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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.

Likelihood Ratio Calculator — 실시간 비율 미리보기
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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 ▼
        LR+ = Sensitivity / (1 - Specificity)

        Sensitivity 95%, Specificity 90%: LR+ = 0.95 / (1 - 0.90) = 0.95 / 0.10 = 9.5.

        2 Negative Likelihood Ratio ▼
        LR- = (1 - Sensitivity) / Specificity

        Sensitivity 95%, Specificity 90%: LR- = (1-0.95) / 0.90 = 0.05 / 0.90 = 0.056.

        3 Post-Test Odds (Fagan Nomogram) ▼
        Post-Test Odds = Pre-Test Odds × Likelihood Ratio

        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:

        1

        수치 입력하기

        입력 칸에 알고 있는 비율 값을 입력합니다. 구하려는 미지수 자리의 칸 하나는 비워둡니다.

        2

        모드 선택하기

        비율 모드(풀기, 간소화, 스케일링)를 선택합니다. 각 모드는 입력한 수치에 맞춰 다른 공식들을 적용합니다.

        3

        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
        1 Calculate Positive Likelihood Ratio: LR+ = Sensitivity / (1 - Specificity) = 0.90 / (1 - 0.85) = 0.90 / 0.15 = 6.00.
        2 Calculate Negative Likelihood Ratio: LR- = (1 - Sensitivity) / Specificity = (1 - 0.90) / 0.85 = 0.10 / 0.85 = 0.118.
        ✓ LR+ is 6.00 | LR- is 0.12
        입력 2 Calculate post-test probability
        1 Given Pre-test probability = 20% (Pre-test odds = 0.20 / 0.80 = 0.25).
        2 Post-test odds = Pre-test odds × LR+ = 0.25 × 6.0 = 1.50.
        3 Post-test probability = Odds / (1 + Odds) = 1.50 / 2.50 = 0.60 (60%).
        ✓ Post-Test Probability is 60.0%
        입력 3 Highly sensitive test: 99% sensitivity, 50% specificity
        1 Calculate LR- = (1 - 0.99) / 0.50 = 0.01 / 0.50 = 0.02.
        2 Interpret: Extremely low LR- (< 0.1) provides strong diagnostic rule-out capability.
        ✓ LR- is 0.02 (Excellent Rule-Out Diagnostic Utility)

        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.

        비율 이론 학습하기

        비율이란 정확히 무엇인가요?

        비율(Ratio)은 두 가지 이상의 양의 크기를 서로 견주어 비교해 나타낸 수치입니다. 기호로는 A : B 와 같이 나타내며, '앞엣것 A의 단위량당 뒤엣것 B의 분량이 매칭된다'는 상호 관계입니다. 3 : 4 비율이라면 A가 3개 배분될 때 B는 4개 매칭된다는 정비례 관계를 갖습니다. 요리 레시피 배량, 기계 설계, 금융 재무 분석 등에 두루 사용됩니다.

        비례식은 어떻게 푸나요?

        비례식은 두 비율의 가치가 같다는 것을 뜻하는 수학 등식입니다 (A : B = C : D). 외항의 곱(A × D)과 내항의 곱(B × C)은 항상 같습니다. 미지수 D를 구하려면 내항을 곱한 뒤 남은 외항 A로 나눕니다: D = (B × C) / A. 비율 계산기의 비례식 해결 모드에 알고 있는 세 숫자를 넣으면 미지수를 즉각 도출할 수 있습니다.

        비율은 어떻게 간단하게 정리하나요?

        두 숫자의 최대공약수(GCD)를 구한 다음 두 수를 모두 그 최대공약수로 나누어 약분하면 됩니다. 예컨대 24 : 36 의 경우 24와 36의 최대공약수가 12이므로 양쪽을 12로 나누면 가장 간단한 자연수의 비인 2 : 3이 됩니다. 비율 계산기가 GCD 연산과 약분을 자동으로 처리해 줍니다.

        비율 크기 스케일링은 언제 사용하나요?

        비율 관계를 흩뜨리지 않고 전체 양을 늘리거나 줄일 때 사용합니다. 예컨대 2 : 5 비율의 자재가 있을 때 양쪽 모두에 3을 곱하면 6 : 15 가 되어 동일한 비중을 가지면서 3배 많은 배합물을 준비할 수 있습니다. 빵 굽기 반죽 용량 증감, 조립 도면 축소 스케일링 등에서 필수적입니다.

        비율과 분수의 차이점은 무엇인가요?

        비율(A : B)은 대등한 성분끼리 양의 크기를 비교하는 것(부분 대 부분)에 가깝고, 분수(A/B)는 전체 수량의 파이 속에서 특정 부위가 차지하는 지분율(부분 대 전체)을 표현하는 경우가 많습니다. 다만 비율 3 : 4 역시 분수 3/4 (소수 0.75)의 가치로 나타낼 수 있습니다. 쓰임새와 의미 맥락에서 미세한 뉘앙스 차이가 존재합니다.