Preface to First Edition - lib

200 SURVIVAL ANALYSISspect to time from randomisation and the start of therapy until death. In thiscase, the event of interest is the death of a patient, but in other situations,it might be remission from a disease, relief from symptoms or the recurrenceof a particular condition. Other censored response variables are the time tocredit failure in financial applications or the time a roboter needs to successfullyperform a certain task in engineering. Such observations are generallyreferred to by the generic term survival data even when the endpoint or eventbeing considered is not death but something else. Such data generally requirespecial techniques for analysis for two main reasons:1. Survival data are generally not symmetrically distributed – they will oftenappear positively skewed, with a few people surviving a very long timecompared with the majority; so assuming a normal distribution will not bereasonable.2. At the completion of the study, some patients may not have reached theendpoint of interest (death, relapse, etc.). Consequently, the exact survivaltimes are not known. All that is known is that the survival times are greaterthan the amount of time the individual has been in the study. The survivaltimes of these individuals are said to be censored (precisely, they are rightcensored).Of central importance in the analysis of survival time data are two functionsused to describe their distribution, namely the survival (or survivor) functionand the hazard function.11.2.1 The Survivor FunctionThe survivor function, S(t), is defined as the probability that the survivaltime, T, is greater than or equal to some time t, i.e.,S(t) = P(T ≥ t).A plot of an estimate Ŝ(t) of S(t) against the time t is often a useful way ofdescribing the survival experience of a group of individuals. When there areno censored observations in the sample of survival times, a non-parametricsurvivor function can be estimated simply asnumber of individuals with survival times ≥ tŜ(t) =nwhere n is the total number of observations. Because this is simply a proportion,confidence intervals can be obtained for each time t by using the varianceestimateŜ(t)(1 − Ŝ(t))/n.The simple method used to estimate the survivor function when there areno censored observations cannot now be used for survival times when censoredobservations are present. In the presence of censoring, the survivor functionis typically estimated using the Kaplan-Meier estimator (Kaplan and Meier,© 2010 by Taylor and Francis Group, LLC