Combining assays for estimating prevalence of human herpesvirus 8 infection using multivariate mixture models

For many diseases, it is difficult or impossible to establish a definitive diagnosis because a perfect "gold standard" may not exist or may be too costly to obtain. In this paper, we propose a method to use continuous test results to estimate prevalence of disease in a given population and to estimate the effects of factors that may influence prevalence. Motivated by a study of human herpesvirus 8 among children with sickle-cell anemia in Uganda, where 2 enzyme immunoassays were used to assess infection status, we fit 2-component multivariate mixture models. We model the component densities using parametric densities that include data transformation as well as flexible transformed models. In addition, we model the mixing proportion, the probability of a latent variable corresponding to the true unknown infection status, via a logistic regression to incorporate covariates. This model includes mixtures of multivariate normal densities as a special case and is able to accommodate unusual shapes and skewness in the data. We assess model performance in simulations and present results from applying various parameterizations of the model to the Ugandan study.