Back-calculating the incidence of infection of leprosy in a Bayesian framework

Ronald E. Crump, Graham F. Medley

The number of new leprosy cases reported annually is falling worldwide, but remains relatively high in some populations. Because of the long and variable periods between infection, onset of disease, and diagnosis, the recently detected cases are a reflection of infection many years earlier. Estimation of the numbers of sub-clinical and clinical infections would be useful for management of elimination programmes. Back-calculation is a methodology that could provide estimates of prevalence of undiagnosed infections, future diagnoses and the effectiveness of control. A basic back-calculation model to investigate the infection dynamics of leprosy has been developed using Markov Chain Monte Carlo in a Bayesian context. The incidence of infection and the detection delay both vary with calendar time. Public data from Thailand are used to demonstrate the results that are obtained as the incidence of diagnosed cases falls. The results show that the underlying burden of infection and short-term future predictions of cases can be estimated with a simple model. The downward trend in new leprosy cases in Thailand is expected to continue. In 2015 the predicted total number of undiagnosed sub-clinical and clinical infections is 1,168 (846-1,546) of which 466 (381-563) are expected to be clinical infections. Bayesian back-calculation has great potential to provide estimates of numbers of individuals in health/infection states that are as yet unobserved. Predictions of future cases provides a quantitative measure of understanding for programme managers and evaluators. We will continue to develop the approach, and suggest that it might be useful for other NTD in which incidence of diagnosis is not an immediate measure of infection.