An Introduction to Survival Analysis

This chapter provides an introduction to some commonly used statistical methods for the analysis of survival time data in medical research with a focus on Kaplan–Meier and Cox regression.

Abstract

Survival analysis makes inference about event rates as a function of time. This chapter provides an introduction to some commonly used statistical methods for the analysis of survival time data in medical research. The two primary methods to estimate the true underlying survival curve are Kaplan–Meier and Cox regression. Kaplan–Meier is simple and supports stratification factors, but cannot evaluate covariates. The Cox model does provide a framework for making inferences about covariates and requires proportional hazards, although it is quite flexible when used and interpreted correctly. Independent censoring, either directly in the Kaplan–Meier or given covariates in the Cox model, is a requirement for consistent unbiased estimates. Survival analysis can handle right censoring, staggered entry, recurrent events, competing risks, and much more as long as we have available representative risk sets at each time point to allow users to model and estimate event rates. The analysis of survival time data is complicated by the fact that the follow-up length is often different for each participant, and the event of interest, such as myocardial infarction, is often not observed in all the subjects by the end of the study. For those participants in whom the event is not observed, what is known is that their survival times are longer than their time spent in the study, but their exact survival times are unknown. The chapter also discusses features of survival time data and product-limit estimator for the survival function.