Estimating the Asymptomatic Proportion of 2019 Novel Coronavirus onboard the Princess Cruises Ship, 2020

The potential infectiousness of asymptomatic COVID-19 cases together with a substantial fraction of asymptomatic infections among all infections, have been highlighted in clinical studies. We conducted statistical modeling analysis to derive the delay-adjusted asymptomatic proportion of the positive COVID-19 infections onboard the Princess Cruises ship along with the timeline of infections. We estimated the asymptomatic proportion at 17.9% (95% CrI: 15.5%-20.2%), with most of the infections occurring before the start of the 2-week quarantine.

The clinical and epidemiological characteristics of COVID-19 continue to be investigated as the virus continues its march through the human population [2][3]. While reliable estimates of the reproduction number and the death risk associated with COVID-19 are crucially needed to guide public health policy, another key epidemiological parameter that could inform the intensity and range of social distancing strategies to combat COVID-19 is the asymptomatic proportion, which is broadly defined as the proportion of asymptomatic infections among all the infections of the disease. Indeed, the asymptomatic proportion is a useful quantity to gauge the true burden of the disease and better interpret estimates of the transmission potential. This proportion varies widely across infectious diseases, ranging from 8% for measles and 32% for norovirus up to 90-95% for polio [4][5][6]. Most importantly, it is well established that asymptomatic individuals are frequently able to transmit the virus to others [7][8].
. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.02.20.20025866 doi: medRxiv preprint COVID-19 is not the exception to this pattern, with accumulating evidence indicating that a substantial fraction of the infected individuals with the novel coronavirus are asymptomatic [9][10][11].
As an epidemic progresses over time, suspected cases are examined and tested for the infection using polymerase chain reaction (PCR) or rapid diagnostic test (RDT). Then, time-stamped counts of the test results stratified according to the presence or absence of symptoms at the time of testing are often reported to the public in near real-time.
Nevertheless, it is important to note that the estimation of the asymptomatic proportion needs to be handled carefully since real-time outbreak data are influenced by the phenomenon of right censoring, due to the time lag between the time of examination and sample collection and the development of illness.
In this paper, we conduct a statistical modeling analysis to estimate the asymptomatic proportion among infected individuals who have tested positive for COVID-19 infections onboard the Princess Cruises Ship along with their time of infections, accounting for the delay in onset of symptoms and right-censoring.
. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.   (Table 1). Soon after identification of the first infections, both symptomatic and asymptomatic cases were transported to designated medical facilities specialized in infectious diseases in Japan. However, these patients were treated as external (imported) cases, and a detailed description of their clinical progression is not publicly available.
The asymptomatic proportion was defined as the proportion of asymptomatically infected individuals among the total number of infected individuals.
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Statistical modelling
Here, we describe the statistical model that was employed to estimate the asymptomatic proportion using the time-series dataset described above. Given an individual was exposed during the interval [a i, b i ] the probability for them being asymptomatic at time c is . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.  We conducted sensitivity analyses to examine how varying the mean incubation period between 5.5 and 9.5 days affects our estimates of the true asymptomatic proportion. Estimates of the true asymptomatic proportion among the reported asymptomatic cases are somewhat sensitive to changes in the mean incubation period, ranging from 0.28 (95%CrI: 0.23-0.33) to 0.40 (95%CrI: 0.36-0.44), while the . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
is the (which was not peer-reviewed) The copyright holder for this preprint Heat maps were used to display the density distribution of infection timing by individuals ( Figure S1) where the vertical line corresponds to the date of February 5, 2020. Among the symptomatic cases, the infection timing appears to have occurred just before or around the start of the quarantine period, while the infection timing for asymptomatic cases appears to have occurred well before the start of the quarantine period.

Discussion
We have conducted statistical modeling analyses on publicly available data to elucidate the asymptomatic proportion, along with the time of infection among the COVID-19 infected cases onboard the Princess Cruises ship.
Our estimated asymptomatic proportion is at 17.9% (95% CrI: 15.5%-20.2%), which overlaps with a recently derived estimate of 33.3% (95% CI: 8.3%-58.3%) from data of Japanese citizens evacuated from Wuhan [13]. Considering the similarity in viral loads and the high possibility of potent transmission potential, the high proportion of asymptomatic infections has significant public health implications [14]. For instance, self-isolation for 14-day periods are also recommended for contacts with asymptomatic cases [15].
. CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity. Our study is not free from limitations. First, laboratory tests by PCR were conducted focusing on symptomatic cases especially at the early phase of the quarantine.
If asymptomatic cases where missed as a result of this, it would mean we have underestimated the asymptomatic proportion. Second, it is worth noting that the data of passengers and crews employed in our analysis is not a random sample from the general population. Considering that most of the passengers are 60 years and older, the nature of this age distribution may lead to underestimation if older individuals tend to experience more symptoms. An age standardized asymptomatic proportion would be more appropriate in that case. Third, the presence of symptoms in cases with COVID-19 may correlate with other factors unrelated to age including prior health conditions such as cardiovascular disease, diabetes, immunosuppression. Therefore, more detailed data documenting the baseline health of the individuals including the presence of underlying diseases or comorbidities would be useful to remove the bias in estimates of the asymptomatic proportion.
In summary, we have estimated the proportion of asymptomatic cases among individuals who have tested positive for novel COVID-19 along with the times of . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
is the (which was not peer-reviewed) The copyright holder for this preprint  . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
is the (which was not peer-reviewed) The copyright holder for this preprint . https://doi.org/10.1101/2020.02.20.20025866 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a author/funder, who has granted medRxiv a license to display the preprint in perpetuity.