• Annibale Biggeri, Silvia Forni, and Mario Braga.
• Department of Statistics, Computer Science, Applications G. Parenti, University of Florence, Florence (Italy).
• Epidemiol Prev. 2020 Sep 1; 44 (5-6 Suppl 2): 184-192.

Backgroundsince the beginning of the COVID-19 pandemic, the importance of developing a serological test has emerged and a debate on test accuracy and reliability become an issue widely discussed in the media. The importance of communication during this pandemic has been strongly underlined by public health experts, epidemiologists, media expert, psychologists, sociologists. In the case of serological tests, there are several aspects that have to be considered: why we perform the test, what population is tested, which are the parameters conditioning the results and their interpretation.Objectivesto show how to quantify the uncertainty related to the validity of the serological test with respect to its predictive value and in particular the positive predictive value.Methodsthe evaluation of a qualitative diagnostic test includes four distinct assessments: accuracy, empirical evidence, practical importance, and prevalence of the pathology. Accuracy is measured by the sensitivity and specificity of the test; empirical evidence is quantified by the likelihood ratio, respectively for a positive and negative test result; the practical importance of the result of a diagnostic test is assessed by the positive or negative predictive value. Prevalence of COVID-19 is substantial uncertainty and it is possible to estimate the apparent prevalence starting from the results obtained with a diagnostic test.Resultsat the moment, the knowledge about the accuracy of serological tests is limited and little attention is paid to confidence interval on point estimates. In terms of practical importance of testing at individual level, while negative predictive values are high whatever the level of sensitivity of the test, the interpretation of a positive results is very cumbersome. Positive predictive values above 90% can be reached only by tests with specificity above 99% at the expected prevalence rate of 5%. There is a linear relationship between apparent - testing positive - prevalence and real prevalence. The apparent prevalence in the context of serological test for COVID-19 is always larger than real prevalence. The level of specificity is crucial.Conclusionsthe main applications of the serological test in the epidemic contest are: to study the seroprevalence of the virus antibodies in the general population; to screen the healthcare workers for the early identification of contagious subjects' health care settings and to screen the general population in order to identify new incident cases. In the first two cases, seroprevalence study and screening of a high-risk population, the consequences of the uncertainty associated to the statistics are already accounted for in the first situation, or are overcome by repeating the screening on the healthcare workers, and using the molecular test to verify the presence of the virus in those tested positive. The case of screening of general population is more complex and of major interest for the implication it may have on individual behaviours and on the implementation of public health interventions by the political decision makers. A positive result has, per se, no practical value for individuals since the probability of being really infected by the virus is low. The uncertainty associated with the different estimates (sensitivity, specificity and disease prevalence) play a double role: it is a key factor in defining the informative content of the test result and it might guide the individual actions and the public policy decisions.

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