title: Estimation of infection prevalence from correlated binomial samples.
abstract: Infection prevalence in a population often is estimated from grouped binary data expressed as proportions. The groups can be families, herds, flocks, farms, etc. The observed number of cases generally is assumed to have a Binomial distribution and the estimate of prevalence is then the sample proportion of cases. However, the individual binary observations might not be independent--leading to overdispersion. The goal of this paper was to demonstrate random-effects models for the estimation of infection prevalence from data which are correlated and in particular, to illustrate a nonparametric random-effects model for this purpose. The nonparametric approach is a relatively recent addition to the random-effects class of models and does not appear to have been discussed previously in the veterinary epidemiology literature. The assumptions for a logistic-regression model with a nonparametric random effect were outlined. In a demonstration of the method on data relating to Salmonella infection in Irish pig herds, the nonparametric method resulted in the classification of herds into a small number of distinct prevalence groups (i.e. low, medium and high prevalence) and also estimated the relative frequency of each prevalence category in the population. We compared the estimates from a logistic model with a nonparametric distribution for the random effects with four alternative models: a logistic-regression model with no random effects, a marginal model using a generalised estimating equation (GEE) and two methods of fitting a Normally distributed random effect (the GLIMMIX macro and the NLMIXED procedure both in SAS). Parameter estimates from random-effects models are not readily interpretable in terms of prevalences. Therefore, we outlined two methods for calculating population-averaged estimates of prevalence from random-effects models: one using numerical integration and the other using Monte Carlo simulation.
authors.affiliation: Department of Applied Mathematics and Theoretical Physics, The Queen's University of Belfast, Belfast BT7 1NN, Northern Ireland, UK. j.condon@qub.ac.uk
authors.forename: J
authors.initials: J
authors.lastname: Condon
authors.forename: G
authors.initials: G
authors.lastname: Kelly
authors.forename: B
authors.initials: B
authors.lastname: Bradshaw
authors.forename: N
authors.initials: N
authors.lastname: Leonard
mesh_terms: D000818:Animals; D003718:Denmark / Q000453:epidemiology; D015233:Models, Statistical; D015995:Prevalence; D012481:Salmonella Infections, Animal / Q000453:epidemiology* / Q000209:etiology; D013552:Swine; D013553:Swine Diseases / Q000453:epidemiology* / Q000209:etiology