Coronavirus Antibody Tests Have a Mathematical Pitfall
The accuracy of screening tests is highly dependent on the infection rate
With a test that is not 100 percent accurate, there are four possible outcomes for each individual:
you are positive and test positive
you are negative and test negative
you are positive but test negative (a false negative)
you are negative but test positive (a false positive)
If a test has a 95 percent specificity and a 95 percent sensitivity, that means it correctly identifies 95 percent of people who are positive and 95 percent of those who are negative. Even with very effective screening tests, depending on the infection rate in the population, and individual’s test result may not be reliable.
If a test with 95 percent specificityand 95 percent sensitivity is used in a community of 500 people with a 5 percent infection rate, the results look like this:
In this scenario, an individual who tests negative has a 99.8 percent chance of actually being negative. But an individual who tests positive has only a 50 percent chance of being positive.
If an equally accurate test is used on a group of 500 people with a 25 percent infection rate, the results may look like this:
In this scenario, and individual who tests negative has a 98.3 percent chance of actually being negative. And and individual who test positive has an 86 percent chance of actually being positive.
Sensitivity and specificity
Sensitivity and specificity are statistical measures of the performance of a binary classification test, also known in statistics as a classification function, that are widely used in medicine:
Sensitivity (also called the true positive rate, the epidemiological/clinical sensitivity, the recall, or probability of detection[1] in some fields) measures the proportion of actual positives that are correctly identified as such (e.g., the percentage of sick people who are correctly identified as having the condition). It is often mistakenly confused with the detection limit[2][3], while the detection limit is calculated from the analytical sensitivity, not from the epidemiological sensitivity.
Specificity (also called the true negative rate) measures the proportion of actual negatives that are correctly identified as such (e.g., the percentage of healthy people who are correctly identified as not having the condition).
The terms "positive" and "negative" do not refer to the value of the condition of interest, but to its presence or absence; the condition itself could be a disease, so that "positive" might mean "diseased", while "negative" might mean "healthy".
