False negatives of screening in large-scale population

Objective To explore the changing trend of negative predictive value and number of false negatives in screening tests under the condition of low infection rate of infectious diseases.

Methods Assuming that the population is 20 million， to calculate the negative predictive value， numbers of true negatives and false negatives of the combination of different sensitivity （75.0%， 80.0%， 85.0%， 90.0%， 95.0%， 99.0%） and specificity （90.0%， 95.0%， 99.0%， 99.9%） when the disease infection rate of the population is 0.10%， 1.0% and 5.0% respectively.

Results When the population infection rate is 0.1%， with the screening test sensitivity ≥75.0% and specificity ≥90.0%， the number of true negatives in 20 million people is about 17.98‒19.96 million. When the sensitivity is 75.0%， the negative predictive value is 99.972%‒99.975%， and the number of false negatives is 5 000； When the sensitivity increases to 99.0%， the negative predictive value is 99.999%， and the number of false negatives decreases to 200. When the population infection rate is 1.0%， a screening test with sensitivity ≥75.0% and specificity ≥90.0% can detect about 17.82‒19.78 million true negatives in 20 million population. When the sensitivity is 75.0%， the negative predictive value is 99.720%‒99.748%， and the number of false negatives is 50 000； When the sensitivity increases to 99.0%， the negative predictive value increases to 99.990%， and the number of false negatives decreases to 2 000. When the population infection rate is 5.0%， with sensitivity ≥75.0% and specificity ≥90.0%， the number of true negatives in 20 million people is about 17.10‒18.98 million； when the sensitivity is 75.0%， the negative predictive value is 98.559%‒98.700%， and the number of false negatives can reach 250 000； When the sensitivity is 99.0%， the negative predictive value increases to 99.942%‒99.947%， and the number of false negatives decreases to 10 000. The lower the infection rate of the population， the fewer false negatives will appear in the screening.

Conclusion The number of false negatives in large-scale screenings increases exponentially with the increase of infection rate. Screenings should be carried out as early as possible in a pandemic of infectious diseases， so as to control the spread of the pandemic as soon as possible.