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.