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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 — リアルタイム比率プレビュー
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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.

        使用される計算公式・方程式

        この計算ツールは5つの主要な公式を使用しています:

        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 比率計算ツール home page.

        比率計算ツールの使い方

        この比率計算ツールは、以下の3ステップで簡単にご利用いただけます:

        1

        数値を入力

        入力欄に既知の比率の値を入力します。求めたい未知数の入力欄は空欄のままにしておきます。

        2

        モードを選択

        比率モード(解く、簡素化、スケーリング)を選択します。各モードで異なる計算式が適用されます。

        3

        結果を確認

        計算するボタンを押します。結果画面に答えと、視覚的な比率バー、円グラフ、詳細なステップバイステップの解決プロセスが表示されます。

        実例問題と段階的な解説

        本比率計算ツールを使って、以下の3つの例題をステップバイステップで解決するプロセスです:

        入力 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
        入力 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%
        入力 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)

        よくある質問 (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.

        比率の理論を学ぶ

        比率とは具体的に何ですか?

        比率とは、2つ以上の数量の大きさを互いに比較して相対的な割合を表した数値です。記号では A : B のように表し、「Aの量に対してBの量が対応する」という相互関係を意味します。例えば、3 : 4 の比率は、Aが3つ分配されるときBは4つマッチするという正比例関係を持ちます。料理、工学設計、財務分析など日常のあらゆる場面で使われます。

        比例式はどのように解きますか?

        比例式は、2つの比率の値が等しいことを表す等式です(A : B = C : D)。外項の積(A × D)と内項 of 積(B × C)は常に等しくなります。未知数 D を求めるには、内項の積を求め、それをもう一方の外項 A で割ります: D = (B × C) / A。当ツールの比例式解決モードに既知の3つの数値を入力すれば、未知数を即座に算出できます。

        比率はどのように簡単に整理しますか?

        2つの数値の最大公約数(GCD)を求めた後、両方の数値をその最大公約数で割って約分します。例えば 24 : 36 の場合、24と36の最大公約数が 12 なので、両方を 12 で割ると最も簡単な自然数の比である 2 : 3 になります。比率計算ツールがGCDの算出と約分を自動的に処理します。

        比率のスケーリングはいつ使用しますか?

        比率の関係を崩さずに全体の分量を増やしたり減らしたりするときに使用します。例えば、2 : 5 の割合の材料があるとき、両方に 3 を掛ければ 6 : 15 になり、同じ比重を保ったまま3倍の量の配合物を準備することができます。パン生地の容量変更や、図面の縮尺変更に欠かせません。

        比率と分数の違いは何ですか?

        比率(A : B)は同等の要素同士の大きさの比較(部分対部分)に適しており、分数(A/B)は全体の中である要素が占める割合(部分対全体)を表現することが多いです。ただし、比率 3 : 4 も分数 3/4(小数で0.75)として表現できます。使われる文脈や意味合いにおいてニュアンスの違いがあります。