Survival Analysis

Censoring and Truncation

Time-to-event data present themselves in unique ways that create special obstacles in analyzing such data. The most important one is known as censoring. Loosely speaking, censoring means that the data are incomplete. Although there exist many censoring mechanisms, we shall mainly focus on the two most frequently encountered types of censoring: right censoring and interval censoring.

Table 1 presents a typical right-censored data set resulting from a clinical trial. The purpose of this clinical trial was to evaluate the efficacy of maintenance chemotherapy for acute myelogenous leukemia (AML). In all, 23 patients were treated by chemotherapy, which led to remission, and then randomly assigned to two groups. The first group contained 11 patients and received maintenance chemotherapy. The second group contained 12 patients and did not receive maintenance chemotherapy. Time until relapse, the response variable denoted by T hereafter, was recorded in weeks. The objective of the survival analysis was to see if the maintenance chemotherapy prolonged time until relapse. In later sections, we will answer this question by applying appropriate survival analysis methods.

In Group 1, the first and the second patients had relapse times of precisely 9 weeks and 13 weeks, respectively. That is, T1 = 9 and T2 = 13. The third patient, however, was not able to provide an exact [Page 983]relapse time, perhaps due to being dropped out of the study. All we know is that, at Week 13, this patient was still relapse free. Thus this patient's relapse time should be greater than 13 weeks, which is denoted by 13+ in the table. One can see that for this patient, we have only “incomplete” information because instead of knowing the exact value of T3, we know only that T3 > 13. Such censoring is called right censoring.

...