15.1 : Introduction To Survival Analysis

Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.

The primary goal of survival analysis is to estimate survival time—the time until a specified event occurs—and to understand the factors that influence it. Key concepts include the survival function (S(t)), which gives the probability of surviving beyond a given time, and the hazard function (h(t)), which describes the instantaneous event rate at any time. These functions provide insights into survival patterns and risks over time.

Common methods include the Kaplan-Meier estimator, a non-parametric approach that generates survival curves and allows comparison of survival rates across groups, and the Cox proportional hazards model, a semi-parametric method that examines how covariates influence survival without assuming a specific distribution for survival times.

Survival analysis is extensively used in medicine to assess treatment effects and predict patient outcomes, in engineering to estimate product lifespans, and in social sciences to analyze durations like unemployment or time-to-life events. Its ability to handle censored data and model time-dependent phenomena makes it an essential tool for understanding and predicting outcomes in various fields.