positive predictive value

DEFINITION / FORMULA - PPV = TP / (TP + FP) = true positives / all positive test results. - Answers: "Given a positive test, what is the chance the patient actually has the disease?" - Read across the "test positive" row of a 2x2 table (sensitivity and specificity are read down the columns).

2x2 TABLE - Disease present / test positive = TP; disease absent / test positive = FP; disease present / test negative = FN; disease absent / test negative = TN. - Sensitivity = TP/(TP+FN). Specificity = TN/(TN+FP). NPV = TN/(TN+FN).

PREVALENCE DEPENDENCE (high-yield) - Sensitivity and specificity are intrinsic properties of the test and do not change with prevalence. PPV and NPV do change. - Prevalence up: PPV up, NPV down. - Prevalence down: PPV down, NPV up. - In low-prevalence populations (e.g., screening the general population), even a highly specific test yields many false positives, so PPV is low. This is why confirmatory testing is needed after a positive screening test (e.g., ELISA then Western blot/HIV-1/2 differentiation assay). - Bayes' theorem link: PPV is the post-test probability after a positive result, based on pre-test probability (prevalence) and the test's likelihood ratio.

EFFECT OF TEST CHARACTERISTICS - Higher specificity means fewer FPs, so PPV rises. A highly specific test is good for ruling IN disease (SpPIn: Specificity, Positive rules In). - Higher sensitivity mainly raises NPV and is good for ruling OUT disease (SnNOut: Sensitivity, Negative rules Out). It has a smaller effect on PPV. - Raising the cutoff to call a test positive increases specificity and PPV and decreases sensitivity. Lowering the cutoff does the reverse.

WORKED EXAMPLE - 1000 people; prevalence 10% = 100 diseased. Sensitivity 90%, specificity 90%. - TP = 90, FN = 10. TN = 810, FP = 90. PPV = 90/(90+90) = 50%. - If prevalence falls to 1% (10 diseased): TP = 9, FP = 99. PPV = 9/108 ≈ 8%.

CLINICAL SIGNIFICANCE - Guides interpretation of screening tests (HIV, mammography, PSA, prenatal cell-free DNA screening, newborn screens). Low-prevalence screening leads to many false positives. - Tests are most useful (higher PPV) when applied to higher-risk populations or patients with high pre-test probability. - A very high PPV (approaching 100%) means a positive result is almost diagnostic; this is typical of highly specific tests in higher-prevalence settings.

COMMON EXAM TRAPS - Do not confuse PPV with sensitivity. Sensitivity = P(test+ | disease). PPV = P(disease | test+). - Changing the sample size alone (with the same prevalence) does not change PPV. - A new, more specific test in the same population raises PPV. A new population with lower prevalence lowers PPV, even if the test is unchanged. - Precision (in statistics/ML) is equivalent to PPV.