Prevalence estimation under heterogeneity in the example of bovine trypanosomosis in Uganda

We examine variance estimators of a binomial parameter established under cluster sampling using data from a cross-sectional study of bovine trypanosomosis in Mukono County, Uganda. Fifty farms (referred to as clusters), were sampled with a total sample size of 487 cattle. Trypanosomes were found in 17.9% (87/487) of the total sample. The cluster-level (CL) prevalences were not homogeneously distributed. According to maximum-likelihood parameters established by mixture-distribution analysis, 18% of the cluster had 0% prevalence whereas 48% and 34% of the clusters could be allocated to subpopulations of clusters with mean prevalences 11.6% and 31.9% respectively. We show that this form of heterogeneity invalidates the applicability of the Beta distribution as a model for the distribution of CL prevalences. Furthermore, we provide empirical evidence for a variance inflation due to heterogeneity (inflation factor 2.07) that exceeds the design-based variance inflation due to clustering alone (inflation factor 1.82). The variance inflation due to heterogeneity is given in a closed form so that the approach can be conveniently applied to survey data that involve cluster sampling under heterogeneity.