Since the outbreak of the novel coronavirus disease (COVID-19) in December 2019, the coronavirus has spread all over the world at an unprecedented rate. By May 21, 2020, more than 200 countries and territories have been affected by COVID-19, with a total of more than 5 million confirmed cases and over 330,000 deaths [1]. In addition, both the numbers of cases and deaths continue to climb up quickly. On March 11, 2020, COVID-19 was declared an international public health emergency by the World Health Organization [2]. Many countries have taken the most restrictive travel bans and quarantine policies in an attempt to stop the coronavirus from infecting their healthy populations. The worldwide economy has also been greatly set back.

During the disease incubation period, a percentage of coronavirus carriers may have no symptoms or minimal symptoms and thus often go undetected. These covert coronavirus carriers may not even be aware of the infection themselves but would be confirmed as positive cases if tested using the reverse transcriptase polymerase chain reaction (RT-PCR). If the percentage of asymptomatic carriers is large and if their transmissibility of coronavirus is as high as the symptomatic cases, this would pose a great threat to the public health worldwide. Therefore, it is critical to determine the percentage and the transmissibility of asymptomatic coronavirus carriers in the population.

There has been some work in the literature on the estimation of the asymptomatic proportion of COVID-19 cases. Based on the infected cases on the Diamond Princess cruise ship, the asymptomatic ratio was estimated to be 0.179 with a 95% Bayesian credible interval of 0.155-0.202 [3]. Another study [4] indicated that the asymptomatic ratio could be as high as 0.416 by using the information on Japanese nationals who were evacuated from Wuhan, China on charter flights. An analysis on the COVID-19 infected cases from Tibetan Autonomous Prefecture [5] found that the proportion of asymptomatic carriers was 0.217. In a study with 36 children with COVID-19 in Zhejiang, China [6], it was found that there were 10 asymptomatic cases out of 36 infections (27.7%). Another investigation in a skilled nursing facility in King County, Washington identified that, out of 48 residents that tested positive for COVID-19, 27 (56%) were asymptomatic at the time of testing [7]. The aforementioned studies indicate that the proportion of asymptomatic carriers in the total infected cases is considerably high, but the sample sizes of these studies are rather small.

There has been evidence for transmission of coronavirus from asymptomatic carriers. It was reported that the viral load detected in the asymptomatic patients was similar to that in the symptomatic patients, which suggests the potential transmissibility of asymptomatic carriers [8]. A familial cluster of 5 patients in Anyang, China demonstrated transmission of the coronavirus from an asymptomatic carrier with normal chest computed tomography but tested positive after all 5 contacted family members had shown symptoms and confirmed positive RT-PCR test results [9]. A similar case of the familial cluster of 5 members associated with COVID-19 in Luzhou, China also suggested that coronavirus can be transmitted by asymptomatic carriers [10]. Another example of coronavirus infection by an asymptomatic patient was a German case through the usual contact in business meetings [11]. Moreover, the mathematical model developed to estimate the basic reproductive number of COVID-19 and quantify the contribution of different transmission routes also indicated the transmissibility of the asymptomatic individuals [12]. In a study on a cluster of 22 close contacts of a male 22 years of age with COVID-19 [13], the asymptomatic patient showed the rapid human-to-human transmissibility. Via a detailed literature review conducted at the Centers for Disease Control and Prevention [14], it was demonstrated from the epidemiologic, virologic, and modeling studies that COVID-19 is transmittable by persons with presymptomatic or asymptomatic infection.

Chen et al [15] carried out an important study using the COVID-19 data from Ningbo, China to estimate the transmission rates of the coronavirus by the symptomatic and asymptomatic cases. The estimated transmission rates for the symptomatic and asymptomatic patients were 0.063 and 0.041, respectively, and the chi-square test yielded a P value of .29, which indicates that there is no statistically significant difference between the two transmission rates. They further investigated the transmission rates for different relationships and different types of contact with the infected patients including both symptomatic and asymptomatic cases. The conclusions were that there are statistically significant differences in the transmission rates across different relationships and different types of contact. As expected, the closer the contact is with the infected patients, the higher the chance of infection.

The following is the permutation test algorithm:

However, in their original statistical analysis [15], the chi-square tests were unduly used because the counts in some cells of the contingency tables were rather small and sometimes even zero, which violates the assumptions of a chi-square test and thus casts doubt on the validity of the hypothesis test. Moreover, when comparing the transmission rates of symptomatic and asymptomatic cases, Chen et al [15] included the cases associated with a super-spreader who mainly transmitted the disease in an air-conditioned bus and a Buddhism activity gathering. However, this may reduce the generalization of the findings, as the super-spreader should be regarded as an outlier and removed from the primary analysis.

In summary, we provided a more in-depth analysis of the Ningbo COVID-19 data to examine the difference in the transmissibility of the coronavirus for symptomatic and asymptomatic patients. The conclusion remains the same, that there is no statistically significant difference in the transmissibility of the coronavirus between symptomatic and asymptomatic patients, but our evidence for no difference appears to be stronger with larger P values than the original analysis [15].

As the proportion of asymptomatic carriers in the total infected cases is considerably high [3-7], such findings are crucial to the public health and can help to guide the relevant government agencies on policy making about the asymptomatic cases.

However, our analysis only focuses on the data from the city of Ningbo, China, and the sample size is small. Therefore, the generalization of our findings to a larger and more diverse population is limited. More work is warranted to study the transmissibility of coronavirus by the asymptomatic coronavirus carriers.