Glossary

Survival Analysis

Survival analysis is a branch of statistics focused on modelling the time until an event occurs — such as death, disease recurrence, machine failure, or customer churn. Key tools include Kaplan–Meier survival curves for non-parametric estimation, log-rank tests for group compa...

Definition

Survival analysis is a branch of statistics focused on modelling the time until an event occurs — such as death, disease recurrence, machine failure, or customer churn. Key tools include Kaplan–Meier survival curves for non-parametric estimation, log-rank tests for group comparison, and Cox proportional-hazards regression for assessing covariate effects while handling censored observations.

Why It Matters

In clinical trials and reliability engineering, not every participant experiences the event by the end of the study. These right-censored observations contain valuable information and must be included rather than discarded. Survival analysis provides methods that naturally accommodate censoring, making it indispensable for any longitudinal study where the timing of events matters more than simple binary outcomes.

Example

A cancer trial compares a new chemotherapy regimen against standard care. Over two years, 40% of patients in the new treatment group and 60% in the standard-care group experience disease progression. However, 30% of patients in each group are still progression-free when the study ends. A Kaplan–Meier curve incorporates the censored patients and shows that median progression-free survival is 18 months for the new regimen versus 12 months for standard care, with a log-rank test p-value of 0.04.

Related Terms

Software Notes

  • SPSS: Analyze > Survival > Kaplan-Meier or Cox Regression. Define the status variable (event indicator) and time variable. The Compare Factor Levels option runs log-rank tests.
  • R: survival::survfit(Surv(time, status) ~ group, data = df) for Kaplan–Meier curves. survival::coxph(Surv(time, status) ~ x1 + x2, data = df) for Cox regression. ggsurvplot() from survminer publishes-ready curves.
  • Stata: stset time, failure(status) declares survival data. sts graph, by(group) plots Kaplan–Meier curves. stcox x1 x2 fits a Cox model. stcurve, survival plots predicted survival functions.