Prior Precision, Prior Accuracy, and the Estimation of Disease Prevalence Using Imperfect Diagnostic Tests

Estimates of disease prevalence in any host population are complicated by uncertainty in the outcome of diagnostic tests on individuals. In the absence of gold standard diagnostics (tests that give neither false positives nor false negatives), Bayesian latent class inference can be applied to batteries of diagnostic tests, providing posterior estimates of the sensitivity and specificity of each test, alongside posterior estimates of disease prevalence. Here we explore the influence of precision and accuracy of prior information on the precision and accuracy of posterior estimates of these key parameters. Our simulations use three diagnostic tests, yielding eight possible diagnostic outcomes per individual. Seven degrees of freedom allow the estimation of seven parameters: sensitivity and specificity of each test, and disease prevalence. We show that prior precision begets posterior precision but only when priors are accurate. We also show that analyses without gold standard can use imprecise priors as long as they are initialised with accuracy. Imprecise priors risk the divergence of MCMC chains towards inaccurate posterior estimates, if inaccurate initial values are used. We note that inaccurate priors can yield inaccurate and imprecise inference. Bounded priors should certainly not be used unless their accuracy is well established. Inaccurate estimates of sensitivity or specificity can yield wildly inaccurate estimates of disease prevalence. Our analyses are motivated by studies of bovine tuberculosis in a wild badger population.