Ambitious World Health Organization targets for disease elimination require monitoring of epidemics using routine health data in settings of decreasing and low incidence. We evaluated two methods commonly applied to routine testing results to estimate incidence rates that assume uniform probability of infection between consecutive negative and positive tests based on: 1. the midpoint of this interval; and 2. a randomly selected point on this interval. We compared these with an approximation to the Poisson-binomial distribution which assigns partial incidence to time-periods based on the uniform probability of occurrence in these intervals. We assessed bias, variance and convergence of estimates using simulations of Weibull distributed failure times with systematically varied baseline incidence, and varying trend. We considered results for quarterly, half-yearly and yearly incidence estimation frequencies. We applied methods to assess human immunodeficiency virus (HIV) incidence in HIV-negative patients from the Treatment with Antiretrovirals and their Impact on Positive And Negative men study between 2012 and 2018. The Poisson-binomial method had reduced bias and variance at low levels of incidence and for increased estimation frequency, with increased consistency of estimation. Application of methods to real-world assessment of HIV incidence found decreased variance in Poisson-binomial model estimates, with observed incidence declining to levels where simulation results had indicated bias in midpoint and random-point methods.
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