The new Minister of Health has an explanation of why it is necessary to do mass testing (100% of the population?) He said that with the sample test plan, the test cost is very cheap. [1]. I think otherwise, because pooled testing still costs a lot of money. Below, I explain why.

Explaining the reason for mass testing, the minister took the example of people in China doing such tests, and Vietnam also followed. He explained: “There is no other way we can prevent early detection without testing. If we don’t do that, it means we accept in the community that there must still be infected people“.

But he did not specifically explain why. However, one important piece of information he said is that the testing program will follow a ‘sampling’ approach, and he specifically says that 10 samples can be pooled, and therefore the cost will be low. This requires serious evaluation, and I offer one below.

1. What is pooled testing?

This pooled testing option is not new, as it has been around since 1943 and has been used for bowel cancer screening. But like any alternative, pooled testing has its strengths and weaknesses.

But perhaps many of you are not clear about this option, so I would like to have a few lines of explanation for you to understand what I mean. Sample pooling means mixing samples from more than one person (n) into a sample, and then use the test method on that pool. Many people here may be individuals in a family, or in an alley, or in a group. There are two situations where this happens:

• If the test result is negative, it means all n everyone is negative.

• If the result is positive, that means at least 1 person in the sample may be infected. This also means testing again, but this time testing samples one by one.

As you can see, the pooled testing option effectively reduces the number of tests. Instead of testing 10 million people (for example), authorities only need to test N times (N < 10 million). And, therefore, save money.

2. The problem of pooled testing

But because the test method is flawed in terms of false positives and false negatives (expressed in sensitivity and specificity), the problem is not as simple as above. When we mix samples from many people into 1 pooled sample it saves, but if the number of samples n the more, the higher the probability of false negatives (because the sample becomes dilute). On the contrary, if n low, may increase the probability of false positives.

Therefore, the problem is to determine how many samples need to be aggregated to be optimal? The minister gave an example number n = 10, but it is not clear on what assumptions. I think differently the minister.

Actually, the number n This depends on the following parameters: infection rate in the community (p); the sensitivity of the test method (se); specificity of the test method (sp); and the error we accept. It is possible to make the problem a multiple tests of hypothesis, but for brevity we can use approximations. And, as an approximation, the number of samples to include in a test is:

n = 0.35/p

In Hanoi today, the infection rate is still low, so we can assume that p = 1%. And, with this assumption, 35 samples should be pooled in one test.

3. Test for detail on pooled testing

But the problem doesn’t stop there. The reason is that if the pooled sample test result is positive, the test must be repeated for each individual in the sample. At this point, the problem starts to get more complicated. I have to use a little notation:

• p = rate of covid infection in the community = 1%
• WOMEN = the number of people who will test the whole city = 10 million
• n = number of individuals in the pooled sample = 35
• se is the sensitivity of the test method = 87%
• sp is the specificity of the test method = 95%

Probability of a sample giving a positive result:

P_spec = (p * se) + (1 – sp)*(1 – p) = 0.058

Probability of a pooled sample giving a positive result:

P_pool = 1 – (1 – P_spec)^n = 0.877

Number of pooled samples that will give a positive result:

N.pos = (N / n)*P_pool = 250,681

From there, the number of cases that need to be retested (step 2):

N.pos * n = 8,773,835

In short, if testing is pooled, it still costs a lot of money. The first time will cost 285,714 tests. But the second time costs 8,773,835 (since each pooled sample is positive, each individual must be retested).

Therefore, in theory, pooled testing can be economical, but if calculated specifically and adjusted for the accuracy of the test method, it is still very expensive. In my opinion, instead of doing mass testing, karma testing should be done in a way that focuses on high-risk groups.

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[1] https://cafebiz.vn/ha-noi-xet-nghiem-100-nguoi-dan-se-lang-phi-bo-truong-bo-y-te-ly-giai-nhu-the-nao-20210910181151694. chn