Can we have a negative probability

Corona rapid tests - it's the prevalence that counts!

With the third coronavirus test regulation, rapid antigen tests for SARS-CoV-2 have become very relevant. They can then be used for screening in healthcare facilities, for example, but also to test visitors to care facilities.

However, understanding the test situation is crucial for evaluating the results of such tests. Because depending on the occasion and setting, the meaningfulness of the tests changes, as we show in the graphic. She compares mass tests or screenings on the general population at very lower prevalence rates with more targeted tests on people with COVID-19 symptoms.

Present results in an understandable way

We use icon arrays for representation. They are based on natural frequencies (Gigerenzer 2011) and represent case numbers as simply and concretely as possible - here of true positive, false positive, true negative and false negative test results. Scientific studies show that icon arrays help people understand numbers and risks more easily.

This has been validated in a medical context (e.g. McDowell et al. 2019, Garcia-Retamero & Cokeley 2014) and it also applies to people with lower numerical skills - i.e. people who have problems dealing with numbers - and to people with little interest in numerical information (Galesic, Garcia-Retamero & Gigerenzer 2009; Garcia-Retamero, Okan & Cokeley 2012).

In the graphic we have simulated two different test principles: one out of 10,000 people tested, five (left, mass test) and once 1000 people (right, targeted test) are actually infected. This leads to very differently reliable test results.

The rapid antigen test for SARS-CoV-2 is positive: How likely is it that the person tested is actually acutely infected? Or the test is negative: How likely is it that the person tested is actually not acutely infected? How would you answer these questions to your patients?

The test group is crucial ...

Different factors have to be considered in the answer. Here we explain why the interpretation of rapid antigen test results does not only depend on the test quality criteria, but also on how widespread the SARS-2 coronavirus is in the group tested.

As is well known, the quality of tests is measured using the two test quality criteria sensitivity and specificity. The sensitivity (true positive rate) of a test describes its ability to correctly identify people infected with SARS-CoV-2.

The specificity (true negative rate) of a test describes its ability to correctly identify those people who are not infected with SARS-CoV-2. A review article gives sensitivities of 29.7 to 79.8 percent and specificities of 98.8 to 99.9 percent for rapid antigen tests (Dinnes et al. 2020).

In contrast, various manufacturers of antigen tests tend to give sensitivities of 90 to 98 percent and specificities of 98 to 100 percent.

However, the manufacturer's information relates to samples that were all positive according to the PCR test. In practice, however, only around 80 percent of all samples from infected people contain the virus, for example due to preanalytical errors in the smear test (Kucirka et al. 2020). Therefore, the maximum clinical sensitivity is usually estimated more conservatively at 80 percent.

... and the spread of the virus

However, these test quality criteria must not be viewed in isolation, because the significance of the test also depends significantly on how large the proportion of people actually infected in the group tested is. In the general population, the proportion of people acutely infected with SARS-CoV-2 is low.

For our example, the probability that a person with a positive test result is actually infected with the virus is assumed to be 4 / (4 + 200) 0.019 (1.9 percent) for mass examinations and 800 / (800 + 180) 0.816 ( 81.6 percent) for more targeted examinations. Ideally, a positive test result should be confirmed by an additional PCR test.

The probability that a person with a negative test result is actually not infected is 9.795 / (9.795 + 1) 0.9999 (99.99 percent) for mass exams and 8.820 / (8.820 + 200) 0.978 (97.8 percent) for targeted exams Investigations.

Positive results are more reliable with higher prevalence

Depending on the test approach, the probability that a person is infected despite negative test results is 0.01 percent (mass test) or 2.2 percent (targeted test).

In summary, this means for clinical practice: the lower the prevalence, the less certain are positive test results and the higher the prevalence, the less certain are negative test results. In mass tests, i.e. with a low prevalence, many false positive test results are generated with SARS-CoV-2 antigen rapid tests.

In contrast, positive test results are more reliable with more targeted testing (e.g. of symptomatic persons), i.e. with a higher prevalence. The informative value of the tests therefore depends heavily on the test approach and the spread of the virus.

About the authors

The team around Miss Dr. Jenny1,3,4 has been responsible for the scientific communication of the Robert Koch Institute aimed at the general public since July of this year. The interdisciplinary communication, research and transfer team is currently focused on topics related to the COVID-19 pandemic, but will in future cover all RKI topics.

The cognitive scientist Dr. Jenny leads the group, the chemist Dr. Ines Lein1,4 coordinates and writes for the (professional) public, the microbiologist Dr. Esther-Maria Antão1 heads the museum at the RKI and is responsible for graphics and design and the cognitive psychologist Dr. Christina Leuker1,3 researches on topics related to the search for information, risk perception and communication.

Dr. from Kleist2 is a bioinformatics scientist and mathematician and heads the bioinformatics department at the RKI. He is currently engaged in the bioinformatic analysis of SARS-CoV-2 genomes, incidence estimation and the modeling of test and containment strategies.

  • 1: Science Communication Project Group, Robert Koch Institute, Berlin
  • 2: Bioinformatics, Robert Koch Institute, Berlin
  • 3: Adaptive Rationality, Max Planck Institute for Human Development, Berlin
  • 4: Harding Center for Risk Literacy, Faculty of Health Sciences, University of Potsdam


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  • Garcia Retamero, R., & Cokely, E. T. (2014). The influence of skills, message frame, and visual aids on prevention of sexually transmitted diseases. Journal of Behavioral Decision Making, 27 (2), 179-189.
  • Garcia-Retamero, R., Okan, Y., & Cokely, E. T. (2012). Using visual aids to improve communication of risks about health: a review. The Scientific World Journal, 2012.
  • Gigerenzer, G. (2011). What are natural frequencies? BMJ, 343, d6386.
  • Kucirka, L. M., Lauer, S. A., Laeyendecker, O., Boon, D., & Lessler, J. (2020). Variation in false-negative rate of reverse transcriptase polymerase chain reaction-based SARS-CoV-2 tests by time since exposure. Annals of Internal Medicine.
  • McDowell, M. E., Gigerenzer, G., Wegwarth, O., & Rebitschek, F. G. (2019). Effect of tabular and icon fact box formats on comprehension of benefits and harms of prostate cancer screening: A randomized trial. Medical Decision Making, 39, 41-56.