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).
Kullanılan Formüller & Denklemler
Bu Hazard Ratio Calculator aracı 5 temel denklem kullanır:
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.
Bu Hesaplayıcı Nasıl Kullanılır?
Bu Oran Hesaplayıcıyı kullanmak için 3 adımı takip edin:
Değerleri Girin
Bilinen oran değerlerini giriş alanlarına yazın. Bir alanı boş bırakın — Oran Hesaplayıcının çözdüğü bilinmeyen değer budur.
Mod Seçin
Oran modunu seçin — Çöz, Basitleştir veya Ölçeklendir. Her mod, giriş değerlerinize farklı denklemler uygular.
Sonuçları Alın
Hesapla'ya tıklayın. Sonuç ekranı, cevabı görsel bir oran çubuğu, pasta grafiği ve adım adım çözüm dökümü ile görüntüler.
Örnek Problemler & Adım Adım Çözümler
İşte bu Oran Hesaplayıcıyı kullanan adım adım çözümlü 3 örnek problem:
Giriş 1 Cancer trial: HR = 0.72 for new drug
Giriş 2 Compare two treatments: HR = 1.15
Giriş 3 Estimate median survival improvement
Sıkça Sorulan Sorular
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.