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Example 1. Imagine that, in a clinic, 500 patients with suspected chlamydial genital tract infection are tested. In our unrealistic round number clinic, 100 are true positives, and 400 are true negative. The lab test is positive in 95 of the 100 positives, and is negative in 380 of the 400 negatives. The sensitivity [see the previous truth table] is 95 / (95 + 5) = 95%; the specificity is 380 / (380 + 20) = 95%; false positives are 20 / (20 + 380) = 95% and false negatives are 5 / (5 + 95) = 5%. 

The positive predictive value is the probability a test positive is a true positive: a / (a + b)

The negative predictive value is the probability a test negative is a true negative: d / (c + d)

Prevalence is the number infected at a given time compared with the total in the test population.

Incidence is the rate of acquisition of new infection in the population over a defined period of time.

Example 2. It is desired to compare the performance of the same test, in a genitourinary medicine clinic of 1300 patients and a 25% prevalence of chlamydial infection, versus a maternity unit of 3,200 patients and only 4% prevalence of infection.  The truth table becomes:

For the GU clinic

The positive predictive value is 309 / (309 + 49) = 86.3%

The negative predictive value is 926 / (926 + 16) = 98.3%

For the maternity unit

The positive predictive value is 122 / (122 + 154) = 44.21%

The negative predictive value is 2918 / (2918 + 6) = 99.8%

This shows the crucial effect of the prevalence of infection on test performance. Here,  the same test had a positive predictive value of 86.3% for a population with 25% prevalence of infection, versus only  44.21% for a population with 4% prevalence of infection. The negative predictive values, however, were hardly changed at 98.3 and 99.8% respectively. 

Example 3. Imagine that the maternity unit was offered an 'improved' test with specificity increased from 95 to 98% at the expense of sensitivity, which fell from 95 to 80%. Is this useful? Doing the maths, this leads to a huge increase in positive predictive value from 44.21 to 76.7% while the considerable reduction in sensitivity decreased the negative predictive value by only 0.6%.

To summarise:

The next section looks at the problem of defining the reference standards for the performance of a diagnostic kit, particular where two or more tests yield discrepant results.

[Comment: It is important to understand the underlying maths; in particular how prevalence and specificity greatly influences positive predictive value. These particular examples are based on a document provided several years ago. The author is sadly unknown, but an appropriate acknowledgment will be posted if s/he recognises their maths! The figures given are appropriate for antigen detection EIAs that are still in widespread use. Nowadays, the best nucleic acid-based tests have specificity close to 100% and sensitivity >90%. This has made it feasible to screen for infection in low prevalence populations, particularly where samples are first pooled before testing ].

[MEW] April 2002

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