The way to approach this would be meta-analysis. The reason for this is that the effect varies between the trials, and this effect may vary more than sampling variation would predict. Meta-analysis will give you a measure of the heterogeneity – though, with only three trials the precision, of course, low.

I agree with Ronán Michael Conroy. If you say what statistical software you use, someone can likely give specific advice about how to carry out a meta-analysis. Alternatively, you could try this online calculator (which I found just now):

• https://meta-mar.shinyapps.io/meta-analysis-calculator/

For clinical trials with dichotomous outcomes (e.g., response vs no response), some docs I used to work for liked to report risk ratios. If that's what you want, select the log-RR option in the calculator. Statisticians, on the other hand, often like the odds ratio better. For that one, select log-OR as the effect size measure. HTH.

What is it that you are wanting to do? You have 3x2 design (three sites by the experimental condition) and one binary outcome. Do you want something like the log-odds ratio for each site, do you want to stick all the data into, for example, a logistic regression? You say weighted mean. Weighted by what (and for what purpose)? Note that with n=3 trials, treating as a fixed factor in whatever model makes more sense than random.

Daniel Wright's reply reminded me of a demonstration I programmed several years ago. The original demo was done using SPSS, but I updated it later using Stata. The Stata version is in the attached text file. In a nutshell, it shows that the pooled estimate of the odds ratio computed via standard meta-analysis is virtually identical to the odds ratio obtained via logistic regression (without the interaction term in the model).

The simplest if all studies have the same design, endpoints is to pool the data. If there are differences, the meta analyses as mentionned by Roman and Bruce are the best way. However, it goes with signifiant limitations on the quality of the proof. Historical comparison are a 3 rd options , which means that you have one well controlled study that drive your thinking, other are supportive.

Hello Abhishek Rajput. I think most of the rest of us who follow this thread understood that Wong Chun Hoong wanted a pooled estimate of the treatment effect, not pooled estimates of the proportions of responders in the treatment & placebo groups separately.

Clinical trials were mentioned, and in that case, many people (or many clinicians, at least) seem to prefer the risk ratio (RR) over the odds ratio (OR) as the measure of effect size. Therefore, I used Stata to meta-analyze the 3 trials using ln(RR) as the measure of effect size--see the results in the attached text file. The executive summary is that the pooled estimate of the RR is 4.267 (95% CI, 1.223 to 14.880).

PS- If I did want to get pooled estimates of the proportion of responders in Treatment and Placebo groups, I would use meta-analysis of proportions, perhaps with a logit transformation. I did that for fun too--see the last couple of analyses in the attached text file. Here are my estimates:

Treatment groups: 0.325 (95% CI, 0.124 to 0.622)

Placebo groups: 0.071 (95% CI, 0.032 to 0.149)

NOTE: The post I was responding to has now been deleted.