Effect of diagnostic testing error on intracluster correlation coefficient estimation

Estimation of the intracluster correlation coefficient (ICC) for infectious animal diseases may be of interest for survey planning and for calculating variance inflation factors for estimators of prevalence. Typically, diagnostic tests with imperfect sensitivity and specificity are used in surveys. In such studies, where animals from multiple herds are tested, the ICC often is estimated using apparent (test-based) rather than true prevalence data. Through Monte Carlo simulation, we examined the effect of substituting diagnostic test outcomes for true infection status on an ANOVA estimator of ICC, which was designed for use with true infection status data. We considered effects of diagnostic test sensitivity and specificity on the estimated ICC when the true ICC value and infection status of the sampled individuals were known. The ANOVA estimator underestimated the true ICC when the diagnostic test was imperfect. We also demonstrated, under the beta-binomial model, that the ICC based on apparent infection status for individuals is ≤ ICC based on true infection status. In addition, we propose a Bayesian model for estimating the ICC that incorporates imperfect sensitivity and specificity and illustrate the Bayesian model using a simulation study and one example; a seroprevalence survey of ovine progressive pneumonia in U.S. sheep flocks.