Inference for serological surveys investigating past exposures to infections resulting in long-lasting immunity -- an approach using finite mixture models with concomitant information

This paper is concerned with developing a latent class mixture modelling technique which efficiently exploits data from serological surveys aiming to investigate past exposures to infections resulting in long-term or life-lasting immunity. Mixture components featured by antibody assays’ distribution are associated with the serological groups in the population, whilst the probability mixture that an individual belongs to the positive serological group is regarded as an age-dependent prevalence. The latter embeds a mechanistic model which explains the infection process, accounting for heterogeneities, contact patterns in the population and incorporating elements of study design. A Bayesian framework for statistical inference using Markov chain Monte Carlo estimation methods naturally accommodates missing responses in the data and allows straightforward assessement of uncertainties in nonlinear models. The applicability of the method is illustrated by investigating past exposure to varicella zoster virus infection in pre-school children, using data from a large scale UK cohort study which included a cross-sectional serological survey based on oral fluid samples.