Likelihood ratio (LR): How good is this test at ruling in or ruling out disease?
LR measures the utility of a test to modify the likelihood that an individual patient has a disease or condition.
LR allows us to use our test result and the estimate of the pretest probability of disease to calculate the posttest probability of disease.
Use of LR is a classic application of Bayes Theorem.
- For Pretest probability of disease we use our best guess.
- We think in probability, but the LR formula requires us to use Odds. Fortunately it’s easy to convert Odds <-> probability (see table below*).
Pretest odds of disease x LR = Posttest odds of disease
- LR is calculated from sensitivity and specificity and is independent of disease prevalence. Positive LR = change in odds of having the disease given positive test = sensitivity/(1-specificity)
- Negative LR = change in odds of having disease given a negative test = (1-sensitivity)/specificity
- Higher positive LR helps rule in a disease, lower negative LR (close to zero) helps rule out a disease.
Approximate Change in Probability of Disease for LR (works for pretest probabilities between 10-90%):
* Converting Pretest Probability to Odds and Post-test Odds to Probability
Note that odds and probability are not equivalent but are similar at small probabilities (<10%).
- Probability = odds/(1+odds)
- Odds = probability/(1+probability)
How to Use LR: Clinical Example
Does My Patient Have an Acute Pulmonary Embolus (PE)?
Step 1: Calculate your pre-test probability based on your clinical assessment, expert opinion or a validated scoring tool.
In this case, use the Simplified Revised Geneva Criteria (all factors 1 pt, except HR ≥95 is 2 pt) and assume your patient has 0-1 total points.
|
Age >65 years |
Unilateral leg pain |
|
Previous DVT or PE |
Hemoptysis |
|
Surgery or lower limb fracture ≤1 months |
Heart rate 75-94 |
|
Active malignancy (or in remission <1 year) |
Heart rate ≥95 (2 points) |
|
Pain on LE palpation & unilateral edema |
Pre-test probability of PE using Simplified Revised Geneva Score
|
Score |
0-1 Low |
2-4 Intermediate |
≥5 High |
|
% PE |
7 % |
30% |
64% |
Step 2: Calculate your likelihood ratio for a negative D-dimer result.
- Assume a highly sensitive D-dimer assay has a sensitivity of 97% and specificity of 40%.
- A negative LR for a D-dimer test = (1-sensitivity)/specificity = (1-0.97)/0.4 = 0.075
Step 3: Calculate posttest probability using pretest probability of PE = 7% and Negative LR for D-dimer = 0.075.
3 ways to do this:
- Online LR calculator: plug in values for pretest probability and LR.
- Use the formula: Pretest Odds X LR = Posttest Odds
Note Probability = Odds for small values:
0.07 X 0.075 = 0.005 = 0.5% posttest probability of PE
- Use a LR nomogram: Draw a straight line from your pre-test probability (7%) through the calculated likelihood ratio (0.075) and you will find a posttest probability (<1%).
Step 4: Assess how the posttest probability changes your clinical suspicion for the disease.
In this example, a person with a low revised simplified Geneva score and a negative D-dimer has a posttest probability of PE of <1%.
This demonstrates how a negative D-dimer can be used to rule out PE in the low-risk patient.