Enter Events and Total Subjects for Treatment and Control Groups, Confidence Level, and Median Survival times, and the Hazard Ratio Calculator returns the HR, CI bounds, and Standard Error of ln(HR).
Hazard Ratio (HR)
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Lower Confidence Interval
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Upper Confidence Interval
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Standard Error of ln(HR)
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Z-Score
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P-Value (Two-sided)
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Median-based HR Approximation
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A hazard ratio compares the instantaneous risk (hazard) of an event occurring between two groups. HR = 1 means equal risk, HR < 1 means treatment reduces risk, HR > 1 means treatment increases risk. For example, HR = 0.6 means 40% risk reduction.
Hazard ratio considers the timing of events and instantaneous risk at any given time, while relative risk is a simple ratio of event probabilities at a fixed time point. HR is more appropriate for survival analysis and time-to-event studies.
The confidence interval shows the range of plausible HR values. If the interval includes 1.0, the difference between groups may not be statistically significant. A narrower interval indicates more precise estimates.
The basic formula is HR = hazard in treatment group / hazard in control group. This calculator uses event counts and total subjects to estimate HR, along with standard error calculations for confidence intervals.
When median survival times are available, HR can be approximated as the ratio of median control survival to median treatment survival, assuming exponential survival distributions.
The p-value tests the null hypothesis that HR = 1 (no difference between groups). A p-value < 0.05 typically indicates statistically significant difference between treatment and control groups.
Adequate sample sizes and sufficient number of events are crucial for reliable HR estimates. Small event counts can lead to unstable estimates and wide confidence intervals.