BiostatisticsTier 1Medical Sciences concept

Positive predictive value calculation from prevalence, sensitivity, specificity (Bayes theorem)

Core concept

*Sens/spec are properties of the test. PPV/NPV are properties of the test in this population.*

```

Disease + Disease -

Test + TP FP

Test - FN TN

```

Bayes form (when you are given percentages, not counts)

```

PPV = (sens x prev) / [ (sens x prev) + (1 - spec) x (1 - prev) ]

```

Worked - the standard exam pattern

Sens 97%, spec 90%, prevalence 5%, n = 1000
- Disease + = 50 -> TP = 0.97 x 50 = 48.5
- Disease - = 950 -> FP = 0.10 x 950 = 95
- PPV = 48.5 / (48.5 + 95) = ~34%
- Two-thirds of positives are false, with a 97%/90% test - because the well vastly outnumber the sick
Sens 80%, spec 60%, pre-test 50%
- PPV = (0.8 x 0.5) / [(0.8 x 0.5) + (0.4 x 0.5)] = 0.40/0.60 = ~67%

Likelihood ratio shortcut

LR+ = sens / (1 - spec); LR- = (1 - sens) / spec
post-test odds = pre-test odds x LR; odds = p/(1-p), p = odds/(1+odds)
Rules of thumb: LR+ >10 or LR- <0.1 shifts management; LR near 1 is a useless test

LR+	approx absolute inc in probability
2	+15%
5	+30%
10	+45%

SpPin / SnNout: a highly Specific test when Positive rules in; a highly Sensitive test when Negative rules out

The argument against screening low-prevalence populations - troponin in undifferentiated chest pain, D-dimer without a Wells score, ANA in non-specific fatigue
- Use a pre-test probability rule first to lift prevalence, then test
Explains why a positive result in a high-risk unit means something different from the same result in outpatients
Confirmatory testing is sequential Bayes: a second, more specific test applied only to positives (HIV EIA -> Western blot/differentiation assay; RPR -> TPHA)
A test does not become "less accurate" in a low-prevalence setting - sens and spec are unchanged. Only the predictive value falls.
Prevalence-independent: sensitivity, specificity, likelihood ratios. Prevalence-dependent: PPV, NPV

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