Hypothesis test on a mixture forward-incubation-time epidemic model with application to COVID-19 outbreak

TL;DR

This paper develops a statistical test for a COVID-19 incubation model based on a mixture distribution, providing theoretical guarantees and applying it to real outbreak data to improve understanding of disease incubation periods.

Contribution

It introduces a likelihood ratio test for the mixture forward-incubation-time epidemic model, establishing its limiting distribution and demonstrating its effectiveness through simulations and real data analysis.

Findings

The LRT has good control of type I error and high power.

The model's parameters are identifiable under certain conditions.

Application to COVID-19 data illustrates the test's practical utility.

Abstract

The distribution of the incubation period of the novel coronavirus disease that emerged in 2019 (COVID-19) has crucial clinical implications for understanding this disease and devising effective disease-control measures. Qin et al. (2020) designed a cross-sectional and forward follow-up study to collect the duration times between a specific observation time and the onset of COVID-19 symptoms for a number of individuals. They further proposed a mixture forward-incubation-time epidemic model, which is a mixture of an incubation-period distribution and a forward time distribution, to model the collected duration times and to estimate the incubation-period distribution of COVID-19. In this paper, we provide sufficient conditions for the identifiability of the unknown parameters in the mixture forward-incubation-time epidemic model when the incubation period follows a two-parameter distribution. Under the same setup, we propose a likelihood ratio test (LRT) for testing the null hypothesis that the mixture forward-incubation-time epidemic model is a homogeneous exponential distribution. The testing problem is non-regular because a nuisance parameter is present only under the alternative. We establish the limiting distribution of the LRT and identify an explicit representation for it. The limiting distribution of the LRT under a sequence of local alternatives is also obtained. Our simulation results indicate that the LRT has desirable type I errors and powers, and we analyze a COVID-19 outbreak dataset from China to illustrate the usefulness of the LRT.