Calculator
Person-time units should be consistent (e.g., patient-months, patient-years). HR = Rate_A / Rate_B.
Hazard Ratio Calculator
Calculate hazard ratio, 95% confidence interval, p-value, and risk reduction percentage for survival analysis and clinical trial endpoints. Two input modes: from a reported HR+CI, or from event counts and person-time.
About Hazard Ratios
The hazard ratio (HR) is the standard measure of treatment effect in survival analysis and time-to-event studies. It compares the instantaneous risk (hazard) of an event between two groups at any given moment during follow-up. HR < 1 means the treatment group is reaching the event more slowly (beneficial for death/relapse); HR > 1 means the treatment accelerates events.
From HR and CI: SE(log HR) = [ln(UCI) − ln(LCI)] / (2 × 1.96). Z = ln(HR) / SE. p = 2 × (1 − Φ(|Z|)). Risk reduction = (1 − HR) × 100%.
From events and person-time: HR = (E_A / T_A) / (E_B / T_B). SE(log HR) = √(1/E_A + 1/E_B). CI = exp(ln(HR) ± 1.96 × SE).
Reporting format: HR = 0.72 (95% CI: 0.55–0.94), p = 0.016 — representing a 28% reduction in hazard.
Frequently Asked Questions
What is a hazard ratio?
A hazard ratio (HR) compares the rate at which events occur in the treatment group vs the control group in time-to-event data. HR = 0.62 means the treatment group has 38% lower hazard at any point in time. It is the standard effect measure in Cox regression and Kaplan-Meier survival analyses.
How do I interpret a hazard ratio?
HR < 1: treatment reduces hazard (benefit). HR = 1: no difference. HR > 1: treatment increases hazard (harm). If the 95% CI excludes 1.0, the result is statistically significant (p < 0.05). HR = 0.72 means a 28% reduction in hazard; HR = 1.45 means 45% increased hazard.
What is the difference between HR and relative risk?
Relative risk (RR) compares the probability of an event over a fixed time period. HR compares the instantaneous event rate, accounting for when events occur and censored observations. They are numerically similar when events are rare. HR is preferred when follow-up time varies across subjects.
How do I calculate HR from event counts?
HR = (Events_A / Person-time_A) / (Events_B / Person-time_B). SE(log HR) = √(1/Events_A + 1/Events_B). 95% CI = exp(log HR ± 1.96 × SE). This assumes constant proportional hazards over time.
How do I report a hazard ratio in a paper?
Report: HR = value (95% CI: lower–upper), p = value, and the clinical interpretation. Example: "Patients in the immunotherapy arm had a 28% lower hazard of disease progression (HR = 0.72, 95% CI: 0.55–0.94, p = 0.016)."
What does it mean if the HR confidence interval crosses 1?
If the 95% CI includes 1.0 (e.g., 0.55–1.10), the result is not statistically significant at p = 0.05. The true hazard ratio may be anywhere from a 45% reduction to a 10% increase, and you cannot conclude a significant treatment effect.