The desire to have diagnostic tests that are as accurate as possible seems logical. But what does the accuracy actually mean? In fact, it has two aspects: sensitivity – the ability of a test to correctly identify those with the disease, a.k.a. true positive rate, and specificity – the ability of the test to correctly identify those without the disease, a.k.a. true negative rate. Accuracy is often determined by taking a product of the sum of the true positive and true negative results, divided by the sum of all test results, and… it can be rather useless: a 90% accurate test can miss all of 10% of true positive cases in the tested population.
It is intuitive to think that the ideal test should be both highly sensitive and highly specific, preferably 100%. However, that is impossible – the increase in sensitivity comes at the expense of the decrease in specificity and vice versa. Therefore, a test with a sensitivity and specificity of around 90% or higher is considered satisfactory in many settings. Which parameter is more important and what values are acceptable depends the goal of testing.
If testing is performed for screening for Covid-19, we want it to be as sensitive as possible – we would not want to miss true positives. It is important for testing individuals and even more important for testing a “pooled sample” of employees, a method proposed to reduce the cost of testing in occupational environments. If the test of a pooled sample comes positive, it is split into smaller subsamples that are tested again. Can do. Whereas a false negative can lead to missing more than one case of infection, and consequences of this can be severe: the cost of a false positive – self-isolation – is not as high as the damage from letting a Covid-19-positive person re-join the workforce and infect up to 7.5 coworkers or clients.
When the purpose of testing is diagnostic, and an individual with Covid-19 symptoms has a false-positive test result, the test can be repeated, or a more sensitive test (RT-PCR) can be administered. Abbott system – that as we have learned recently doesn’t have a good sensitivity – still may be useful as an initial test in this situation.
Now, let’s say someone’s test comes back positive, but this person does not have any definite symptoms of Covid-19. How worried should we be? This is where the positive predictive value of a test comes handy. It uses the information on the proportion of infected in the population and reflects the probability that a positive test correctly indicates infection. So, in a hypothetical scenario where 1% of the population is infected, a test has a 90% specificity and a 90% sensitivity, the probability of a positive test result correctly indicating the infection is not 90%, as many might think, but only 8.3%! We use Bayes theorem for conditional probabilities to obtain positive predictive value, or, in other words, the probability of actually being infected if the test is positive. It is calculated as: