Are exact binomial or poisson confidence intervals ok for prevalences?

I want to get confidence intervals for the prevalence of a certain condition. I think it is correct to model the phenomenon with a Binomial distribution

Surfing CrossValidated I see a bunch of methods for extracting such intervals but no one cited exact binomial or exact Poisson as alternatives. Why is that? Those are not correct models for modeling prevalence?

Second questions: the two methods on R give slightly different results, eg:

binom.test(142, 742) # 0.1636684 0.2215588
poisson.test(142, T = 742) # 0.1611933 0.2255661


Why is that and what should I prefer for measures like prevalence (and incidence too

• Thanks for the link, It's a problem I also investigated a lot, so good to have new infos! Actually for curiosity I also tried to estimate the proportion via logistic regression: glm(cbind(142, 742 - 142) ~ 1, binomial()) %>% confint.default() %>% exp() but it gave results shifted by few perc. points (0.1971068 0.2841663), with more variance e biased up. Any ideas why (didn't want to overload my question) Apr 5, 2018 at 15:08
• @Bakaburg First off, you'd transform binom CIs with plogis and not exp, exp just gives you an odds but you want the probability. There's still some differences. Looking at the code for binom.test, it seems the CI is calculated from the Bayes estimator. $F_1^{-1}(0.025)$ and $F_2^{-1}(0.975)$ where the $F_1$ and $F_2$ have a Beta distribution with parameters $\alpha=x+1, \beta=n-x$ $\alpha=x, \beta=n-x+1$. I think this is the Agresti method. Also covered in Rothman. See body(binom.test)[11:12]. Apr 5, 2018 at 15:32