Hopefully a simple question; here's the setup:
- I'm trying to estimate the prevalence of a medical condition in a specific population.
- The size of the population(s) of interest is itself uncertain.
- I want to construct a confidence interval for the prevalence. I'd like also to be able to do some hypothesis testing to compare the prevalence of the condition between different populations of uncertain size, to ask questions like: is the prevalence of the condition higher or lower in population A than population B, and is the difference statistically significant?
- If N was fixed, I'd simply use a Clopper–Pearson interval or similar and be done. What I have instead is a best estimate and 95% credible interval for N from a paper that neglected to mention how they arrived at their results.
- The lower and upper bounds on N are not symmetric around N.
Is it acceptable to estimate the prevalence and the 95% confidence interval by:
- Use the best estimate of N to calculate the best estimate of the prevalence,
- Use the lower limit on N to calculate the lower limit of the prevalence,
- Use the upper limit on N to calculate the upper limit of the prevalence?
Does it make sense to use a similar procedure to construct a range of p-values for a hypothesis test and discriminate on the basis of whether the range of p-values contains values ≤ 5%?
If this procedure is not good (and why?), what procedure would you recommend instead? Is there any literature that backs up my procedure or any alternative suggested procedure?