The Analysis of Survival Data

Survival data is characterised by a dichotomous outcome variable (the event) and the time till the event occurs. The analysis of survival data is specifically developed for analysing mortality data, but it is also used in other situations, such as time to recovery, etc. To describe survival data and to compare survival data between groups, Kaplan-Meier curves are normally used, while the log-rank test can be used to compare Kaplan-Meier curves with each other. To obtain effect estimates, Cox regression analysis can be used. Cox regression analysis is comparable to linear regression analysis and logistic regression analysis, in a way that the regression coefficients have the same interpretation, only the outcome variable is different. In Cox regression analysis, the outcome variable is the natural log of the hazard function. Because of that the regression coefficient of an independent variable can be transformed into a hazard ratio, i.e. a relative risk on average over time. Because the effect estimate is on average over time, this is only a good effect estimate when the hazards are proportional over time. Cox regression analysis is, therefore, also known as Cox proportional hazards regression analysis. Whether the hazards are proportional can, for instance, be investigated with a Cox regression analysis with a time-dependent covariate. In this chapter, furthermore, the evaluation of linearity of the relationship with a continuous independent variable, the adjustment for confounding and the investigation of effect modification are discussed. The way this is done in Cox regression analysis is exactly the same as in linear and logistic regression analysis.