Cox Proportional Hazards Regression

Cox Regression models time-to-event outcomes against multiple covariates simultaneously, producing hazard ratios that quantify how each covariate affects the event rate while adjusting for all others.

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Step 1 — Provide your data

Each row needs:

• Time — follow-up time
• Event — 1 (event) or 0 (censored)
• Covariates — numeric or categorical predictors

Supports Excel Import (with ColumnSelector and CategoryMapper), Sample Data Selector, and Manual Entry.

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Step 2 — Choose reference categories

For categorical covariates, pick the baseline level. HRs are reported relative to this reference.

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Step 3 — Results

Covariate table:

• Coefficient (beta), HR = exp(beta), 95% CI, SE, Z-score, p-value

Model Fit:

• Log-likelihood, Chi-square (LR test), df, overall p-value
• Concordance Index (C-index)
• Pseudo R-squared, Partial AIC

Proportional Hazards Test — Schoenfeld residual-based test per covariate.

Visualisations:

• Hazard Ratio Forest Plot
• Survival Plot at representative covariate values

A UniversalChatBot is available for discussion.

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Statistical methods used

Model

h(t|X) = h0(t) * exp(beta1*X1 + ... + betap*Xp)

Semiparametric: baseline hazard h0(t) left unspecified.

Estimation — Partial Likelihood via Newton-Raphson

• Max iterations: 20
• Convergence: max |score| < 1e-6
• Step halving when |beta| > 10

Hazard Ratios with 95% CI (Wald)

HR = exp(beta), CI: exp(beta +/- 1.96 * SE)

Overall model — Likelihood Ratio Test

chi2 = 2 * (logL_full - logL_null) with df = p.

Concordance Index

Proportion of concordant pairs (higher risk score = shorter survival).

Proportional Hazards Assumption

Schoenfeld residuals test for time-varying effects. p < 0.05 suggests violation.