# Prior specification for sensitivity and specificity of prevalence model

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?

why put the same prior on both sensitivity and specificity?

have you seen this paper? http://www.stat.columbia.edu/~gelman/research/published/specificity.pdf
Stan jupyter notebooks here: example-models/jupyter/covid-inf-rate at master · stan-dev/example-models · GitHub
this is for the case where you have data on the tests, but without that data, your approach will work.

for covid modeling, estimates from our collaborators on specificity put the test kits at 99.5% or so, sensitivity was lower - maybe 95 or 97?

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Thank you @mitzimorris . Yes, I’m following the papers you linked above. I thought it will be ok to consider same priors for sensitivity and specificity to start with but constraining sensitivity > 1- specificity