Understanding Hazard Ratios
A hazard ratio compares the instant risk of an event between two groups. It is common in survival analysis, clinical trials, insurance studies, and reliability work. The event may be death, relapse, churn, failure, or recovery. A value of 1 means both groups have equal hazard. A value above 1 means the numerator group has higher hazard. A value below 1 means it has lower hazard.
Why This Calculator Helps
Manual hazard ratio work can be slow. You must find the correct hazard measure first. You also need a confidence interval for interpretation. This calculator supports three useful entry methods. Use event counts and exposure time when you have rates. Use Cox model data when you already have a regression coefficient. Use survival probabilities when only survival proportions and follow time are available. Each method shows the main formula and related checks.
Interpreting The Result
A hazard ratio should be read with its confidence interval. For example, a hazard ratio of 0.70 suggests a thirty percent lower hazard in the numerator group. That statement is stronger when the interval stays below 1. If the interval crosses 1, the evidence is less clear. The result may still be useful, but uncertainty is wider. Always review study design, censoring, follow up, and sample size.
Good Data Practices
Use person time when follow up differs between groups. Use the same time unit for both groups. Days, months, and years should not be mixed. Check that event counts are valid whole numbers. Avoid using crude rates when a Cox model is required for adjusted analysis. Adjusted models can include age, sex, treatment arm, baseline risk, and other predictors. The calculator does not replace a full survival model. It gives a transparent estimate for reporting and learning.
Exports And Reporting
The CSV export is useful for spreadsheets. The PDF export gives a compact record of inputs and outputs. Keep those files with your analysis notes. Add the data source and assumptions in your report. Clear notes make the hazard ratio easier to audit later.
Limitations
Use caution with small samples. Zero events can make intervals unstable. This page can apply a correction, but expert review is still important before final publication.