Likelihood Ratio Calculator (LR+ and LR−)
This calculator computes positive and negative likelihood ratios for a diagnostic test. Likelihood ratios describe how much a test result changes the probability of disease and provide a direct bridge between test characteristics and clinical decision-making.
Positive LR > 10 = very useful rule-in test | Negative LR < 0.1 = very useful rule-out test
Formulas
Likelihood Ratios (from Sensitivity and Specificity)
Sensitivity and Specificity (from 2×2 Table)
Understanding Likelihood Ratios
Likelihood ratios quantify how much a diagnostic test result changes the probability of disease. Unlike predictive values, likelihood ratios are independent of disease prevalence and can be applied across different clinical settings.
A positive likelihood ratio (LR+) describes how much more likely a positive test result is in a patient with disease compared with a patient without disease. Higher LR+ values indicate stronger evidence for ruling in disease.
A negative likelihood ratio (LR−) describes how much less likely a negative test result is in a patient with disease compared with a patient without disease. Lower LR− values indicate stronger evidence for ruling out disease.
Likelihood ratios can be combined with a pre-test probability to calculate post-test probability using Bayes' theorem.
Interpreting LR+ and LR− Values
As a general guide:
- LR+ > 10 — Strong evidence to rule in disease
- LR+ 5–10 — Moderate evidence to rule in disease
- LR+ 2–5 — Small but sometimes meaningful increase in disease probability
- LR− < 0.1 — Strong evidence to rule out disease
- LR− 0.1–0.2 — Moderate evidence to rule out disease
- LR− > 0.5 — Little change in disease probability
Likelihood ratios near 1 indicate that the test result provides minimal diagnostic information.
Specific Examples
A diagnostic test with a high LR+ substantially increases the likelihood of disease when positive. Example: A highly specific imaging finding for pneumothorax yields a large LR+, making a positive result strongly confirmatory.
A diagnostic test with a low LR− substantially decreases the likelihood of disease when negative. Example: A highly sensitive screening test for pulmonary embolism like D-dimer yields a low LR−, making a negative result reassuring in low- to moderate-risk patients.
Tests with modest sensitivity and specificity may still be clinically useful if they produce meaningful likelihood ratios.
Assumptions & Limitations
- Assumes binary test outcomes
- Requires valid estimates of sensitivity and specificity
- Confidence intervals may be unstable with small sample sizes or zero cells
- Likelihood ratios describe diagnostic information but do not account for treatment thresholds or patient preferences
- Clinical interpretation still depends on the pre-test probability of disease
Formula Reference
For more reading on likelihood ratios, see the Oxford Centre for Evidence-Based Medicine.
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