Diagnostic reasoning · Bayesian inference

Reading a positive IGRA

An interferon-gamma release assay comes back positive. Does this patient actually have latent TB? Drag the three dials and watch the answer move — the same machinery a Bayesian trial uses to turn a prior into a posterior.

Post-test probability of true LTBI

If the IGRA is positive, there's a 48% chance this patient truly has latent TB.

A negative result, by contrast, rules LTBI out with 99.8% confidence (NPV) — IGRAs excel at ruling out, not ruling in, when pretest probability is low.

The dials

Pretest probability2.0%

How likely LTBI is before testing

Sensitivity90%

P(IGRA+ | LTBI present)

Specificity98.0%

P(IGRA− | LTBI absent)

Jump to a population

True positiveLTBI+ · IGRA+ · 160

False positiveLTBI− · IGRA+ · 196

False negativeLTBI+ · IGRA− · 40

True negativeLTBI− · IGRA− · 9,604

The same answer, as Bayes' rule

PPV = sens × prev sens × prev + (1−spec) × (1−prev)

The numerator is the true-positive cell. The denominator is every positive result — true positives plus the false positives that swamp it at low prevalence. That second term is where diagnostic intuition usually fails.

The 2×2, per 10,000 tested

	LTBI present	LTBI absent	Total
IGRA positive	160TRUE +	196FALSE +	356
IGRA negative	40FALSE −	9,604TRUE −	9,644
Total	200	9,800	10,000