Cox Regression Calculator

Cox regression models the association between predictors and the hazard of an event over time. Copy your data into the table above and select a time variable, a status variable coded 0 for censored and 1 for event, and one or more categorical or metric predictors. The model is calculated automatically.

Cox regression results

The calculator reports:

• the overall model test, coefficients, standard errors, z statistics, and p-values,
• hazard ratios with 95% confidence intervals,
• the reference category used for every categorical predictor,
• predicted survival curves at the covariate means, and
• formal proportional hazards tests and scaled Schoenfeld residual plots.

Tied event times are handled with the Efron method. For a categorical predictor, the hazard ratio compares a category with the displayed reference category. For a metric predictor, it describes the multiplicative change in the hazard for a one-unit increase.

Proportional hazards diagnostics

The proportional hazards assumption means that a predictor's hazard ratio remains constant over time. numiqo tests this assumption for each model term and for the model as a whole using scaled Schoenfeld residuals. A small p-value provides evidence that an effect changes over time. A large p-value means that no violation was detected; it does not prove that the assumption is true.

The residual plots complement the tests. A systematic trend or curvature can indicate a time-varying effect and should be investigated before interpreting a single constant hazard ratio.

Cox regression or Fine-Gray regression?

Cox regression is appropriate when the selected status distinguishes the event from censoring. When another event can prevent the event of interest from occurring, use the competing risks calculator. It reports cumulative incidence and Fine-Gray subdistribution hazard ratios instead of treating the competing event as ordinary censoring.

For definitions, interpretation, and a worked example, see the Cox regression tutorial.