David W. Hosmer

English

Research Papers in Economics

The Stata Journal (2002)
2,N umber 4, pp. 428 431
Review of An Introduction to Survival Analysis
Using Stata
David W. Hosmer
University of Massachusetts
hosmer@schoolph.umass.edu
Abstract. The new book by Cleves et al. (2002)i sr e viewed.
Keywords: gn0004, survival time regression models, time to event analysis
1I ntroduction
The Stata staﬀ principally responsible for the st suite of programs in Stata, Mario A.
Cleves, William W. Gould, and Roberto G. Gutierrez, have written a book that builds
on a web course they oﬀer on survival analysis. The preface states that the intended
audience is a professional data analyst. As such, the goal is for this reader to emerge with
ac lear understanding of what a survival analysis is, the models, their estimators and
what information they are based on. The book has 15 chapters covering essentially four
broad areas: seven chapters discussing survival data and how to use the stset command
to describe survival data to Stata; one chapter on classic nonparametric methods; three
chapters dealing with the Cox proportional hazards model; and four chapters dealing
with parametric regression models. My comments will address each of the four broad
areas.
2S u r v i val analysis, the data, and using stset
The authors begin by using a modeling approach to compare and contrast analysis of
survival time data and the usual normal errors linear regression model and to compare
the three methods of analysis to be discussed in the book: nonparametric, semipara-
metric, and fully parametric models. This is followed by a careful presentation of the
various functions of time used in survival analysis: survival, hazard, and cumulative
hazard. The numerical examples on interpretation of these functions will be quite use-
ful to readers, especially those new to the concept of hazard. This is followed by a
careful discussion of analysis time, another topic that someone new to survival time will
 nd most helpful.
The chapter on censoring and truncation was mixed in my opinion. The treatments
of right censoring and left truncation (delayed entry) were clear and easy to follow. The
discussions of left censoring and right truncation were too brief to be informative or
useful. Granted these do not occur frequently in practice, but the authors should have
provided some references. (In my opinion, one of the biggest weaknesses of the book is
the lack of references for further study or alternative points of view.)
c ￿ 2002 Stata Corporation gn0004D. W. Hosmer 429
The next three chapters consider how survival data is likely to be recorded in prac-
tice, how to describe the data using stset,a n dhow to interpret output from stset.
Since stset may be Stata s most complicated command, the eﬀort placed here to demys-
tify it will be especially appreciated by users new to Stata s survival analysis commands.
At the conclusion of the  rst seven chapters, readers should have a good idea as to
what constitutes a survival analysis and how to get their data into the format required
by the st suite of commands.
3N onparametric survival time methods
The authors present in Chapter 8 standard nonparametric methods such as the Kaplan 
Meier estimator, the Nelson Aalen estimator, log-rank tests etc. One topic not discussed
is estimation, point and interval, of survival-time quantiles. Since these are routinely
reported in the subject-matter literature in conjunction with Kaplan Meier curves, the
omission, in my opinion, is substantial. Again, this is a topic with no references.
4T he Cox proportional hazards model
In the next three chapters, the authors discuss the Cox proportional hazards model,
estimation of regression coeﬃcients, and post-estimation of the baseline and covariate-
adjusted survival function. In my opinion, a clear strength of the chapter is the discus-
sion of estimation in the presence of ties. To my knowledge, Stata is the only package
that provides two  exact  methods. I assume that the authors do not want to acknowl-
edge their competition by name, but an oblique reference as to which exact method is
used in (say) TBT would be useful and informative. In addition, more explicit guidance
about which method to use to correct for ties, and when, would have been helpful, or
at least some references discussing this topic.
The authors  chapter on model building (Chapter 10) is, in my opinion, the weakest
chapter in the book. They really do not provide a discussion of model building, only
relatively super cial discussions of inclusion of categorical and continuous covariates
and interactions. Given that Stata is the only package with the method of fractional
polynomials, I was surprised that they did not use the opportunity to toot their horn.
One positive aspect is the enhanced discussion of the various ways to include time-
varying covariates.
The  nal chapter dealing with the Cox model considers methods for assessing model
adequacy and  t. Some of the methods discussed, for example, determining functional
form, to my way of thinking are basic steps in a careful model building and should
have been discussed in the previous chapter. The authors suggest using the linktest
command to assess adequacy in speci cation of the linear predictor. I have never found
this test to be especially useful. The more focused tests and methods found in fractional
polynomials combined with appropriate graphical displays are most certainly going to
 nd inadequacies in the linear predictor with greater power than the omnibus link test.
The authors carefully present Stata s test for proportional hazards based on the Schoen-430 Review of Cleves, Gould, and Gutierrez
feld residuals. One omission is any guidance on what to do when the methods indicate
that the hazard may be nonproportional in one or more covariates. They consider this
in the context of parametric models later in the book but leave the reader with little
help in this chapter. The authors  discussion of goodness-of- t is limited to graphical
displays based on Cox Snell residuals. Again, this is a topic where considerably more
work has been done, much of which is easily done in Stata, and yet no references are
provided. The discussion and presentation of diagnostics for in uence is quite brief.
Since I have the  oor, I will ask why these authors of the st commands did not include
an option for obtaining the in uence measures similar to the options for obtaining the
score and Schoenfeld residuals. If these measures are useful and important, shouldn t
Stata do all the calculations for us?
In summary, the three chapters dealing with the Cox proportional hazards model
provide a reasonable introduction to modeling survival data with this much used and
important model. However, considerably more could have been done, or at the very
least a more inclusive set of references given for additional information.
5P arametric survival-time models
In my opinion, the chapters on parametric models are the best in the book. This may
be due to the fact that being more familiar with the Cox model, I learned the most
from them. I found especially informative the explanations in Chapter 12 on the dif-
ferences in the data and likelihood functions used by the semiparametric Cox model
and parametric models likelihood and the comparison of the proportional hazards ver-
sus accelerated failure-time parameterizations. In Chapter 13 the authors compare the
diﬀerent parametric survival-time models available in Stata: exponential, Weibull, Gom-
pertz, log-normal, gamma, and log-logistic. They have put together a nice collection
of numerical examples that use parametric models to explore and then model a variety
of diﬀerent-shaped hazard functions. In Chapter 14 they discuss the various functions
and statistics that can be obtained after a model has been  t. Goodness of  t and
diagnostics are not speci cally discussed, and the reader is referred to the chapter on
the Cox model, which, as noted above, is not especially well done. Chapter 15 consid-
ers extensions such as strati ed models and random eﬀects frailty parametric models.
The discussion of random eﬀects frailty parametric models is well done. Given current
interest in these models, it is not clear to me why frailty model extensions were not
provided in Stata for the Cox model. Soon to come?
6S ummary and conclusions
In summary, I think the authors provide a good overview of survival analysis with Stata.
The strengths of the book are the discussions of the stset command, methods for time-
varying covariates, and the comparisons and modeling tricks shown in the chapters on
parametric models. While not comprehensive enough to use as a stand-alone reference,
It hink the book would be a valuable addition to the library of analysts who use Stata
to perform survival analyses.D. W. Hosmer 431
7R e f erences
Cleves, M., W. Gould, and R. Gutierrez. 2002. An Introduction to Survival Analysis
Using Stata. College Station, TX:S tata Press.
About the Author
David Hosmer is an emeritus professor of biostatistics in the Department of Biostatistics and
Epidemiology of the University of Massachusetts School of Public Health and Health Sciences
in Amherst, Massachusetts.

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