Survival Analysis

Kaplan-Meier curves & Cox Proportional Hazards regression

About Survival Analysis

Kaplan-Meier estimators model time-to-event data with censoring. The log-rank test compares survival distributions between groups. Cox Proportional Hazards regression estimates the effect of covariates on the hazard rate, producing hazard ratios (HR) that quantify relative risk of the event over time.

Simulation Parameters

Sample Size: 200

Median Survival (control): 24 mo

Hazard Ratio (treatment): 1.5

Censoring Rate: 20%

Age Effect (β): 0.3

Sex Effect (β): 0.2

Kaplan-Meier Survival Curves

Log-rank χ² = 7.58, p = 0.023

Cox Proportional Hazards Model

Covariate	β	HR	SE	z	p
Treatment (group)	0.219	1.244	0.203	1.08	0.56
Age (per 10yr)	0.492	1.636	0.203	2.42	0.053
Sex (male)	0.36	1.433	0.203	1.77	0.208

n events = 189·n censored = 11·Concordance = 0.589

Summary Statistics

Control Events

93/101

Treatment Events

96/99

Log-rank p

0.023

True HR

1.5

Interpretation

The log-rank test shows a statistically significant difference between survival curves (χ² = 7.58, p = 0.023). The Cox model estimates a treatment hazard ratio of 1.244 — indicating that the treatment group has a 24% higher hazard of the event compared to controls. Concordance index: 0.589 (poor discrimination).