Random-effect models for survival data
In this chapter we study how the GLM class of models can be applied for the analysis of data in which the response variable is the lifetime of a component or the survival time of a patient. Survival data usually refers to medical trials, but the ideas are useful also in industrial reliability experiments. In industrial studies interest often attaches to the average durations of products: when we buy new tyres we may ask how long they will last. However, in medical studies such a question may not be relevant. For example some patients may have already outlived the average lifetime. So a more relevant question would be ‘now that the patient has survived to the present age, what will his or her remaining lifetime be if he or she takes a certain medical treatment?’ Thus, hazard modelling is often more natural in medical studies, while in industrial reliability studies modelling the average duration time is more common.
In survival-data analysis censoring can occur when the outcome for some patients is unknown at the end of the study. We may know only that a patient was still alive at certain time, but the exact failure time is unknown, either because the patient withdrew from the study or because the study ended while the patient was still alive. Censoring is so common in medical experiments that statistical methods must allow for it if they are to be generally useful. In this chapter we assume that censoring occurs missing at random (MAR) in Section 4.8. We show how to handle more general types of missingness in Chapter 12.