Inference of the generalized-growth model via maximum likelihood estimation: A reflection on the impact of overdispersion.

Recently, the generalized-growth model was introduced as a flexible approach to characterize growth dynamics of disease outbreaks during the early ascending phase. In this work, by using classical maximum likelihood estimation to obtain parameter estimates, we evaluate the impact of varying levels of overdispersion on the inference of the growth scaling parameter through comparing Poisson and Negative binomial models. In particular, under exponential and sub-exponential growth scenarios, we evaluate, via simulations, the error rate of making an incorrect characterization of early outbreak growth patterns. Simulation results show that the ability to correctly identify early outbreak growth patterns can be affected by overdispersion even when accounted for using the Negative binomial model. We exemplify our findings using data on five different outbreaks. Overall, our results show that estimates should be interpreted with caution when data are overdispersed.