An Introduction to the Counting Process Approach to Survival Analysis

We refer to the counting process approach to the analysis of survival time throughout the text. This method has been the source of many new developments in the field since it was first used by Aalen [(1975) and (1978)1. Two texts document the mathematical details of this powerful method in a thorough manner. Fleming and Harrington (1991) and Andersen, Borgan, Gill and Keiding (1993). Fleming and Harrington (1991) focus primarily on the analysis of survival time while Andersen et al. (1993) consider analysis of survival time as well as other, more general statistical problems. We encourage readers of this text to see Andersen et al. (1993, Chapter 1) for an excellent overview of the types of statistical problems that can be formulated as counting processes. Fleming and Harrington (1991, Chapter 0) and Andersen et al. (1993, Section II.1) provide nontechnical mathematical introductions to the approach. This appendix introduces a few of the key ideas and constructs used in the counting process approach to the analysis of survival time. For this reason, many of the more technical mathematical assumptions and details will not be discussed.

Suppose we follow a single subject from time of enrollment, t = 0 , in a study of a particular cancer until the subject dies from this cancer. Furthermore, we assume it is a 5-year study and that this subject is enrolled on the first day of the study. Thus the maximum ...

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