Bayes' Theorem: Disease Testing

A test can be highly accurate and still be wrong more often than right when the disease is rare. Adjust prevalence, sensitivity, and specificity to see how the population splits — and why a positive test result isn't the same as having the disease.

Prevalence (% with disease)

Sensitivity (% true positive rate)

Specificity (% true negative rate)

Population Size

Randomize population grid layout

Counts

True Positive: -

False Negative: -

False Positive: -

True Negative: -

Predictive Value

PPV — P(Disease | +): -

NPV — P(No Disease | −): -

Bayes' Theorem

$$P(D \mid +) = \dfrac{\text{Sens} \times \text{Prev}}{\text{Sens} \times \text{Prev} + (1-\text{Spec})(1-\text{Prev})}$$

Population Grid (Natural Frequencies)

True Positive (has disease, tests +)

False Negative (has disease, tests −)

False Positive (no disease, tests +)

True Negative (no disease, tests −)

Bayes' Theorem: Disease Testing

Counts

Predictive Value

Population Grid (Natural Frequencies)

Out of Every 100 People