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Number Needed to Misdiagnose

A Measure of Diagnostic Test Effectiveness

Habibzadeh, Farrokh; Yadollahie, Mahboobeh

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doi: 10.1097/EDE.0b013e31827825f2
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To the Editor:

Diagnostic tests are an important clinical tool. No test, however, is perfect, and every test can have false-positive (FP) and false-negative (FN) results. The sensitivity (Se) of a test provides the likelihood of a positive test in a person with a disease; the specificity (Sp) is the probability of a negative test in a person without the disease. Although these parameters are informative, clinicians are often more interested in the likelihood of the disease in a person with a positive test, or the probability of no disease in a person with a negative test. These reverse conditional probabilities are known as the positive (or negative) predictive values.

Managing two numbers for assessing the effectiveness of a test is a bit cumbersome for physicians, so researchers have developed additional measures of test effectiveness. For example, test accuracy is defined as:

where TP and TN represent true positive and true negative test results, respectively. Test accuracy reflects the likelihood that a correct diagnosis is made based on the test result. However, like other probabilities, it is hard to find a tangible interpretation for the test accuracy in a clinical setting.

Another index for assessing test effectiveness is the likelihood ratio, which is calculated from the sensitivity and specificity, but is still not easily comprehended by clinicians. Youden’s index (Se + Sp — 1) is yet another index,1 from which “the number needed to diagnose” was developed2:

Still, none of these indices is intuitively appealing to clinicians; the numbers do not correspond well to a clinically tangible parameter.

Inspired by the idea of “the number needed to treat,”3 we propose a new index for assessing the effectiveness of a diagnostic test—“the number needed to misdiagnose” (NNM), defined as the number of patients who need to be tested in order for one to be misdiagnosed by the test. The index can be calculated as follows:

where Pr represents pretest probability (prevalence of the disease). Like the number needed to treat, the NNM is easily understood by clinicians. For example, the NNM for prostate-specific antigen test to diagnose prostate cancer in an otherwise healthy 50-year-old man (Pr 10%) using a cutoff value of 4ng/mL (Se 90%, Sp 60%)4 is 2.7; this means that one out of 2.7 (10 of 27) men tested is misdiagnosed (either FP or FN results). Obviously, more effective tests have higher NNM. One limitation is that this new parameter treats FP and FN test results as equally important. In this example, both types of error do have drawbacks. A FP test in a healthy person leads to extra charges and possible medical risk for more diagnostic procedures, as well as unnecessary psychological distress. A FN test can lead to late diagnosis or misdiagnosis of a potentially fatal disease. It thus can be difficult to decide how to weight FP and FN test results. Nevertheless, we believe that using the NNM, which is intuitively easy to grasp, can be a step forward.

Farrokh Habibzadeh

Mahboobeh Yadollahie

NIOC Health Organization Medical Education and Research Center Shiraz, Iran [email protected]


1. Youden WJ. Index for rating diagnostic tests. Cancer. 1950;3:32–35
2. Bandolier. How Good is that Test?. II. Available at: Accessed 31 May 2012
3. Laupacis A, Sackett DL, Roberts RS. An assessment of clinically useful measures of the consequences of treatment. N Engl J Med. 1988;318:1728–1733
4. Nicoll CD, Jeffrey JG, Dreyer J. Routine acid phosphatase testing for screening and monitoring prostate cancer no longer justified. Clin Chem. 1993;39:2540–2541
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