Hazard Ratio Calculator

The Hazard Ratio Calculator compares how quickly events — such as deaths or treatment failures — occur between two groups in a clinical or survival study, giving you a single ratio that captures the relative risk over time. Enter the events and total subjects for your treatment group and control group, then select a confidence level to calculate the Hazard Ratio (HR). Secondary outputs include the confidence interval, p-value, z-score, and standard error — plus an optional median-based HR approximation if you provide median survival times for each group.

Number of events (deaths, failures, etc.) in treatment group

Total number of subjects in treatment group

Number of events (deaths, failures, etc.) in control group

Total number of subjects in control group

Optional: Used for median-based HR approximation

Optional: Used for median-based HR approximation

Results

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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Frequently Asked Questions

What is a hazard ratio (HR) and how is it interpreted?

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.

How is hazard ratio different from relative risk?

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.

What does the confidence interval tell me about the hazard ratio?

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.

How do I calculate hazard ratio from survival data?

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.

What is the median-based approximation for hazard ratio?

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.

How should I interpret the p-value in hazard ratio analysis?

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.

What sample size considerations apply to hazard ratio calculations?

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.