Adapting Back-calculation Methods to Estimate the Incidence of Tuberculosis

Background Despite being the leading cause of death, the global tuberculosis (TB) burden is ill-defined. Existing methods to estimate incidence are time and/or resource-intensive and often inaccurate. Back-calculation was developed to estimate HIV incidence by considering reported cases to be a convolution of the disease duration and the incidence of new cases. New estimates of TB natural history parameters allow us to develop Bayesian back-calculation methods for TB to assign case notification data to the time point of onset of disease. Methods Recorded counts of TB cases are underestimates of the true burden of disease, so we include a multiplier derived from prevalence to notification ratios to account for underreporting. We assume a Poisson distribution for notifications and incidence and use a penalized-likelihood before smooth estimates. We estimate sex-stratified TB incidence for Vietnam, Cambodia, and the Philippines via Markov chain Monte Carlo. Results Annual estimated TB incidence was, on average 19% greater than recorded notifications. TB incidence among males was on average 3.8% higher than females in Vietnam, 1.3% in Cambodia, and 2.5% higher in the Philippines. Conclusions These estimates account for the delay between bacteriologically positive subclinical disease and notification and, as such, may be more temporally accurate than existing methods.