Calculate least-cost sample sizes for 2-stage surveys for demonstrating disease freedom, where cluster sizes are unknown. This analysis calculates the number of clusters and the number of units within each cluster to be tested to provide a specified system sensitivity (probability of detecting disease) for the given unit and cluster-level design prevalences and test sensitivity, where actual cluster sizes are unknown. Test specificity is assumed to be 100% (or follow-up testing of any positive will be undertaken to confirm or exclude disease).
Sample sizes are optimised to minimise overall cost for given cluster and unit-level testing costs. A maximum sample size per cluster must be specified and either the number of cluster in the population or a maximum number of clusters to be tested must be specified.
Numbers of units to test in each cluster are calculated using assumed binomial sampling (sample size is small relative to cluster sizes), while numbers of clusters to test are calculated using the hypergeometric distribution approximation (sampling without replacement) if the number of clusters in the population is specified or assuming binomial sampling if not.
Design prevalence (specified level of disease to be detected) must be specified at both unit and cluster levels. Design prevalence can be specified as either:
Inputs required include:
Outputs from the analysis include:
If it is not possible to achieve the desired system sensitivity by testing the specified maximum number of units in all (or the specified maximum number) of the clusters, a message will be returned, along with a summary of the achieved mean SeH and SSe if the maximum numbers of units and clusters were tested.