Robust estimation of the incubation period and the time of exposure using <i>γ</i> -divergence

Estimating the exposure time to single infectious pathogens and the associated incubation period, based on symptom onset data, is crucial for identifying infection sources and implementing public health interventions. However, data from rapid surveillance systems designed for early outbreak warning often come with outliers originated from individuals who were not directly exposed to the initial source of infection (i.e. tertiary and subsequent infection cases), making the estimation of exposure time challenging. To address this issue, this study uses a three-parameter lognormal distribution and proposes a new <i>γ</i>-divergence-based robust approach for estimating the parameter corresponding to exposure time with a tailored optimization procedure using the majorization-minimization algorithm, which ensures the monotonic decreasing property of the objective function. Comprehensive numerical experiments and real data analyses suggest that our method is superior to conventional methods in terms of bias, mean squared error, and coverage probability of 95% confidence intervals.