consists of randomized clinical trials where follow-up starts from the date of
enrollment and randomization of each subject.
Methodology discussed in this book has mostly been directed to the analysis
of cross-sectional and retrospective studies; this chapter is an exception. The
topics covered here in the first few sections—basic survival analysis and Cox’s
proportional hazards regression—were developed to deal with survival data
resulting from prospective or cohort studies. Readers should focus on the
nature of the various designs because the borderline between categorical and
survival data may be somewhat vague, especially for beginning students. Sur-
vival analysis, which was developed to deal with data resulting from prospec-
tive studies, is also focused on the occurrence of anevent, such as death or
relapse of a disease, after some initial treatment—a binary outcome. Therefore,
for beginners, it may be confused with the type of data that require the logistic
regression analysis discussed in Chapter 9. The basic di¤erence is that for sur-
vival data, studies have staggered entry, and subjects are followed for varying
lengths of time; they do not have the same probability for the event to occur
even if they have identical characteristics, a basic assumption of the logistic
regression model. Second, each member of the cohort belongs to one of three
types of termination:
- Subjects still alive on the analysis date
- Subjects who died on a known date within the study period
- Subjects who are lost to follow-up after a certain date
That is, for many study subjects, the observation may be terminated before
the occurrence of the main event under investigation: for example, subjects in
types 1 and 3.
In the last few sections of this chapter we return to topics of retrospec-
tive studies, the analysis of data from matched case–control studies. We put
together the analyses of two very di¤erent types of data, which come from two
very di¤erent designs, for a good reason. First, they are not totally unrelated;
statistical tests for a comparison of survival distributions are special forms of
the Mantel–Haenszel method of Chapter 6. Most methodologies used in sur-
vival analysis are generalizations of those for categorical data. In addition, the
conditional logistic regression model needed for an analysis of data from
matched case–control studies and Cox’s regression model for the analysis of
some type of survival data correspond to the same likelihood function and are
analyzed using the same computer program. For students in applied fields such
as epidemiology, access to the methods in this chapter would be beneficial
because most may not be adequately prepared for the level of sophistication of
a full course in survival analysis. This makes it more di‰cult to learn the anal-
ysis of matched case–control studies. In Sections 11.1 and 11.2 we introduce
some basic concepts and techniques of survival analysis; Cox’s regression
models are covered in Sections 11.3 and 11.4. Methods for matched data begin
in Section 11.5.
380 ANALYSIS OF SURVIVAL DATA