Hazard Ratio Calculator
The Hazard Ratio Calculator computes the ratio of hazard rates between two groups in survival analysis. Interpret hazard ratios from clinical trials, Kaplan-Meier curves, and Cox proportional hazards models for treatment effectiveness.
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What is a Hazard Ratio?
A hazard ratio (HR) compares the instantaneous rate of an event (death, disease recurrence, failure) between two groups at any point in time. An HR of 0.70 means the treatment group has 30% lower hazard (risk at any given moment) than the control group throughout the study period.
Hazard ratios are derived from Cox proportional hazards regression and are the standard measure in survival analysis. Unlike relative risk (which compares cumulative probabilities), HR compares instantaneous rates and handles censored data (patients lost to follow-up).
Formules et Équations utilisées
Ce calculateur s'appuie sur 5 équations fondamentales :
1 Hazard Ratio ▼
HR < 1 favors treatment. HR > 1 favors control. HR = 1 means no difference.
2 Median Survival Ratio (approximation) ▼
If HR = 0.5, the treatment group lives approximately twice as long (median survival ratio = 2).
3 Risk Reduction from HR ▼
HR = 0.65: Risk reduction = (1-0.65) × 100 = 35% reduction in the event rate.
Comment utiliser ce calculateur
Pour utiliser ce Calculateur de Ratio, suivez ces 3 étapes :
Saisir les Valeurs
Saisissez les valeurs de ratio connues dans les champs. Laissez un champ vide — c'est la valeur manquante que le calculateur va chercher à résoudre.
Choisir le Mode
Sélectionnez le mode de ratio — Résoudre, Simplifier ou Mettre à l'échelle. Chaque mode applique des formules différentes à vos valeurs.
Obtenir les Résultats
Cliquez sur Calculer. L'écran de résultats affiche la réponse avec une barre de ratio interactive, un diagramme circulaire et le détail des calculs.
Exemples Pratiques et Solutions Étape par Étape
Voici 3 exemples de calculs résolus avec les étapes détaillées grâce à ce calculateur :
Saisie 1 Cancer trial: HR = 0.72 for new drug
Saisie 2 Compare two treatments: HR = 1.15
Saisie 3 Estimate median survival improvement
Foire Aux Questions
What does a hazard ratio of 0.5 mean? ▼
HR = 0.5 means the treatment group has half the instantaneous risk of the event at any time point compared to the control group. This represents a 50% risk reduction and roughly doubles the time-to-event.
How is hazard ratio different from relative risk? ▼
Relative risk compares cumulative event probabilities over the entire study. Hazard ratio compares instantaneous event rates at any point in time. HR handles censored data and time-varying exposure, while RR cannot.
When is a hazard ratio statistically significant? ▼
When its 95% confidence interval does not include 1.0. HR = 0.70 with CI (0.50, 0.98) is significant. HR = 0.70 with CI (0.45, 1.10) is not significant because the CI crosses 1.0.
What is the proportional hazards assumption? ▼
Cox regression assumes the HR remains constant over time. If the treatment is very effective early but less so later, the proportional hazards assumption is violated. Schoenfeld residuals test this assumption.
Can hazard ratio be used with Kaplan-Meier curves? ▼
HR is typically derived from Cox regression, not directly from Kaplan-Meier curves. However, the log-rank test p-value from KM analysis can assess significance, and HR provides the effect size.