Kaplan–Meier Survival Analysis

Introduction

• What it is — Survival analysis is the branch of statistics dealing with the time between entry to a study and a subsequent event ("time-to-event", TTE). Originally for time-from-treatment-to-death — hence "survival" — but it applies to any well-defined endpoint, not only mortality.
• Each subject contributes two values — A survival time t (a duration) and an event indicator d (1 = event occurred; 0 = censored) — e.g. time to relapse, to contraceptive discontinuation, to fracture healing, or to a transdermal patch being removed.
• Why ordinary statistics fail — Two problems make the t-test / mean ± SD inappropriate: (1) non-Normality — survival times are right-skewed (a long tail of long survivors), so the mean and SD mislead; and (2) censoring — we cannot wait until everyone has had the event, so some subjects are event-free at analysis and carry only partial information.
• The specialised toolkit — Skew + censoring demand a non-parametric estimator (Kaplan–Meier), a specialised hypothesis test (log-rank) and specialised regression (Cox) rather than means, t-tests or ordinary regression.
• Why it matters — TTE endpoints are the workhorse of oncology and cardiovascular trials: overall survival, progression-free survival, time-to-first-MACE. The standard summary triplet for a two-arm trial is the Kaplan–Meier curve + log-rank P + hazard ratio (95% CI).