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).
Fórmulas e Equações Utilizadas
Esta Hazard Ratio Calculator usa 5 equações principais:
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.
Como Usar esta Calculadora
Para usar esta Calculadora de Proporção, siga 3 passos:
Insira os Valores
Digite os valores conhecidos nos campos de entrada. Deixe um campo vazio — esse é o valor desconhecido que a Calculadora de Proporção irá resolver.
Escolha o Modo
Selecione o modo de proporção — Resolver, Simplificar ou Redimensionar. Cada modo aplica equações diferentes aos seus valores de entrada.
Obtenha os Resultados
Clique em Calcular. A tela de resultados exibe a resposta com uma barra de proporção visual, um gráfico de pizza e um detalhamento da solução passo a passo.
Problemas de Exemplo e Soluções Passo a Passo
Aqui estão 3 problemas de exemplo com soluções passo a passo usando esta Calculadora de Proporção:
Entrada 1 Cancer trial: HR = 0.72 for new drug
Entrada 2 Compare two treatments: HR = 1.15
Entrada 3 Estimate median survival improvement
Perguntas Frequentes
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.