Leprosy is an infectious disease with long, variable periods between infection, onset of disease and subsequent diagnosis. Estimation of the numbers of undiagnosed sub-clinical and clinical infections would be useful for the management of elimination programmes.
Back-calculation uses the recorded number of diagnoses and knowledge of the incubation period distribution to make inferences about the unobservable infections. By splitting the period from infection to diagnosis into an incubation period and a detection delay, we are able to make inferences about unobserved sub- clinical and undiagnosed clinical cases. We treat new infections as proportional to the number of undiagnosed clinical cases present, and allow the diagnostic hazard to vary across time periods. The model is implemented in a Bayesian framework; coded in the Stan probabalistic programming language and run via R.
Annual state-level numbers of diagnoses for Brazil were used to illustrate inference about existing unobserved case numbers, and short-term forecasting of the probability of reaching a goal. More detailed results are presented for Espírito Santo state.