Sample size estimation to substantiate freedom from disease for clustered binary data with a specific risk profile.

Disease cases are often clustered within herds or generally groups that share common characteristics. Sample size formulae must adjust for the within-cluster correlation of the primary sampling units. Traditionally, the intra-cluster correlation coefficient (ICC), which is an average measure of the data heterogeneity, has been used to modify formulae for individual sample size estimation. However, subgroups of animals sharing common characteristics, may exhibit excessively less or more heterogeneity. Hence, sample size estimates based on the ICC may not achieve the desired precision and power when applied to these groups. We propose the use of the variance partition coefficient (VPC), which measures the clustering of infection/disease for individuals with a common risk profile. Sample size estimates are obtained separately for those groups that exhibit markedly different heterogeneity, thus, optimizing resource allocation. A VPC-based predictive simulation method for sample size estimation to substantiate freedom from disease is presented. To illustrate the benefits of the proposed approach we give two examples with the analysis of data from a risk factor study on Mycobacterium avium subsp. paratuberculosis infection, in Danish dairy cattle and a study on critical control points for Salmonella cross-contamination of pork, in Greek slaughterhouses.