Likelihood Ratio Calculator
Calculate positive (LR+) and negative (LR−) likelihood ratios from test sensitivity and specificity. Convert pre-test probability to post-test probability using Bayesian reasoning — the essential tool for evidence-based diagnostic interpretation in clinical medicine and medical research.
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What is a Likelihood Ratio?
Likelihood ratios quantify how much a diagnostic test result changes the probability of disease. The positive likelihood ratio (LR+) measures how much the odds of disease increase with a positive test result. The negative likelihood ratio (LR−) measures how much the odds decrease with a negative result. LR+ = Sensitivity ÷ (1 − Specificity), and LR− = (1 − Sensitivity) ÷ Specificity.
Unlike sensitivity and specificity alone, likelihood ratios directly translate into clinically actionable probability changes. An LR+ of 10 means a positive test result makes disease 10 times more likely. An LR− of 0.1 means a negative result makes disease 10 times less likely. Values near 1.0 indicate the test provides no useful diagnostic information. Likelihood ratios are prevalence-independent, making them applicable across different patient populations.
적용 수학 공식 및 방정식
이 Likelihood Ratio Calculator는 5가지 핵심 수학 공식을 사용합니다:
1 Positive Likelihood Ratio ▼
Sensitivity 95%, Specificity 90%: LR+ = 0.95 / (1 - 0.90) = 0.95 / 0.10 = 9.5.
2 Negative Likelihood Ratio ▼
Sensitivity 95%, Specificity 90%: LR- = (1-0.95) / 0.90 = 0.05 / 0.90 = 0.056.
3 Post-Test Odds (Fagan Nomogram) ▼
Pre-test probability 20% → odds = 0.25. LR+ = 9.5 → Post-test odds = 0.25 × 9.5 = 2.375 → probability = 70.4%.
Explore all calculation options on the 비율 계산기 home page.
비율 계산기 사용법
이 비율 계산기는 아래의 3단계로 쉽게 사용할 수 있습니다:
수치 입력하기
입력 칸에 알고 있는 비율 값을 입력합니다. 구하려는 미지수 자리의 칸 하나는 비워둡니다.
모드 선택하기
비율 모드(풀기, 간소화, 스케일링)를 선택합니다. 각 모드는 입력한 수치에 맞춰 다른 공식들을 적용합니다.
결과 확인하기
계산하기 버튼을 누릅니다. 결과 화면에 정답과 함께 시각적인 비율 바, 원형 차트, 상세한 단계별 풀이 과정이 출력됩니다.
실제 예제 문제 및 단계별 풀이
비율 계산기를 활용하여 아래 3가지 예제 문제를 단계별로 해결하는 과정입니다:
입력 1 Test with 90% sensitivity, 85% specificity
입력 2 Calculate post-test probability
입력 3 Highly sensitive test: 99% sensitivity, 50% specificity
자주 묻는 질문 (FAQ)
What is a good likelihood ratio? ▼
LR+ > 10 provides strong evidence for disease. LR+ 5-10 is moderate. LR+ 2-5 is weak but may still be useful. LR− < 0.1 strongly rules out disease. LR− 0.1-0.2 is moderate for exclusion. LR values between 0.5 and 2.0 provide minimal diagnostic information.
Why are likelihood ratios better than sensitivity and specificity? ▼
LRs combine both metrics into a single number that directly translates to clinical probability changes via Bayesian reasoning. They are independent of disease prevalence and can be applied to individual patients using their specific pre-test probability, unlike sensitivity/specificity which describe test properties in populations.
How do I use the Fagan nomogram? ▼
Draw a straight line from your pre-test probability (left axis) through the likelihood ratio (middle axis) and extend it to the right axis to read the post-test probability. A digital version: convert pre-test probability to odds, multiply by LR, then convert back to probability.
Can likelihood ratios be used for tests with multiple result levels? ▼
Yes. Instead of a single positive/negative cutoff, you can calculate interval likelihood ratios for each result range. For example, a blood test might have different LRs for low-normal, high-normal, mildly elevated, and markedly elevated results, providing more nuanced interpretation.
What is pre-test probability? ▼
Pre-test probability is your estimated probability of disease before performing the test, based on disease prevalence in the relevant population, patient symptoms, clinical examination, and results of any prior tests. It serves as the starting point for Bayesian diagnostic reasoning with likelihood ratios.
How do I calculate post-test probability from a likelihood ratio? ▼
Convert pre-test probability to pre-test odds: odds = probability ÷ (1 − probability). Multiply by LR: post-test odds = pre-test odds × LR. Convert back: post-test probability = post-test odds ÷ (1 + post-test odds). Example: 20% pre-test, LR+ = 6: odds = 0.25, post-odds = 1.5, post-probability = 60%.
What is the difference between LR+ and LR−? ▼
LR+ applies to positive test results and indicates how much more likely the disease is after a positive test. LR− applies to negative test results and indicates how much less likely the disease is after a negative test. Both are needed for complete test evaluation.
Can I combine likelihood ratios from multiple tests? ▼
Yes, if the tests are independent (measure different aspects of the disease). Multiply the LRs sequentially: post-test odds = pre-test odds × LR₁ × LR₂. This is the strength of Bayesian reasoning — each independent test further refines the diagnostic probability.
What is an uninformative likelihood ratio? ▼
An LR of 1.0 is completely uninformative — the test result does not change the probability of disease at all. LRs between 0.5 and 2.0 are generally considered clinically useless because they change probability by too little to affect management decisions.
How are likelihood ratios used in evidence-based medicine? ▼
EBM clinicians use LRs to perform bedside Bayesian reasoning: estimate a pre-test probability from clinical findings, apply the LR from the best available test, and determine whether the post-test probability crosses a treatment threshold. This quantitative approach replaces subjective test interpretation.
Do likelihood ratios work for screening tests? ▼
Yes, but screening tests are applied to low-prevalence populations, so even good LR+ values produce many false positives (low positive predictive value). Screening programs require extremely high LR+ or multi-stage testing to achieve acceptable PPV. LR− is more relevant for screening since the goal is ruling out disease.