Estimating the intracluster correlation coefficient for trachomatous inflammation-follicular in population-based trachoma prevalence surveys: results from a meta-regression of 261 standardised pre-intervention surveys in Ethiopia, Mozambique, and Nigeria

Sample sizes in cluster surveys must be greater than those in surveys using simple random sampling to provide similarly precise prevalence estimates, because results from subjects examined in the same cluster cannot be assumed to be independent. Therefore, a crucial aspect of cluster sampling is estimation of the intracluster correlation coefficient (⁠ρ⁠): the degree of relatedness of outcomes in a given cluster, defined as the proportion of total variance accounted for by between-cluster variation. In infectious diseases, this coefficient is related to transmission patterns and the natural history of infection; its value also depends on particulars of survey design. Estimation of ρ is often difficult due to the lack of comparable surveys to provide summary estimates. We use a parametric bootstrap model to estimate ρ for the ocular clinical sign trachomatous inflammation-follicular (TF) in 1–9-year-olds, within population-based trachoma prevalence surveys, presenting the results of a meta-regression analysis of data from 261 such surveys completed using standardised methodologies in Ethiopia, Mozambique, and Nigeria from 2012-2016. Consistent with the underlying theory, we found that ρ increased with increasing overall TF prevalence, and smaller numbers of children examined per cluster. ρ estimates for TF were independently higher in Ethiopia compared to the other countries.