This chapter gives an introduction to the key elements of survival analysis or time-to-event data analysis.
Survival analysis, or time-to-event data analysis, refers to statistical methods for time-to-event data. An event time, or survival time, is defined as the time from an initial event such as diagnosis of a disease to the occurrence of an event of interest such as death. Time-to-event data arise commonly in clinical trials and other follow-up studies. For example, time to death or treatment failures is a primary clinical outcome variable to evaluate the effectiveness of oral cyclophosphamide as a treatment for patients with scleroderma-related lung disease in the Scleroderma Lung Study discussed in Section 1.1.1. For convenience, we will use the words event, failure, and death interchangeably.
A common phenomena associated with time-to-event data is censoring, which refers to a situation where the event time of interest is only partially known. There are many types of censoring including right-censoring, left-censoring, interval censoring, and double censoring . In this chapter, we will confine our attention to right censoring when the event time is not observed due to the occurrence of a competing censoring event such as the end of a study, but is known to be greater than the observed censoring time.