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.
 A: 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.
A: 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.
A: 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:


*

*The difference of proportions: prop - null

*The ratio of proportions: prop/null

*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.  
