Inferencing superspreading potential using zero-truncated negative binomial model: exemplification with COVID-19.

Affiliation

Zhao S(1)(2), Shen M(3), Musa SS(4)(5), Guo Z(6), Ran J(7), Peng Z(8), Zhao Y(9), Chong MKC(6)(10), He D(11), Wang MH(6)(10).
Author information:
(1)JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China. [Email]
(2)CUHK Shenzhen Research Institute, Shenzhen, China. [Email]
(3)School of Public Health, Xi'an Jiaotong University Health Science Center, Xi'an, 710061, Shaanxi, China.
(4)Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China.
(5)Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria.
(6)JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China.
(7)School of Public Health, Shanghai Jiao Tong University School of Medicine, Shanghai, China. [Email]
(8)Department of Epidemiology and Biostatistics, School of Public Health, Nanjing Medical University, Nanjing, China.
(9)School of Public Health and Management, Ningxia Medical University, Yinchuan, China.
(10)CUHK Shenzhen Research Institute, Shenzhen, China.
(11)Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China. [Email]

Abstract

BACKGROUND: In infectious disease transmission dynamics, the high heterogeneity in individual infectiousness indicates that few index cases generate large numbers of secondary cases, which is commonly known as superspreading events. The heterogeneity in transmission can be measured by describing the distribution of the number of secondary cases as a negative binomial (NB) distribution with dispersion parameter, k. However, such inference framework usually neglects the under-ascertainment of sporadic cases, which are those without known epidemiological link and considered as independent clusters of size one, and this may potentially bias the estimates. METHODS: In this study, we adopt a zero-truncated likelihood-based framework to estimate k. We evaluate the estimation performance by using stochastic simulations, and compare it with the baseline non-truncated version. We exemplify the analytical framework with three contact tracing datasets of COVID-19. RESULTS: We demonstrate that the estimation bias exists when the under-ascertainment of index cases with 0 secondary case occurs, and the zero-truncated inference overcomes this problem and yields a less biased estimator of k. We find that the k of COVID-19 is inferred at 0.32 (95%CI: 0.15, 0.64), which appears slightly smaller than many previous estimates. We provide the simulation codes applying the inference framework in this study. CONCLUSIONS: The zero-truncated framework is recommended for less biased transmission heterogeneity estimates. These findings highlight the importance of individual-specific case management strategies to mitigate COVID-19 pandemic by lowering the transmission risks of potential super-spreaders with priority.