After I multiply imputed my dataset m times I wanted to calculate a binomial proportion confidence interval. I did that formerly using the
Hmisc::binconf() function in R, but pooling seemed to be impossible using the
mice package. How do I combine these confidence intervals into one considering within and in-between imputed dataset variance? Can I use Rubin's rules?
After reading the article mentioned in the comments, I may have found a way to pool binomial proportion confidence intervals. First I used the Wilson Score Interval formula:
Then I calculated the relocated centre estimate p' using the following formula for every complete dataset:
And after that I calculated the correct standard deviation s' for every complete dataset using a formula found in this article:
By calculating the standard deviation and relocated centre for every complete dataset I was able to pool the results using
mice::pool.scalar(Q, U, n = 100), and calculate the final confidence interval using the
qnorm(0.975, Q, sqrt(U) function. Can anybody confirm whether this is correct or not?