On the estimation of the reproduction number based on misreported epidemic data

Abstract

Epidemic data often suffer from underreporting and delay in reporting. In this paper, we investigated the impact of delays and underreporting on estimates of reproduction number. We used a thinned version of the epidemic renewal equation to describe the epidemic process while accounting for the underlying reporting system. Assuming a constant reporting parameter, we used different delay patterns to represent the delay structure in our model. Instead of assuming a fixed delay distribution, we estimated the delay parameters while assuming a smooth function for the reproduction number over time. In order to estimate the parameters, we used a Bayesian semiparametric approach with penalized splines, allowing both flexibility and exact inference provided by MCMC. To show the performance of our method, we performed different simulation studies. We conducted sensitivity analyses to investigate the impact of misspecification of the delay pattern and the impact of assuming nonconstant reporting parameters on the estimates of the reproduction numbers. We showed that, whenever available, additional information about time-dependent underreporting can be taken into account. As an application of our method, we analyzed confirmed daily A(H1N1) v2009 cases made publicly available by the World Health Organization for Mexico and the USA.

Keywords: MCMC; composite link model; delay in reporting; epidemic renewal equation; underreporting.