Observational case study.
“Five-in-one” pooled testing for COVID-19 in Wuhan
Wuhan was locked down from January 23, 2020. After the epidemic was controlled, Wuhan lifted travel restrictions on April 8 after an 11-week (77-day) lockdown. However, a small number of local cases emerged, including asymptomatic carriers, within a short period after lifting travel restrictions. The Chinese government was highly concerned about locally spreading cases and worried that this would lead to a second wave of the epidemic. Consequently, Wuhan performed a citywide intensive nucleic acid testing of COVID-19 from May 14 to June 1 and comprehensively checked for asymptomatic infections to control the local epidemic, allowing work and production to resume. To improve the detection efficiency and control the spread of the epidemic, the “five-in-one” pooled testing method was adopted using nucleic acid detection for all the people in Wuhan. Specifically, the method used samples of five people as a set and then sampled the sets separately. As shown in Fig. 1, before collecting the samples, the people’s information, including name, identity card number, contact phone number, sample collection site, sample collection date, and sample collection time, was collected and registered. Collection tubes were numbered according to the sets. The following items were collected: throat swabs, nasal swabs, blood samples and stool samples. For large-scale sample collection work, such as in Wuhan, throat swab collection has a significant advantage in operative convenience. The sampling workers used a plastic swab with a polypropylene fibre tip to wipe the subject's bilateral pharyngeal tonsils and posterior pharyngeal wall during the throat swab collection from the population. The swabs were stored in the same sampling tube for nucleic acid testing with the swabs from the other four people.
The principle of “five-in-one” pooled testing is shown in Fig. 2. The samples collected from five people are mixed before testing. If the result of the pooled sample is negative, all five samples in the set are negative, i.e., the five people in the pooled sample are safe. On the opposite, if the pooled sample yielded positive result, the five people are notified as soon as possible. Those people are immediately isolated and tested separately to identify the positive sample. “Five-in-one” pooled testing saves both time and costs and reduces sampling inspections, thereby reducing the workload of the health sector. Especially in large cities such as Beijing, Wuhan and Qingdao, each of which has over 10 million people, pooled testing can be relied on for the general prevention-oriented coronavirus nucleic acid screening. Pooled testing can be promoted when coronavirus activity in the sample and nucleic acid testing sensitivity are not affected by dilution. According to research conducted by the Institute of Virology of Saarland University in Germany, the method of “pooled samples” can merge up to 30 samples, which is sufficient to ensure testing accuracy, although testing sensitivity is slightly reduced. Since the PCR testing initially needs to be amplified, the dilution has almost no effect on the testing results. However, the actual pooled sample ratio should be controlled at 5–10 people, and the maximum should not exceed 20 people to ensure that the testing sensitivity does not decrease 21.
Wuhan's feat of testing 10 million people in ten days benefited from pooled testing. In addition, it was verified that pooled testing does not affect the virus activity or the nucleic acid testing sensitivity. The testing results were as follows: 9,998,828 people in Wuhan were subjected to nucleic acid testing, of which 9,865,404 had no history of confirmed COVID-19 and 34,424 of previous coronavirus pneumonia patients had recovered. Among subjects without a history of COVID-19, no confirmed cases were found, while 300 asymptomatic infections emerged. The testing rate of asymptomatic infections was 0.303 per 10,000. It is worth noting that large-scale pooled testing is implemented primarily for prevention, meaning that results can only be achieved during the early stages of the epidemic. For high-risk sets, such as symptomatic patients and close contacts in fever clinics, individual collection and individual testing should be implemented. On the opposite, pooled testing is preferred for screening virus carriers in low-risk and high-density populations.
“Ten-in-one” pooled testing for COVID-19 in Qingdao
On October 11, 2020, after three asymptomatic cases of COVID-19 were found in Qingdao, Shandong Province, the Qingdao government immediately organised large-scale investigations and classified testing to prevent the spread of the epidemic. At 23:00 on October 11, six confirmed cases and six asymptomatic infection cases were identified in Qingdao. This was caused by the sharing of CT (computed tomography) scan rooms with patients in general wards during infected hospitalisation. For that reason, the Qingdao government formulated and launched a full-staff nucleic acid testing programme. It was necessary, but formidable, to complete an assessment of six million people in the primary urban area within three days and to cover the entire city within five days. Therefore, based on Wuhan's “five-in-one” pooled testing method, the Qingdao government adopted the improved “ten-in-one” pooled testing for nucleic acid testing. The Chinese government has currently issued the new coronavirus nucleic acid “ten-in-one” standardized technical specifications for pooled testing. Compared to Wuhan's “five-in-one” pooled testing technology, the “ten-in-one” pooled testing method significantly expands testing capacity, which increases its efficiency. In addition, the “ten-in-one” pooled testing method can detect infections in advance and isolate them, which is conducive in reducing the virus spread. The principle of the “ten-in-one” pooled testing method, which increases pooled samples, is similar to that of the “five-in-one” pooled testing method. The “ten-in-one” pooled testing method of Qingdao strictly follows the requirements of “Technical Specifications for the Detection of COVID-19 with Ten in One Pooled Testing” promulgated by China for nucleic acid sampling and testing. As shown in Fig. 3, pooled samples collected from ten people are mixed before testing. If the pooled sample is negative, all ten samples are negative, and the ten people in the pooled testing are safe. However, if the result of the pooled sample is positive, the ten people are notified immediately, isolated and individually-checked to identify those who are positive. Compared to the “five-in-one” pooled testing method in Wuhan, the “ten-in-one” pooled testing method increases the number of pooled samples and the efficiency of the process. At 18:00 on October 16, 10,899,145 nucleic acid testing were completed in Qingdao, from which nearly 10 million people had been tested within five days. The testing speed was twice as fast as that in Wuhan. All nucleic acid testing results of the citizens in Qingdao were negative, which virtually eliminated the risk of community transmission of the epidemic.
Optimisation of the “ten-in-one” testing method: the pentagram mini-pooled testing method
As noticed above, the “five-in-one” pooled testing method used in Wuhan and the “ten-in-one” pooled testing method utilised in Qingdao provide new strategies for large-scale nucleic acid testing of the COVID-19 epidemic for other countries. These two methods, using different numbers of pooled samples, have significantly increased the speed of nucleic acid testing in the first round of testing. However, both methods still use “individual-sample testing” in the second round of testing. Especially in Qingdao's “ten-in-one” pooled testing method, when a sample testing becomes positive in the first round of nucleic acid testing, all 10 individual specimens require individual-sample testing in the second round. This individual-sample testing method not only increases the cost of testing by significantly increasing the number of testing kits and the workload on the health sector, but also reduces the efficiency of the nucleic acid testing and controlling the spread of the epidemic. Accordingly, some scholars have explored the second-round testing method of pooled testing to improve the testing efficiency. As early as the 1940s, Dorfman22, an economist at Harvard University, proposed pooled testing for screening the syphilis carriers among soldiers in World War II. Dorfman suggested that after the individual blood sera were drawn, they were pooled in groups of N and that the groups rather than the individual sera were subjected to chemical analysis. For positive samples in the first round of testing, the individuals constituting the pool must be retested to determine which of the members are infected. Subsequently, some scholars have improved the pooled testing method. Many people in South Africa are infected by human immunodeficiency virus (HIV) every year, and the prevalence is almost 17% among adults 15–49 years of age. Therefore, many scholars in South Africa have investigated HIV testing methods. van Zyl et al. 23 adopted matrix strategies to reduce the costs of virologic monitoring. Specifically, using nine specimens as an example, the specimens are labelled to form a 3×3 matrix. Each row and column of the matrix is detected by “three-in-one” pooled testing. If the testing results of two pooled samples are positive, bearing in minds that the rows and columns intersect in the matrix platform, then the intersection identifies the positive sample. This method only requires that six testing be performed on nine specimens to determine an individual or more confirmed patients. Recently, scientists in Rwanda proposed a hypercube algorithm testing method suitable for areas with low infection rates to suppress infections of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)24. This method quickly identifies and isolates individuals infected with the virus. Taking 27 (N = 33 = 27) testing samples as an example, the hypercube (3×3×3) of 27 samples are sliced into 3 slices in each of the 3 principal directions. Each of the slices contains nine samples, and “nine-in-one” pooled testing is performed on each slice to identify the coordinates of the positive sample. Thus, in this example, only nine testing can be used to uniquely identify an individual infected person among 27 people. For the optimised testing methods proposed by the above scholars, the number of pooled samples in the first round is n2 or n3 (n is a natural number), usually 32 or 33. These values can be divided equally in multiple directions, and in each direction, they can be divided in a multidimensional matrix platform. Then, positive patients can be identified through the intersection of different positive pooled samples. However, in Qingdao's “ten-in-one” pooled testing, the number of pooled samples cannot be sorted to form n×n matrix pools. To reduce the number of testing for the second round of “ten-in-one” pooled testing without increasing the time and cost, this paper innovatively proposes the pentagram mini-pooled testing to identify an individual positive patient, as shown in Fig. 4.
Since pooled testing is suitable for areas with low infection rates, a high number of individuals who are positive in the random “ten-in-one” testing is a small probability event from a probabilistic point of view. That is, if a “ten-in-one” pooled testing result is positive, the greatest probability is that only an individual person is infected. Therefore, the pentagram mini-pooled testing (see Fig. 4) proposed in this paper focuses on the circumstance in which only one specimen is infected among the ten specimens of the positive pooled sample. As mentioned above, when a “ten-in-one” pooled testing is positive, the ten people should be isolated and retested in a second round. Pentagram mini-pooled testing works as follows in the second round. Before testing, the people are sorted from one to ten, and two throat swab samples are collected from each person. During testing, the twenty swabs are pooled into six samples according to the pentagram mini-pooled testing method (five “three-in-one” pooled samples (S1-S5) and one “five-in-one” pooled sample (S6), as shown in Fig. 5)). Every three specimens are placed in the same collection tube according to the three serial numbers corresponding to the vertices of the five orange triangles of the pentagram. For example, one swab sample is taken from subjects 1, 6, and 7, and these three swab samples are placed into S1 collection tube for the “three-in-one” pooled testing. By analogy, S2-S5 collection tubes are obtained. The “five-in-one” pooled sample tube (i.e., S6 collection tube) refers to the collected swab samples from subjects 1 to 5. Nucleic acid testing is then performed for the six pooled samples (S1-S6). After the testing are returned, the positive patients are identified by comparing the prediction testing results, as shown in Fig. 5.
Theoretical Basis And Applicable Conditions For Pooled Testing
There are certain applicable conditions for large-scale screening of COVID-19 using the pooled testing method. The applicability of this method and the selection of a reasonable number of pooled samples are importantly related to the infection rate of the region15,25. To verify the efficacy and applicable conditions for pooled testing, the quantitative relationship between the value of pooled samples and the virus infection rate is determined. It is assumed that N is the total population of a certain city; p is the infection rate; x is the number of people in each set of pool testing samples; and Y is the total testing time for the first round of pool testing (Y1) and the second round of individual-sample testing (Y2). p is an unknown and dynamically changing value, but it can be estimated based on the number of confirmed cases.
If x = 1, each person is tested once. Then, the value of Y is equal to N.
When x ≠ 1, the testing should be performed in two rounds.
The first round is pooled testing considering that each x people represent a set, so the testing time required for the first round is Y1 = N/x. The first testing result is positive or negative (only if everyone in a given set is uninfected can a negative result be obtained). Therefore, (1-p)x is the probability of getting a negative result for the set testing of the first round, and 1-(1-p)x is the probability that the result of the set testing is positive for the same round. Hence, the number of sets with positive testing results from the first round can be defined as follows:
(N/x) *(1-(1-p) x), (2)
The second-round testing is for the sets that showed positive testing results in the first round. The total number of people in these sets is as follows:
(N/x)*(1-(1-p)x)*x = N*(1-(1-p)x), (3)
Therefore, the time for testing the second round can be determined as:
Y2 = N*(1-(1-p)x), (4)
After the two-round testing is completed, the total testing time Y can be computed as:
Y = Y1 + Y2 = N/x + N*(1-(1-p)x), (5)