Research ArticleCORONAVIRUS

Estimation of incubation period distribution of COVID-19 using disease onset forward time: A novel cross-sectional and forward follow-up study

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Vol. 6, no. 33, eabc1202

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• RE: Responses to the eletter from Zhao
• Jing Qin
• Other Contributors:
• Chong You
• Xiao-Hua Zhou
• Qiushi Lin
• Taojun Hu
• Shicheng Yu

Dear Dr Zhao,

Thanks for your comments in regard to our paper, “Estimation of incubation period distribution of COVID-19 using disease onset forward time: a novel cross-sectional and forward follow-up study”. We have detailed our responses to your comments point by point below, but before that, we would like to reemphasize the concept of truncation/renewal process and as well as the corresponding formula derivation to make it easier for understanding.

In our study, we only included those patients who were free of symptoms before their departure (in the time period between Feb 19 to 23) of Wuhan and developed symptoms somewhere else later. As indicated in the paper, due to lock out of China after Feb 23, we are quite confident those patients were most likely infected within Wuhan. For example, an individual may contract the disease on Feb 20 and left Wuhan on Feb 23 with no symptom and developed into symptoms on Feb 25, then this individual would be included in our cohort. Hypothetically assuming the date of infection (Feb 20) is known, then we call the time relapse from Feb 20 to Feb 23 as the backward time, i.e. A=3 days, and the time relapse from Feb 23 to Feb 25 as the forward time V=2 days.

Here we call A+V as a renewal process. If the incubation period Y has a density f(y), based on renewal process theory, we can obtain

V~\frac{\bar{F}\left(v\right)}{\mu}, (1)
A~\frac{\bar{F}\left(v\right)}{\mu}, (A,V)~\frac{f\left(a+v\r...

Competing Interests: None declared.
• Incubation period of COVID-19
• Qingyuan Zhao, University Lecturer in Statistics, University of Cambridge

Qin et al. [1] proposed a novel approach to estimate the distribution of the incubation period of COVID-19. Compared with others’ results, their estimated incubation period, with a median of 7.76 days (95% CI 7.02–8.53) and 95th percentile of 16.32 days (95% CI 15.62–17.04), is notably longer. In a related work [2], we also used a cohort of Wuhan-exported COVID-19 cases but estimated that the incubation period has a median of 4.1 days (95% CI 3.7–4.6) and a 95th percentile of 12.3 days (95% CI 11.1–13.8). As their results are now published and becoming adopted in other studies of COVID-19 [3] (we thank Ron Sender for pointing this to us), we would like to make known some comments made to the authors earlier in a private communication.

To overcome potential biases in using exported cases to estimate the incubation period, Qin et al. proposed to treat the incubation period as a renewal and the time between departure from Wuhan and symptom onset as a forward time. Their key assumption is that this renewal process has reached its equilibrium (Assumption A1 in their Supplement S1), so that the forward time has the same marginal distribution as the backward time (the time from infection to Wuhan-departure). We think this is an interesting and novel idea and, if well-justified, can be a robust way to estimate the incubation period. However, we believe there are several potential issues in applying this method to COVID-19:
1. It is unclear whether we can treat the inc...