Sample size calculations for disease freedom and prevalence estimation surveys

We developed a Bayesian approach to sample size calculations for studies designed to estimate disease prevalence that uses a hierarchical model for estimating the proportion of infected clusters (cluster-level prevalence) within a country or region. The clusters may, for instance, be villages within a region, cities within a state, or herds within a country. Our model allows for clusters with zero prevalence and for variability in prevalences among infected clusters. Moreover, uncertainty about diagnostic test accuracy and within-cluster prevalences is accounted for in the model. A predictive approach is used to address the issue of sample size selection in human and animal health surveys. We present sample size calculations for surveys designed to substantiate freedom of a region from an infectious agent (disease freedom surveys) and for surveys designed to estimate cluster-level prevalence of an endemic disease (prevalence estimation surveys). In disease freedom surveys, for instance, assuming the cluster-level prevalence for a particular infectious agent in the region is greater than a maximum acceptable threshold, a sample size combination consisting of the number of clusters sampled and number of subjects sampled per cluster can be determined for which authorities conducting the survey detect this excessive cluster-level prevalence with high predictive probability. The method is straightforward to implement using the Splus/R library emBedBUGS together with WinBUGS.