I have an imperfect test applied to N subjects of which n of them returned a positive result. I was hoping to model the prevalence using the following relationship
p = Se* \pi + (1- Sp) * (1-\pi)
where Se and Sp is the sensitivity and specificity of the test and \pi is the prevalence . Unfortunately, I don’t have data on sensitivity and specificity. I was hoping by varying the levels like 85%, 90% and 95% I would be able to see the impact on the prevalence estimate. To do that, I was planning to use the following priors
Se, Sp \sim dbeta(9, 1) - 90% accuracy on average (mean = 0.9)
Se, Sp \sim dbeta(6, 1) - 85% accuracy on average (mean = 0.85)
Se, Sp \sim dbeta(8, 2) - 80% accuracy on average (mean = 0.8)
Do you think this is a reasonable approach?