Why Doctors Get Medical Tests Wrong: Bayes Factor

Prevalence (% population)

1.0%

How many people actually have the disease

Sensitivity / TPR

90%

P(positive | disease). Test's true positive rate

Specificity / TNR

91%

P(negative | no disease). Lower = more false alarms

Each dot = 1 person out of 1000.
Only red dots have the disease AND tested positive.
Move the sliders to see how rare true positives really are.

1000 Representative People

True Positive

False Positive

False Negative

True Negative

Posterior P(disease | +)

9.2%

Doctor's typical guess: 90%

Positive tests breakdown

TP: 9
FP: 89
FN: 1
TN: 901

Bayes Factor

10.0×

Sensitivity / (1 − Specificity)

= 90% / 9% = 10.0

Prior vs Posterior Odds

Prior odds: 1 : 99
Posterior odds: 1 : 11
Still not 9-in-10!