, you don't necessarily have to use these. You might just be interested in estimating a proportion directly. In which case, you wouldn't want to use these. If there is a meaningful null and these studies compared the observed proportion to that, you could try using the log of the odds ratio.

• 'when a null proportion value is specified.' can you tell me more about it? I only have the measured proportion e.g. 2% died. what's the null proportion then? – Elmahy Jan 29 '16 at 13:07
• The idea is that there is some specific value that has a theoretical basis, & that you are trying to disprove. Eg, everyone believes that 4.5% die, & the point of these studies is to test that proposition. It isn't clear that that's the case in your situation. The other answers are probably more appropriate to your situation, @ahmedmar. – gung - Reinstate Monica Jan 29 '16 at 16:06

You can use the command metaprop in the package meta of r. These type of studies are called incidence meta-analysis or single-proportion meta-analysis.

In this particular case the effect size would be the proportion of the variable studied and the meta analysis would compute a different weight and confidence interval according to the sample size.

• Thank you. It's nice to get an answer from a medical student when I am too a medical student. – Elmahy Jan 24 '16 at 12:38
• I'm glad to know that. If you found the answer useful you can mark it as correct? Thanks, good work – GGA Jan 24 '16 at 12:54

You need to be careful here. Do you really mean an incidence rate? By that I mean that people were followed for a period of time and then the number of events is reported as a rate per person year (or some either measure of time). If you do then I think you need something other than metaprop from meta. I assume you can use some other command in meta (with which I am not too familiar) but metafor (also available from CRAN) has several options for rates.