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Question:

A test is used to diagnose dementia in a population of 1,000 women age ≥75.  The test has a sensitivity of 80% and a specificity of 90%.  The test is then used as a diagnostic tool in 2 other populations of women of the same age: population 1 has a prevalence of dementia of 15%, and population 2 has a prevalence of dementia of 30%.  Which of the following best describes how the negative predictive values (NPV) and the positive predictive values (PPV) from populations 1 and 2 relate to each other?

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Explanation:

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Predictive values are performance measures of diagnostic tests that are dependent on the prevalence of disease in a population of interest.

  • Negative predictive value (NPV) is the probability (ie, likelihood) that an individual truly does not have the disease given a negative test result.  NPV is equal to the number of individuals who do not have the disease and who test negative (true negatives [TN]) divided by all those with a negative test result (TN + false negatives [FN]): NPV = TN / (TN + FN).

  • Positive predictive value (PPV) is the probability (ie, likelihood) that an individual truly does have the disease given a positive test result.  PPV is equal to the number of individuals who have the disease and who test positive (true positives [TP]) divided by all those with a positive test result (TP + false positives [FP]): PPV = TP / (TP + FP).

Disease prevalence affects NPV by changing the number of TN and FN tests.  It affects PPV by changing the number of TP and FP tests (Choice A):

  • Populations with exceptionally low disease prevalence (eg, prevalence close to 0%) have almost all TN (ie, more TN) with almost no TP (ie, fewer TP), and most positive tests would be FP (ie, more FP) with almost no FN (ie, fewer FN).  In this scenario, NPV is close to 100%, and PPV is close to 0%.  This explains why, with decreasing prevalence, NPV increases (more TN, fewer FN) and PPV decreases (fewer TP, more FP).

  • Populations with exceptionally high disease prevalence (eg, prevalence close to 100%) have almost all TP (ie, more TP) with almost no TN (ie, fewer TN), and most negative tests would be FN (ie, more FN) with almost no FP (ie, fewer FP).  In this scenario, NPV is close to 0%, and PPV is close to 100%.  This explains why, with increasing prevalence, NPV decreases (fewer TN, more FN) and PPV increases (more TP, fewer FP).

(Choices B, C, and E)  In this example, population 1 has a lower prevalence (15%) of dementia in women age ≥75 compared to population 2 (30%).  Therefore, NPV in population 1 > NPV population 2, and PPV in population 1 < PPV population 2.

Educational objective:
Predictive values change depending on the prevalence of disease in a study population.  As disease prevalence increases, the positive predictive value increases, and the negative predictive value decreases.