If I want to study whether a post-surgery complication rate (i.e % of people who had a certain complication) is higher for disease 1 than disease 2 and disease 3 which statistical test should I use?
-> Binomial model.
You should adjust for covariables with a known or highly plausible effect on the probability of a complication, like age, BMI, co-morbidities, etc.)
If you want to decide in a closed space without considering the impact of other factors on % of people who had a certain complication, you can use proportion comparison tests.
Hello Joana Silvestre Machado. What is the sample size? Can you show us a 3x2 table? Do you have other variables that you wish to adjust for, as suggested by Jochen? What software do you have access to? Thanks for clarifying.
The difference between Jochen Wilhelm 's and Abolfazl Ghoodjani 's really highlights an aspect of this question. The questioner asks if complications higher but doesn't mention interest in any why questions, so it might be something like for staffing management issues when people arrive at the hospital. In this case comparing unconditioned proportions would make sense if you can argue that the sample in your data are like what you are expecting in the future. As Bruce Weaver says, showing us the contingency table will help. If you are interested in why questions, and this is often the case, going with the model conditioning on other variables may make sense (but be cautious, see for example https://meehl.umn.edu/sites/meehl.umn.edu/files/files/084nuisancevariables.pdf).
So I guess what I am saying we need to know why you are doing this analysis in order to say what approach may be better than others.
Comparing proportions is a very poor way of making comparisons.
Can you use the "time to complication"?
Proportion is "complication rate"?
How do you define it?
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