Modeling incubation period and time of exposure using the four-parameter generalized gamma distribution

Accurately estimating the time of exposure is crucial for identifying infection sources and implementing public health interventions during infectious disease outbreaks. Conventional methods, which assume specific distributions for the incubation period, can potentially lead to biased estimates if the true distribution is misidentified. We propose using a four-parameter generalized gamma distribution that encompasses a wide range of distributions, thereby minimizing the risk of misidentification. Additionally, we introduce a likelihood function tailored for coarsely observed data, such as interval- or right-censored symptom onset times. We employ the maximum a posteriori approach for parameter inference. Simulation studies demonstrate that our method significantly outperforms conventional approaches in terms of bias and mean squared error (MSE). Specifically, the average bias in estimating exposure time decreased from −1.257 to 0.991, an 82.3% reduction, and the average MSE reduced from 5.626 to 3.069, a 45.5% reduction, compared to conventional approaches that misspecify the data-generating distribution. In addition, we demonstrate the practical use of our approach with three real-world cases concerning the identification of the time of exposure.