Biostatistics series module 9: Survival analysis - Hazra, Avijit; Gogtay, Nithya (Indian journal of dermatology, 2017)
Survival analysis is concerned with "time to event" data. Conventionally, it dealt with cancer death as the event in question, but it can handle any event occurring over a time frame, and this need not be always adverse in nature. When the outcome of a study is the time to an event, it is often not possible to wait until the event in question has happened to all the subjects, for example, until all are dead. In addition, subjects may leave the study prematurely. Such situations lead to what is called censored observations as complete information is not available for these subjects. The data set is thus an assemblage of times to the event in question and times after which no more information on the individual is available. Survival analysis methods are the only techniques capable of handling censored observations without treating them as missing data. They also make no assumption regarding normal distribution of time to event data. Descriptive methods for exploring survival times in a sample include life table and Kaplan-Meier techniques as well as various kinds of distribution fitting as advanced modeling techniques. The Kaplan-Meier cumulative survival probability over time plot has become the signature plot for biomedical survival analysis. Several techniques are available for comparing the survival experience in two or more groups - the log-rank test is popularly used. This test can also be used to produce an odds ratio as an estimate of risk of the event in the test group; this is called hazard ratio (HR). Limitations of the traditional log-rank test have led to various modifications and enhancements. Finally, survival analysis offers different regression models for estimating the impact of multiple predictors on survival. Cox's proportional hazard model is the most general of the regression methods that allows the hazard function to be modeled on a set of explanatory variables without making restrictive assumptions concerning the nature or shape of the underlying survival distribution. It can accommodate any number of covariates, whether they are categorical or continuous. Like the adjusted odds ratios in logistic regression, this multivariate technique produces adjusted HRs for individual factors that may modify survival.