Empirical Joint Estimation for Incubation Period and Infection under the Doubly Interval-Censored with Right Truncated Observation

Doubly interval-censoring occurs frequently in infectious disease data, but the nonparametric estimators suitable for doubly interval-censored observed data are not well known. We develop a nonparametric estimator for the distribution function of doubly interval-censored data. Our proposed method analyzes the distributions of the incubation period and the infections simultaneously, and we derive its estimator based on the Bayesian and maximum likelihood methods. The simulation study suggests that this estimator is consistent. The usefulness of the proposed method is shown by a practical example using the reports of the novel coronavirus disease.