Published 7 October 2009, doi:10.1136/bmj.b4030
Cite this as: BMJ 2009;339:b4030

Endgames

Statistical Question

Screening tests II

Philip Sedgwick, senior lecturer in medical statistics,

1 Centre for Medical and Healthcare Education, St George’s, University of London, Tooting, London SW17 0RE

This question follows on from last week’s question on indices used to describe the performance of a screening test.1 These indices help when assessing new screening tools for use in clinical practice.

A new rapid urine test was evaluated as a screening tool for Chlamydia trachomatis infection in men.2 The test was compared with the gold standard diagnostic test for Chlamydia infection—polymerase chain reaction (PCR) assay. The rapid urine screening test was reported to have a positive predictive value of 84.1%, negative predictive value of 98.3%, and a likelihood ratio for a positive result of 53.5.

Which of the following statements, if any, are true?

a) Definition of positive predictive value: out of all of the men with a "positive" result on the rapid urine screening test, 84.1% had a diagnosis of Chlamydia infection on the PCR assay.
b) Definition of negative predictive value: out of all of the men with a "positive" result on the rapid urine screening test, 98.3% did not have a diagnosis of Chlamydia infection on the PCR assay.
c) Definition of a false negative result: a Chlamydia infection that is not diagnosed on the PCR assay.
d) Definition of likelihood ratio for a positive result: a "positive" result on the rapid urine screening test is 53.5 times as likely for men with diagnosed Chlamydia infection relative to those without diagnosed Chlamydia infection on the PCR assay.

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Answers

Answer a is true. The positive predictive value reports the accuracy of a "positive" result on rapid urine screening—that is, the percentage of diagnosed Chlamydia infections on PCR assay that are identified in all "positive" screening results. Of the 107 men in total who had a "positive" ("high risk") result on rapid urine screening, 90 (84.1%) were correctly identified, having been subsequently diagnosed with Chlamydia infection on the PCR assay. The remaining 17 (15.9%) men were incorrectly identified by the rapid urine screening test—they were subsequently diagnosed as not having infection on the PCR assay.

Answer b is false. The negative predictive value reports the accuracy of a "negative" result on rapid urine screening—that is, the percentage of men without diagnosed Chlamydia infections on PCR assay who are identified in all "negative" results on screening. Of the 1104 men in total with "negative" rapid urine screening test results, 1085 (98.3%) were correctly identified—they were subsequently diagnosed as not having infection on the PCR assay.

Answer c is false. Although very unlikely, it is possible that Chlamydia infections are not diagnosed on the PCR assay. We assume that a diagnostic test is correct—that it is as close to the empirical result as possible, so the results of the screening test are compared with those of the gold standard diagnostic test. A "false negative" result is one that is diagnosed as infected on the PCR assay but incorrectly identified as "negative" by rapid urine screening. The term "positive" or "negative" refers to the rapid urine screening test result (figureGo), whereas "true" or "false" refers to the screening test’s correct or incorrect identification relative to the diagnostic PCR assay result. Therefore, a "true positive" is one that is diagnosed as infected by PCR that is also found to be "positive" by rapid urine screening. A "true negative" is one that is not diagnosed as infected by PCR that is also found to be "negative" by rapid urine screening. A "false positive" is one that is not diagnosed as infected by PCR but is incorrectly identified as "positive" by rapid urine screening.


Figure 1
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  		Negative and positive predictive value of the rapid urine screening test

 
Answer d is true. The likelihood ratio for a "positive" result indicates how many times as likely a "positive" rapid urine screening test result will be reported for men with PCR assay diagnosed infections relative to those without a diagnosis. The likelihood ratio for a "positive" result is calculated as sensitivity/(1-specificity). Its role in interpreting screening tests may not be obvious. It is useful when comparing two or more screening tests with the diagnostic assay; the screening test with the higher value would be considered to have enhanced performance.

Cite this as: BMJ 2009;339:b4030

Competing interests: None declared.

References

  1. Sedgwick P. Screening tests. BMJ 2009;339:b3941.[Free Full Text]
  2. Nadala EC, Goh BT, Magbanua JP, Barber P, Swain A, Alexander S, et al. Performance evaluation of a new rapid urine test for Chlamydia in men: prospective cohort study. BMJ 2009;339:b2655.[Abstract/Free Full Text]

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