JDS Journal of Data Science 1683-8602 1680-743X 1680-743X School of Statistics, Renmin University of China JDS992 10.6339/21-JDS992 Statistical Data Science Assessment of Effects of Age and Gender on the Incubation Period of COVID-19 with a Mixture Regression Model ZhengSiming1 QinJing2 ZhouYongyzhou@amss.ac.cn.34∗ Academy of Mathematics and Systems Science, University of Chinese Academy of Sciences, Beijing, China National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland, U.S.A. Key Laboratory of Advanced Theory and Application in Statistics and Data Science, MOE Academy of Statistics and Interdisciplinary Sciences, Faculty of Economics and Management, East China Normal University, Shanghai, China Corresponding author. Email: yzhou@amss.ac.cn.. 2021752021192253268 Supplementary Material

The Supplementary Material including the detailed proofs of Theorems 1 and 2, can be found on the Journal of Data Science website. The data/code used in the analyses can be found at https://github.com/SimonsZheng/Assessment-of-Effects-of-Age-and-Gender-on-COVID-19.

 142020 152020 2021 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2021 Open access article under the CC BY license.

Following the outbreak of COVID-19, various containment measures have been taken, including the use of quarantine. At present, the quarantine period is the same for everyone, since it is implicitly assumed that the incubation period distribution of COVID-19 is the same regardless of age or gender. For testing the effects of age and gender on the incubation period of COVID-19, a novel two-component mixture regression model is proposed. An expectation-maximization (EM) algorithm is adopted to obtain estimates of the parameters of interest, and the simulation results show that the proposed method outperforms the simple regression method and has robustness. The proposed method is applied to a Zhejiang COVID-19 dataset, and it is found that age and gender statistically have no effect on the incubation period of COVID-19, which indicates that the quarantine measure currently in operation is reasonable.

 EM algorithm incubation period length-biased data mixture model References Aitkin M, Rubin D (1985). Estimation and hypothesis testing in finite mixture models. Journal of the Royal Statistical Society, Series B, 47(1): 67–75. Backer JA, Klinkenberg D, Wallinga J (2020). Incubation period of 2019 Novel Coronavirus (2019-nCoV) infections among travellers from Wuhan, China, 20–28 January 2020. Euro Surveill, 25(5): 2000062. Boldea O, Magnus J (2009). Maximum likelihood estimation of the multivariate normal mixture model. Journal of the American Statistical Association, 104(488): 1539–1549. Chen JH (2017). Consistency of the MLE under mixture models. Statistical Science, 32(1): 47–63. Dimitris K, Evdokia X (2003). Choosing initial values for the EM algorithm for finite mixtures. Computational Statistics & Data Analysis, 41(3–4): 577–590. Everitt BS, Hand DJ (1981). Finite Mixture Distributions. Chapman and Hall, London. Guan WJ, Ni ZY, Hu Y, Liang WH, Ou CQ, He JX, et al. (2020). Clinical characteristics of Coronavirus Disease 2019 in China. The New England Journal of Medicine, 382: 1708–1720. Jiang WX, Tanner AM (1999). Hierarchical mixtures-of-experts for exponential family regression models: Approximation and maximum likelihood estimation. Annals of Statistics, 27(3): 987–1011. Khalili A, Chen JH (2007). Variable selection in finite mixture of regression models. Journal of the American Statistical Association, 102(479): 1025–1038. Lauer S, Grantz K, Bi QF, Jones F, Zheng QL, Meredith H, et al. (2020). The incubation period of Coronavirus Disease 2019 (COVID-19) from publicly reported confirmed cases: Estimation and application. Annals of Internal Medicine, 172(9): 577–582. Li Q, Guan XH, Wu P, Wang XY, Zhou L, Tong YQ, et al. (2020). Early transmission dynamics in Wuhan, China, of Novel Coronavirus infected pneumonia. The New England Journal of Medicine, 382(13): 1199–1207. Liang FM, Liu CH, Carroll RJ (2010). Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples. Wiley, New York. Linton NM, Kobayashi T, Yang YC, Hayashi K, Akhmetzhanov A, Jung SM, et al. (2020). Incubation period and other epidemiological characteristics of 2019 Novel Coronavirus infections with right truncation: A statistical analysis of publicly available case data. Journal of Clinical Medicine, 9(2): 538. McLachlan GJ, Peel D (2000). Finite Mixture Model. Wiley, New York. Qin J, You C, Lin QS, Hu TJ, Yu SC, Zhou XH (2020). Estimation of incubation period distribution of COVID-19 using disease onset forward time: A novel cross-sectional and forward follow-up study. Science Advances, 6(33): eabc1202. Qin YC, Priebe CE (2013). Maximum Lq -likelihood estimation via the expectation-maximization algorithm: A robust estimation of mixture models. Journal of the American Statistical Association, 108(503): 914–928. Wolfe J (1971). A Monte Carlo study of the sampling distribution of the likelihood ratio for mixtures of normal distributions. Naval Personnel and Training Research Laboratory San Diego, Technical Bulletin STB 72-2.