Cox Proportional Hazards — multivariable survival with adjusted HRs

Verified

Advanced & specialized

Independently verified. Every statistic this test reports has been re-derived against an independent reference — never the library the pipeline itself calls — the rendered output was read back in a browser, and the result is locked with a committed regression suite.

Run this test straight away on a free built-in teaching dataset — no data of your own needed — or bring your own. Either opens the guided workspace: variable setup, assumption diagnostics, results with effect sizes and confidence intervals, figures, and APA-ready reporting.

Loading teaching datasets…

Or use your own dataset

Loading your datasets…

Models the relationship between predictor variables and the time until an event occurs (survival / time-to-event data), accounting for censoring.

Semi-parametric — leaves the baseline hazard h₀(t) unspecified and estimates the relative-hazard structure exp(βX). Reports hazard ratios per covariate with 95% CIs, the partial-likelihood ratio test for the overall model, Schoenfeld residual tests for the proportional-hazards assumption per covariate, and concordance index (C-index) for discrimination. The standard tool for survival analysis in clinical research, epidemiology, and reliability engineering.

Worked example

Which factors change the risk of relapse, adjusting for the others?

Time-to-relapse in 200 patients was modelled on treatment, age and stage with Cox proportional-hazards regression; effects read as hazard ratios.

Result

Treatment cut the relapse hazard (HR = 0.43, 95% CI [0.31, 0.61], p < .001), independent of age and stage.

How you'd report it (APA)

A Cox regression showed the treatment significantly reduced relapse risk, HR = 0.43, 95% CI [0.31, 0.61], p < .001, adjusting for age and stage.

Try it yourself: Load this ready-made sample and follow the run above.

When to use it

  • Prospective cohort study
    500 cancer patients followed from diagnosis.
  • Randomized clinical trial (survival endpoint)
    Drug A vs Drug B in 300 patients with heart failure.

When NOT to — use instead

Hypotheses

H₀: β_j = 0 for all coefficients — covariates have no effect on the hazard.
Hₐ: at least one β_j ≠ 0.

Parameter tested: adjusted log-hazard coefficients β + Schoenfeld-test per coefficient

Assumptions (and what to do if they fail)

Each covariate's hazard ratio is CONSTANT over time. Violation means the coefficient is time-varying.medium

Check: Global Schoenfeld p-value.

If violated: Violated PH inflates / attenuates the reported HR; the effect may be time-varying.

Continuous predictors enter linearly on the log-hazard scale. Non-linear effects bias the HR estimate.medium

Check: Visual — martingale residuals.

If violated: Non-linearity understates / overstates the effect of extreme predictor values.

No single subject dominates the coefficient estimates. DFBETAS or score residuals flag influence.low

Check: Max |score residual| per subject.

If violated: An outlier can drive a single coefficient.

Ready to run a Cox Proportional Hazards — multivariable survival with adjusted HRs on your own data?

Guided setup, automatic assumption checks, effect sizes, figures and an APA write-up.

Run this test →