Screening tests such as PCR are typically employed to test the likelihood of microbial pathogens in the body. Test results are estimates of probability and are evaluated by trained medical professionals to confirm the illness or to recommend any follow-up actions. Two terms that we have extensively used in the last two years have been the sensitivity and specificity of covid tests.
Sensitivity: Positive Among Infected, P(+|Inf)
Sensitivity is a conditional probability. It is not the ability of the machine to pick ill people from the population, although it could be related. But it is:
- A test’s ability to correctly identify from a group of people who are infected.
- P(+|Inf) – the probability of getting a positive result given the person was infected.
A test has a sensitivity of 0.8 (80%) if it can correctly identify 80% of people who have the disease. However, it wrongly assigns 20% with negative results.
Specificity: Negative Among Healthy, P(-|NoInf)
- A test’s ability to correctly identify from a group of people who are not infected.
- P(-|NoInf) – the probability of getting a negative result given the person was not infected.
A test with 90% specificity correctly identifies 90% of the healthy and wrongly gives out positive results to the rest 10%.
Final Remarks
We’ll stop here but will continue in another post.
Sensitivity = P(+|Inf) = 1 – P(-|Inf). If you are infected, a test can either give a positive or a negative result (mutually exclusive probabilities). In other words, you are either true positive or false negative.
Specificity = P(-|NoInf) = 1 – P(+|NoInf). If you are healthy, a test can either give a negative or a positive test result – a true negative or a false positive.
Does a positive result from the screening test prove the person is infected? No, you need to know the prevalence to proceed further. We’ll see why we developed these equations and how we could use them to evaluate test results correctly.
Sensitivity and Specificity: BMJ
