India has ordered 45 Lakh rapid antibody kits for performing Covid testing . Recently DST secretary Ashutosh Sharma gave a statement to economic times that “To my mind, a 70% test sensitivity and accuracy in the antibody test serves the purpose”  As there are real consequences in terms of health, stigma and compulsory quarantine periods for people tested positive with these kits, I thought of analyzing this and determine the actual probability of a person suffering from Covid-19 given that he was flagged by an antibody test-kit as Covid positive.
As of May 6, the test positivity rate reported in India is 3.8% . Most of these tests are performed on suspected cases. Hence, if a wider population is tested randomly, to estimate the disease prevalence rate, this percentage is expected to go down significantly. But for the sake of our calculation let’s assume 3.8% is the actual disease prevalence rate. We also assume that the prior tests are all conducted using RT-PCR with nearly 100% sensitivity and specificity and our 3.8% prevalence estimate may be considered reliable at-least in symptomatic cases.
I am assuming the sensitivity of antibody test kits being purchased by Government at 70% as stated by Mr. Sharma. As the specificity information of these kits are unavailable I assume it to be a very optimistic 90%. Sensitivity is the ratio of True positives to actual positives and specificity is the ratio of True negatives to actual negatives. Using these values, the calculations of probabilities for True positives, False positives, True negatives and False negatives are shown in figure 1.
Figure 1: The calculation of true and false positive rate by integrating the population prevalence percentages.
If you are diagnosed with Covid19 using the antibody test, your test can either be a true positive or a false positive. The true positives thrown by the test among all its positive detections is the actual probability that you have the disease.
Hence, if the anti-body test kits detects someone as Covid positive it will be correct only about 1 in 5 times. If disease prevalence is less than 3.8% or the specificity is worse than assumed 90%, the correctness of this test will be even worse.
Hence, the policy makers need to be careful while administering this test. The high false positive rate of this test can lead to a lot un-necessary quarantine time for unaffected population leading to mental and physical trauma. My suggestion would be to administer these tests multiple times in order to improve their accuracy. For example, someone tested positive twice using the above test has a probability of 66% of having the disease. Let’s not fall into the misnomer of 70% accuracy of rapid test kit. The actual accuracy is far too worse!