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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.

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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.

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  • $\begingroup$ '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? $\endgroup$ – Elmahy Jan 29 '16 at 13:07
  • $\begingroup$ 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. $\endgroup$ – gung - Reinstate Monica Jan 29 '16 at 16:06
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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.

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

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