How diagnostic test statistics are tested on Step 1

Expect raw numbers to place in a 2×2 table, or a conceptual question about prevalence or cutoffs.

Disease +Disease −
Test +a (true positive)b (false positive)PPV = a/(a + b)
Test −c (false negative)d (true negative)NPV = d/(c + d)
Sensitivity = a/(a + c)Specificity = d/(b + d)Prevalence = (a + c)/total

Read sensitivity and specificity down the columns (by disease status) and predictive values across the rows (by test result).

High sensitivityFew false negativesNegative result rules out (SnNOut)Used for screeningExample: D-dimer for PELower cutoffHigh specificityFew false positivesPositive result rules in (SpPIn)Used to confirmExample: confirmatory biopsyHigher cutoffvs
Screening vs confirmation. A common strategy is a sensitive screening test followed by a specific confirmatory test.

Prevalence and predictive values

Predictive values depend on who is being tested.

Prevalence risesPPV ↑More positives aretrueNPV ↓More negatives aremissed casesSensitivityUnchangedSpecificityUnchanged
Prevalence. The same test has a higher PPV in a high-risk clinic than in general population screening.

Moving the cutoff

Changing the threshold trades false negatives for false positives.

  • Lower the cutoff (call more results positive): sensitivity ↑, specificity ↓, false negatives ↓, false positives ↑, NPV ↑, PPV ↓.
  • Raise the cutoff: specificity ↑, sensitivity ↓, false positives ↓, false negatives ↑, PPV ↑, NPV ↓.
  • ROC curve: plots sensitivity (true-positive rate) against 1 − specificity (false-positive rate) across cutoffs; a larger area under the curve means a better test.
  • Accuracy vs precision: accuracy (validity) is closeness to the true value; precision (reliability) is reproducibility. Random error lowers precision; systematic error lowers accuracy.

Likelihood ratios

Likelihood ratios tell you how much a result changes the probability of disease.

StrengthLR+ > 10Large increase in probability: strongly rules inLR+ 2–10Moderate to small increaseLR = 1No change: the test adds nothingLR− 0.1–0.5Moderate to small decreaseLR− < 0.1Large decrease: strongly rules out
Likelihood ratios combine sensitivity and specificity and, unlike predictive values, do not depend on prevalence.

Worked example

Build the table, then calculate.

functions Worked example — a screening test

A test with sensitivity 90% and specificity 80% is used in 1,000 people, 10% of whom have the disease. What are the PPV and NPV?

  1. Diseased = 100; not diseased = 900.
  2. True positives = 0.90 × 100 = 90; false negatives = 10.
  3. True negatives = 0.80 × 900 = 720; false positives = 180.
  4. PPV = 90/(90 + 180) = 33%. NPV = 720/(720 + 10) ≈ 98.6%.

Answer. PPV ≈ 33% and NPV ≈ 98.6%: at low prevalence most positives are false positives, but a negative result is very reassuring.