Survival analysis: A primer for the clinician scientists

Abstract

Survival analysis is a collection of statistical procedures employed on time-to-event data. The outcome variable of interest is time until an event occurs. Conventionally, it dealt with death as the event, but it can handle any event occurring in an individual like disease, relapse from remission, and recovery. Survival data describe the length of time from a time of origin to an endpoint of interest. By time, we mean years, months, weeks, or days from the beginning of being enrolled in the study. The major limitation of time-to-event data is the possibility of an event not occurring in all the subjects during a specific study period. In addition, some of the study subjects may leave the study prematurely. Such situations lead to what is called censored observations as complete information is not available for these subjects. Life table and Kaplan-Meier techniques are employed to obtain the descriptive measures of survival times. The main objectives of survival analysis include analysis of patterns of time-to-event data, evaluating reasons why data may be censored, comparing the survival curves, and assessing the relationship of explanatory variables to survival time. Survival analysis also offers different regression models that accommodate any number of covariates (categorical or continuous) and produces adjusted hazard ratios for individual factor.

Keywords: Censoring; Cohort study; Cox proportional hazard model; Hazard ratio; Kaplan–Meier plot; Log-rank test; Longitudinal data analysis; Regression model; Time-to-event analysis.

Fig. 1

The timeline plot shows the entry, exit and the observations on severe ulcerative colitis (UC) patients at varying period of time. It describes the experience of 10 UC patients (who are in remission) followed over several weeks. A blue dot denotes a patient who got the event (end of remission period)

Fig. 2

The Kaplan–Meier survival curve for the hypothetical ulcerative colitis data

Fig.3

Illustration of increasing, decreasing Weibull model and lognormal model

Fig.4

Comparing survival probabilities of treatment and placebo group