how many covid 19 pcr positive individuals do weexpect to see on the diamond princess CORD-Papers-2021-10-25 (Version 1)

Title: How many COVID-19 PCR positive individuals do weexpect to see on the Diamond Princess cruise ship?
Abstract: When COVID-19 was detected among passengers on Diamond Princess (DP) cruise ship in the end of January and beginning of February of this year, unfortunately it has become an ideal experimental model for studying the transmission potential of COVID-19 in a closed environment while it is hard to do so in the wider open population. Information collected from such an outbreak is crucial for policy makers to understand and manage the epidemic. To disclose the information such as infection onset time, transmission time, and so on from the available observed incomplete data, we must develop valid statistic models and solid inference methods. Due to the fact that the priority for RT-PCR test for COVID-19 was given to symptomatic and their close contacts and elderly individuals, we have to take this selection bias into considerations in the statistic inference. Based on RT-PCR test data performed on the Diamond Princess cruise, in this paper we propose a novel mixture model where the mixing proportions vary with time to estimate the infection distribution and the total infected individuals after a 14-day of quarantine. Compared with the epidemiologic description of COVID-19 spread in open space, we have found some unique features in the Diamond Princess cruise ship. Our fndings may shed lights on preventing future pandemic outbreaks in cruise ship.
Published: 11/16/2020
Journal: medRxiv : the preprint server for health sciences
DOI: 10.1101/2020.11.14.20230938
DOI_URL: http://doi.org/10.1101/2020.11.14.20230938
Author Name: Qin, J
Author link: https://covid19-data.nist.gov/pid/rest/local/author/qin_j
Author Name: Chen, F
Author link: https://covid19-data.nist.gov/pid/rest/local/author/chen_f
Author Name: Ma, H
Author link: https://covid19-data.nist.gov/pid/rest/local/author/ma_h
Author Name: Liu, Y
Author link: https://covid19-data.nist.gov/pid/rest/local/author/liu_y
Author Name: Follmann, D
Author link: https://covid19-data.nist.gov/pid/rest/local/author/follmann_d
Author Name: Zhou, Y
Author link: https://covid19-data.nist.gov/pid/rest/local/author/zhou_y
sha: 5adbb733ba8028c6446e442f4d7a65854b2833b5
license: medrxiv
source_x: MedRxiv; Medline; WHO
source_x_url: https://www.medline.com/https://www.who.int/
pubmed_id: 33236032
pubmed_id_url: https://www.ncbi.nlm.nih.gov/pubmed/33236032
url: https://doi.org/10.1101/2020.11.14.20230938 http://medrxiv.org/cgi/content/short/2020.11.14.20230938v1?rss=1 https://www.ncbi.nlm.nih.gov/pubmed/33236032/
has_full_text: TRUE
Keywords Extracted from Text Content: households coronavirus disease 2019 COVID-19 sam-7 medRxiv preprint day i individuals Ayer https://doi.org/10.1101/2020.11.14.20230938 doi left F i = F ( · ≤ F COVID-19 λ i N i F i F 1 θ 4 patients Johns Hopkins people i /N i SARS-CoV-2 participants medRxiv preprint Figure 1 − N ) Blue N i θ 1 medRxiv preprint Hung F i 3711−3063=648 medRxiv medRxiv preprint byN F 1 ≤ F 2 F λ i Iso Sun (2006) θ 2 ELS
Extracted Text Content in Record: First 5000 Characters:The coronavirus disease 2019 has become a global epidemic crisis with tens of thousands confirmed cases surfacing everyday. The infection rates in households, offices and public places are quite different from those in encompassed spaces such as airplanes, trains and cruise ships. Studying the behavior of COVID-19 in confined spaces like Diamond Princess cruise is of great importance to understand the disease progression and to manage the epidemic. We propose a novel mixture model to estimate the infection distribution and total infected number after 14 Daily time series of RT-PCR test data from February 5 to February 20 can be found in Table 1 of Mizumoto et al.(2020) , including the number of tests, number of testing positive cases, number of cases in presence or absence of symptoms, etc (Mizumoto et al., 2020) . However, the infection time and the infection rate were unknown. Data from February 11 and February 14 were not available in the original data sources. We carefully address this missing data problem in our statistical analysis. At the beginning, PCR tests had been conducted mainly for symptomatic groups and their high-risk close contacts, and then for almost all persons in the second week. As of February 20, a total 3063 respiratory specimens were tested with 634 positive, including one quarantine officer, one nurse, and one administrative officer. Of these 634 cases, 313 were female and 321 were male. 476 cases had age 60 years or older (Mizumoto et al., 2020) . For convenience, the daily time series data with number of tested individuals and individuals with positive results are provided in Table 1. 4 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted November 16, 2020. ; In this Section, we provide an obvious lower bound estimation of the number of infected individuals and a more sophisticated statistical method to estimate this number and the infection distribution using the daily time-series data described in Table 1 . Let f (x) and F (x) be the density and cumulative distribution functions of infection onset time X calculated from February 4, respectively. Therefore F i = F (i) is the probability of the infection onset time occurring before 5 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted November 16, 2020. ; https://doi.org/10.1101/2020.11.14.20230938 doi: medRxiv preprint day i starting from February 4. For example, F 1 represents the probability of testing positive on February 5. According to the non-decreasing property of the distribution function, F i should satisfy the constraint F 1 ≤ F 2 ≤ · · · ≤ F 14 . First, we may hypothetically assume that no PCR tests were performed in the first 13 days of quarantine. On February 20, the last quarantine day, 52 individuals were selected by the officer on the ship for testing and 13 positives were found. Therefore the infection rate is 13/52 = 25%. Out of the n = 3711 passengers and crew members, we expect to see 3711 * 0.25 = 928 PCR positive results. In reality, the selection of individuals for PCR test in the first week was not random. Symptomatic individuals, elders and closely related individuals were selected first. Therefore, 928 should be a lower bound estimation of total PCR-positive individuals after the end of quarantine, as these 52 should be less likely to be PCR-positive compared to the ship as a whole. We will give a full explanation of the larger estimation of N theoretically below. Next we shall show statistically that a non-random sampling was implemented in the selection for PCR test. Suppose there is no selection bias, i.e., a random sampling was used. Let Let n i and N i be the number of tested positive cases and number of tests at day i respectively, and X ij be the infection time of the jth subject who was tested at day i, j = 1, 2, . . . , N i ; i = 1, 2, . . . , 14. Instead of observing the exact infection time X ij , we can only observe the number of tested positive We use the nonparametric likelihood method directly to estimate F i . The observed likelihood function is This is a standard current status data problem discussed extensively in statistical literature, for 6 All rights reserved. No reuse allowed without permission. perpetuity. preprint (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in The copyright holder for this this version posted November 16, 2020. ; https://doi.org/10.1101/2020.11.14.20230938 doi: medRxiv preprint Figure 1 : Comparison of n i /N i and fitted infection rates using PAVA. n i represents daily number of positive ind
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