Survival and Censored Data

Survival time is a main topic in medical statistics, and many reasons makes it difficult to get complete data in studies of survival time. A study is often finished before the death of all patients, and we may keep only the information that some patients were still alive at the end of the study, disregarding when they really died. That is a motivation of studying theory of censored data. We will see that a first possibility to deal with non-complete (we will say censored) data is to be unaware of them, and compute the statistic only on the rest of the data. However we may lose some information ignoring censored data, and actually our estimator will also be biased because ignoring right-censored data for example ignoring data which has the property to be greater than a given value. In this case, the expectation of our estimator is smaller than the real value of survival time. We introduce in this report some model for the survival time and see how we can handle with censored data. We may first deal with right- and left-censored data, and then we will show how we could use an algorithm to get a nonparametric estimate for interval-censored data. Some applications on data will also be given in order to illustrate the theory.