# Odds ratio meta analysis with no control group

Is it possible to conduct a meta-analysis odds ratio with just an experimental group (no control)?

I am looking at several studies that have an experimental group, with a response rate equal to the number of individuals who responded to the treatment over the total number of individuals in the experimental group.

My understanding is that an odds ratio can not be calculated unless you have a 2x2 contingency table with an experimental group and a control group.

As clarified already by @mdewey, it is inappropriate to talk about odds ratios when you have only one group. In such instance, you can instead focus on proportions (the ratio of patients with events/all patients) or odds (the ratio of patients with events/patients without events). Another possibility is to focus on rates (the ratio of patients with events/all patients over a given period of time).

As reported elsewhere, you can compute the standard error of the proportion as square root of the product of P * (1 - P) / N, where P is the ratio of patients with events/all patients, and N is the sample size (ie all patients). I am not aware of any formula to compute the standard error of an odds, but it is reasonable you could find one.

Once you have for each study the point estimate and the standard error, it is easy to combine them with a statistical package (eg metan in Stata, meta or metafor in R). Note indeed that the R meta package offers the metaprop command which will directly suit you, as clarified by this illustrative code:

library(meta)
studyid <- c(1:10)
events <- sample(5:20, 10, replace = T) # randomly generated event counts
patients <- sample (50:200, 10, replace = T) # randomly generated sample sizes
mydata <- data.frame(cbind(studyid, events, patients))
mydata
metaprop1 <- metaprop(mydata$events, mydata$patients)
metaprop1
# various graphs
forest(metaprop1)
baujat(metaprop1)
funnel(metaprop1)
trimfill1 <- trimfill(metaprop1)
summary(trimfill1)
funnel(trimfill1)

• When working with odds, one would do the meta-analysis with log(odds), whose standard error can be computed (i.e., estimated) with $\frac{1}{n p(1-p)}$. – Wolfgang Apr 10 '16 at 13:04

As you say there is no odds ratio here to analyse but you can ,eta-analyse the proportions using either the raw proportions or some transormation of them like log, logit, arc sine, ... Most software like metafor, or meta in R or metabin in Stata will do this for you.