How is the self-test for covid-19 antigen "300,000 positive, only 9 true"?

On March 15, the joint prevention and control mechanism of the State Council held a press conference. Li Jinming, deputy director of the Clinical Laboratory Center of the National Health Commission, said at the press conference that antigen testing should be used for high-risk, high-prevalence cluster infection population testing, and the general population should not do antigen testing at will.

Li Jinming explained that the population prevalence rate is less than one in a million, if you take the sensitivity of 85%, specificity of 97% of the new crown antigen test kit, to tens of millions of people in the city for screening, you will get 300,000 positives, but only 9 of the 300,000 positives are true, that is to say, most of them are false positives, of course, the results of the test is negative.

Li Jinming said that if you use a 85% sensitive and 97% specific kit in a population with an prevalence rate of 5%, about 60 of the 100 positives are true, and no more than 1% of the missed tests are missed.

The question arises: how do about 300,000 false positives and about 60 of the 100 positives really calculate? The following is a detailed explanation for everyone.

First, the basic knowledge

1. Sensitivity Se: The proportion of positive test results in the affected population, that is, the true positive rate.

2. Specific Sp: the proportion of negative test results in the uninhabited (healthy) population, that is, the true negative rate.

3. Positive predictive value PPV: the proportion of the population that is truly sick in the positive results of the test.

4. Negative predictive value NPV: the proportion of the population that is truly not sick (healthy) in the negative results of the test.

Sensitivity and specificity are intrinsic properties of a diagnostic test and do not change with prevalence. When the prevalence rate increases, the positive predictive value increases and the negative predictive value decreases; when the prevalence decreases, the positive predictive value decreases and the negative predictive value increases. The higher the sensitivity of the diagnostic test, the higher the negative predictive value, and the higher the specificity of the diagnostic test, the higher the positive predictive value.

5. Apparent prevalence AP: the ratio of the number of positive test results to the total number of groups.

6. True prevalence: P(D+):

Second, the effect of detection reagent specificity when the prevalence rate is low

Li Jinming said that the population prevalence rate is less than one part a million, if you take the sensitivity of 85%, specificity of 97% of the new crown antigen test kit, to tens of millions of people in the city to do screening, will get 300,000 positives, but only 9 of the 300,000 positives are true, that is to say, most of them are false positives, of course, the test is negative The results are reliable.

compute

Assuming that the true prevalence P(D+) = 0.0000001 (parts per million), Se = 0.85, sp = 0.97, then the apparent prevalence AP = 0.03.

The number of positive tests = 10 million × 0.03 = 300,000

Number of diseases = 10 million × 0.0000001 = 10

Number of true positives = 10 million × 1/1 million × 0.85 = 8.5≈9

The number of true negatives = 10 million × (1-1/1 million) ×0.97 = 9699990

Number of false positives = 10 million × (1-1/1 million) × (1-0.97) = 300,000

Number of false negatives = 10 million × 1/1 million × (1-0.85) = 1.5≈1

False positive ratio = 300000 / 300009 = 99.997%

Positive predictive value PPV = 0.003%

Negative predictive value NPV = 99.9999%

When the true prevalence rate is equal to 1% the result is similar to one part per million:

Assuming that the true prevalence P(D+) = 0.01 (one percent), Se = 0.85, sp = 0.97, then the apparent prevalence AP = 0.038.

The number of positive tests = 10 million × 0.038 = 380,000

Number of true positives = 10 million

unscramble:

When the prevalence of the epidemic is low (less than 1%), due to the small number of true positives, the number of positives detected is mainly affected by the specificity of the test reagent; that is, the positives detected are basically false positives (1-Sp) caused by the non-specificity of the test reagent. Therefore, when the prevalence of the disease is low (less than 1%), screening of the population requires the use of highly specific reagents.

Third, the impact of detection reagent sensitivity when the prevalence rate is high

Assuming that the true prevalence P(D+) = 0.05 (five percent), Se = 0.85, sp = 0.97, then the apparent prevalence AP = 0.071.

Number of positive tests = 100

Total sample size = 100/0.071 = 1408

Number of diseases = 1408× 0.05≈71

Number of true positives = 1408×0.05×0.85 = 60

Number of true negatives = 1408× (1-0.05) ×0.97 = 1297

Number of false positives = 1408× (1-0.05) × (1-0.97) = 40

Number of false negatives = 1408×0.05× (1-0.85) = 11

Percentage of missed tests (false negatives) = 11/1408 = 0.78%

Positive predictive value PPV = 59.9%

Negative predictive value NPV = 99.2%

When the prevalence of the disease is high (higher than 1%), the number of positives detected is mainly affected by the sensitivity of the test reagent; the higher the sensitivity, the lower the false positive. Therefore, when the prevalence of the disease is high (higher than 1%), highly sensitive reagents are required for population screening.

There are many epidemiological calculation tools on the Internet, and we do not need to calculate these results manually, but with a learning attitude, we will calculate it from scratch. The end of the detection is really math!

Source: Dr. Yuan took you to do the test

Editor: Ren Mileage Reviewer: Xiao Ran