Likelihood Ratio Calculator
The Likelihood Ratio Calculator computes positive likelihood ratio (LR+) and negative likelihood ratio (LR-) from a diagnostic test's sensitivity and specificity. Evaluate how much a test result shifts the probability of disease for evidence-based clinical decisions.
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What is a Likelihood Ratio?
A likelihood ratio quantifies how much a test result changes the probability of having a condition. The positive likelihood ratio (LR+) measures how much a positive test increases disease probability. The negative likelihood ratio (LR-) measures how much a negative test decreases it. LR+ above 10 or LR- below 0.1 are considered strong evidence.
Likelihood ratios combine sensitivity and specificity into a single metric that is independent of disease prevalence. Clinicians use LRs with pre-test probability (Bayesian reasoning) to calculate post-test probability, making them more useful than sensitivity/specificity alone for clinical decision-making.
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 ▼
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%.
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：
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。
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。
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
入力 2 Calculate post-test probability
入力 3 Highly sensitive test: 99% sensitivity, 50% specificity
よくある質問 (FAQ)
What is a good likelihood ratio? ▼
LR+ > 10 is strong evidence for disease. LR+ 5-10 is moderate. LR+ 2-5 is weak. LR- < 0.1 strongly rules out disease. LR- 0.1-0.2 is moderate. LR values near 1.0 provide no useful information.
Why are likelihood ratios better than sensitivity/specificity? ▼
LRs combine both metrics into a single number and are independent of disease prevalence. They can be applied directly to individual patients using pre-test probability. Sensitivity and specificity are prevalence-independent but don't directly give post-test probability.
How do I use the Fagan nomogram? ▼
Draw a line from your pre-test probability (left axis) through the likelihood ratio (middle axis) to find the post-test probability (right axis). This visual tool quickly converts LRs into clinically useful probability changes.
Can likelihood ratios be used for multi-level test results? ▼
Yes. Interval likelihood ratios can be calculated for different result ranges (e.g., low, moderate, high values) rather than just positive/negative. Each interval has its own LR for more nuanced interpretation.
What is pre-test probability? ▼
Pre-test probability is your estimated chance of disease before conducting the test, based on prevalence, symptoms, and clinical judgment. It's the starting point for Bayesian reasoning with likelihood ratios.