Now that many states are moving from the population-based mitigation strategy towards case-base interventions, we hear a lot about testing, contact tracing, and isolation. Apart from questions of whether the states are ready for this move, and whether these strategies are going to be successful, many of us will face the need to be tested, especially if it is required for coming back to the office. Organizations and business owners may think about testing for their employees as a factor in a decision on safe re-opening. Hence, we may want to have a better understanding of terms used more and more widely in relation to tests: accuracy, sensitivity, specificity, false-positive and false-negative.
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:
Sensitivity*P(Infection) 0.9*0.01 0.009
—————————————————————————- = ——————————– = ——- = .083 or 8.3%.
Sensitivity*P(Infection) + (1 – Specificity)*(1 – P(Infection) 0.9*0.01+(1-0.9)*(1-0.01) 0.108
If the proportion of infected in the population, P(infection), increases, so would the positive predicted value of the test.
What this means is: even if your test for Covid-19 comes back positive, your confidence in the results should be a function of sensitivity, specificity of the test and of the proportion of infected in the population (or, ideally, in the subpopulation you belong to).
Unfortunately, we do not know the percentage of people in the population that are infected in this pandemic – yet. This limits the usefulness of testing for Covid-19 “just in case” when there are no other indications of infection. A correctly conducted survey for antibodies that is run on a good representation of the population and not only the people who have previously had symptoms of Covid-19 can help us get to that percentage. And that, in turn, will help with ruling out or confirming Covid-19 infection in cases of atypical symptoms or asymptomatic infections that are causing so much confusion right now.
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