Update: Jan. 27, 2021
Medical Test Paradox video presents examples of clinical decisions that are taking into account the probability of false positive and false negative results. A quote from the video:
The paradox is that you can take a test which is highly accurate, in the sense that it gives correct results to a large majority of the people taking it, and yet under the right circumstances when assessing the probability that your particular test result is correct, you can still land on a very low number. Arbitrarily low in fact. In short, an accurate test is not necessarily a very predictive test.
False Positive and False Negative
Diagnosis and treatment of patients experiencing symptoms similar to COVID-19 cannot be solely dependent on the diagnostic molecular test result, since a certain fraction of the results can be false positive or false negative.
In case of a false positive, there is a risk that a patient will undergo unnecessary treatment or therapy and delayed diagnosis of the true infection. In case of a false negative, there is a risk of delayed treatment and spreading COVID-19 within the community.
Similarly, there is risk involved in making decisions about a person’s immunity to COVID-19 based on a positive result of a screening antibody test, which can be a false positive.
What are the false negative and false positive test results?
Are some tests more reliable than others and how are medical tests evaluated?
Discussion of these subjects in the scientific literature is complex and likely out of reach of a layperson.
We describe several test characteristics and demonstrate how they are calculated, based on the Guidance for Industry and FDA Staff Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests [Ref.1].
Hypothetical Test Results
Suppose you are validating results of a study for a new diagnostic test, where the condition of interest is presence of the SARS-CoV-2 virus and the reference standard is the clinical diagnosis of the COVID-19 disease in subjects of the study.
For verifying presence of the SARS-CoV-2 virus in the patient test samples, you collected 51 samples from subjects diagnosed by clinicians with COVID-19 and you expect 51 test outcomes to be positive. However, you receive 44 positive test outcomes and 7 negative test outcomes. Also, you have 169 patient test samples taken prior to COVID-19 epidemic, assumed to be free of the SARS-CoV-2 virus. You expect 169 test outcomes to be negative, but you receive 168 negative outcomes and 1 positive outcome.
The numbers were borrowed from an example on page 23 of Ref. 1. Names and descriptions of the tests and the reference standard are not to be taken literally, as they are used only as an example, to simplify presentation of the concepts.
Definitions
Table 1 presents a common 2×2 table format for comparing test outcomes to the reference standard outcomes. It was borrowed from Ref. 1, page 22 including the definitions and formulas. The new test has two possible outcomes, positive (+) or negative (−). Subjects with the condition of interest are indicated as the reference standard (+), and subjects without the condition of interest are indicated as the reference standard (−).
TP = number of true positive results
FP = number of false positive results
TN = number of true negative results
FN = number of false negative results.
True Positive Result — a positive test result for a subject in whom the condition of interest is present (as determined by the reference standard)
False Positive Result — a positive test result for a subject in whom the condition of interest is absent
True Negative Result — a negative test result for a subject in whom the condition of interest is absent
False Negative Result — a negative test result for a subject in whom the condition of interest is present
Sensitivity — the proportion of subjects with the target condition in whom the test is positive; calculated as 100xTP/(TP+FN)
Specificity — the proportion of subjects without the target condition in whom the test is negative; calculated as 100xTN/(FP+TN)
Predictive value of a positive result (sometimes called positive predictive value or PPV) — the proportion of test positive subjects who have the target condition; calculated as 100xTP/(TP+FP)
Predictive value of a negative result (sometimes called negative predictive value or NPV) — the proportion of test negative subjects who do not have the target condition; calculated as 100xTN/(TN+FN)
Estimation
Table 2 presents how test results compare to the reference standard.
Estimated Sensitivity = 100% x 44/51 = 86.3%
Estimated Specificity = 100% x 168/169 = 99.4%
Estimated Positive Predictive Value (PPV) = 100% x 44/45 = 97.8%
Estimated Negative Predictive Value (NPV) = 100% x 168/175 = 96.0%
The values above are estimates based on a subset of subjects from the intended use population. If another subset of subjects were tested, the results would be numerically different.
Last Updated on April 23, 2021 by covid
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