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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 — Anteprima Rapporto in Tempo Reale
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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.

        Formule ed Equazioni Utilizzate

        Questo Likelihood Ratio Calculator utilizza 5 equazioni fondamentali:

        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 Calcolatore di Rapporto home page.

        Come Usare Questo Calcolatore

        Per utilizzare questo Calcolatore di Rapporto, segui 3 semplici passaggi:

        1

        Inserisci i Valori

        Digita i valori noti nei campi di input. Lascia un campo vuoto: è il valore incognito che il Calcolatore di Rapporto risolverà.

        2

        Scegli la Modalità

        Seleziona la modalità: Risolvi, Semplifica o Scala. Ogni modalità applica equazioni diverse ai tuoi valori di input.

        3

        Ottieni i Risultati

        Fai clic su Calcola. La schermata dei risultati mostra la risposta con una barra grafica del rapporto, un grafico a torta e una spiegazione dettagliata passo dopo passo.

        Problemi di Esempio e Soluzioni Passo dopo Passo

        Ecco 3 problemi di esempio con soluzioni dettagliate passo dopo passo che utilizzano questo calcolatore:

        Input 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
        Input 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%
        Input 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)

        Domande Frequenti

        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.

        Approfondisci i Rapporti

        Cos'è un rapporto?

        Un rapporto è una comparazione tra due o più quantità che indica la grandezza relativa di una rispetto all'altra. Scritto come A : B, significa 'per ogni A unità della prima quantità, ce ne sono B della seconda'. Ad esempio, un rapporto 3 : 4 indica che per ogni 3 parti di A ci sono 4 parti di B. Si usa in cucina, edilizia, finanza, scienze e quotidianità.

        Come risolvo una proporzione?

        Una proporzione è un'uguaglianza tra due rapporti: A : B = C : D. Per ricavare un termine incognito si usa la regola del tre (prodotto incrociato). Se D è incognito: D = (B × C) / A. Questo perché in rapporti equivalenti i prodotti incrociati sono sempre uguali: A × D = B × C. Il nostro strumento lo fa in automatico: inserisci 3 valori per trovare il quarto.

        Come semplifico un rapporto?

        Per semplificare un rapporto, trova il Massimo Comun Divisore (MCD) di entrambi i numeri e dividili per esso. Ad esempio, 24 : 36 — il MCD di 24 e 36 è 12. Di conseguenza, 24 ÷ 12 = 2 e 36 ÷ 12 = 3, che dà il rapporto ridotto di 2 : 3. Il semplificatore trova il MCD e riduce il rapporto per te.

        Cos'è il ridimensionamento dei rapporti e quando è utile?

        Scalare un rapporto significa moltiplicare entrambi i termini per uno stesso fattore in modo da generare un rapporto equivalente più grande (o più piccolo). Ad esempio, scalando 2 : 5 per 3 si ottiene 6 : 15. È molto utile per le ricette (triplicare le dosi), nell'edilizia (scalare le planimetrie), nella chimica o quando occorre mantenere costante una proporzione su scala differente.

        Qual è la differenza tra un rapporto e una frazione?

        Un rapporto A : B mette in relazione due quantità tra loro (parte-parte), mentre una frazione A/B di solito rappresenta un rapporto parte-tutto. Tuttavia, ogni rapporto può essere scritto come frazione: 3 : 4 è equivalente a 3/4 = 0.75. La differenza risiede nel contesto d'uso.