ProbID Methods

← Back

ProbID uses likelihood ratios (LRs) and Bayes’ theorem to update a pretest probability into a post-test probability. This page explains what an LR is, how it’s calculated from test performance, and shows a worked example.

1) What is a likelihood ratio?

A likelihood ratio tells you how much a test result changes the odds of a diagnosis. It links the result you observe (positive or negative) to how likely that result would be in people with the disease versus without the disease.

LR+ (positive likelihood ratio)

How much more likely a positive result is in disease vs no disease.

LR+ = Sensitivity / (1 − Specificity)

LR− (negative likelihood ratio)

How much less likely a negative result is in disease vs no disease.

LR− = (1 − Sensitivity) / Specificity

How to interpret LRs (rule of thumb)

LR+ > 10: strong “rule-in” effect
LR+ 5–10: moderate rule-in
LR+ 2–5: small-to-moderate rule-in
LR− 0.1–0.2: moderate-to-strong “rule-out” effect
LR− < 0.1: strong rule-out

2) Bayes’ theorem in odds form (what ProbID does)

ProbID updates odds, not probabilities, because odds update by simple multiplication.

Convert probability → odds

Pretest odds = p / (1 − p)

Update odds with LR

Post-test odds = Pretest odds × LR

Convert odds → probability

Post-test probability = odds / (1 + odds)

Combining multiple findings

When multiple independent findings are selected, ProbID multiplies their likelihood ratios to create a combined LR. This is convenient, but assumes conditional independence—correlated findings can overestimate certainty.

Combined LR = LR₁ × LR₂ × LR₃ × …

3) Worked example (step-by-step)

Suppose a test has Sensitivity = 0.80 and Specificity = 0.90. And your patient’s pretest probability is 20%.

Step A — Calculate LR+ and LR−

LR+

LR+ = 0.80 / (1 − 0.90) = 0.80 / 0.10 = 8.0

LR−

LR− = (1 − 0.80) / 0.90 = 0.20 / 0.90 = 0.22

Step B — Update probability for positive test

Pretest odds

Pretest odds = 0.20 / 0.80 = 0.25

Post-test odds

Post-test odds = 0.25 × 8.0 = 2.0

Post-test probability

Post-test p = 2.0 / (1 + 2.0) = 0.667 (≈ 67%)

What if the test is negative?

Same pretest probability (20%), but use LR− instead:

Pretest odds

0.20 / 0.80 = 0.25

Post-test odds

0.25 × 0.22 ≈ 0.055

Post-test p

0.055 / (1 + 0.055) ≈ 0.052 (≈ 5%)

4) Decision Layer: How Harms and Thresholds Are Computed

ProbID now includes a decision layer that estimates whether to observe, test further, or treat now, based on post-test probability.

A) Harm inputs

Harms are auto-estimated from:

Syndrome-specific baseline harm pair
Incremental adjustments from selected high-impact findings

In the app, each baseline and increment includes a literature anchor shown in the expanded harm panel.

Current implementation is a transparent heuristic, not a validated utility model.

B) Treatment threshold

Once harms are estimated, treatment threshold is calculated as:

P(treat) = H(unnecessary treatment) / (H(unnecessary treatment) + H(missed diagnosis))

C) Observation threshold and recommendation

MVP uses:

P(observe) = 0.5 × P(treat)

If post-test p ≤ P(observe): Observe/monitor
If P(observe) < post-test p < P(treat): Pursue further testing
If post-test p ≥ P(treat): Treat now

The harm model is configurable in lib/probidDecision.ts.