That is not the only way to apply logistic regression to this problem
(although it is a common error in the analysis of cancer studies).
One can discretize time and apply logistic regression to survival over
each short time period (jointly): doing so comes pretty close to what the
Cox proportional hazard models do but can be harder to interpret. But
that is a far more sophisticated analysis than looking at crude relative
risks for subgroups, and my understanding of Sir David Cox's motivation
was to be able to do regression modelling of prognostic factors, not just
comparison of groups.
I would claim that the analysis of the Australian AIDS data in MASS needs
regression-like methods to extract all the information from what is a
limited and expensive set of data (and I happen to know Cox agrees).
On Wed, 28 Mar 2007, Christos Hatzis wrote:
On the same point, transforming time-to-event data to binary outcomes so
that contingency-table analysis (odds ratios etc) or logistic regression can
be applied will result in loss of information that could lead to misleading
conclusions.
For example, assuming that there is a good-prognosis group (low risk) and a
poor-prognosis group (high risk) that need to be compared. By definition,
patients in the good prognosis group are those that have been followed up
for a longer time in the study, whereas patients with poor prognosis will
tend to die earlier. Therefore censoring will occur later in the good
prognosis group and thus the two groups will not have a homogeneous
censorship structure. In this case, naïve analysis could be misleading.
For more details and a simulation example take a look at
http://jnci.oxfordjournals.org/cgi/data/99/2/147/DC1/3
HTH
-Christos
Christos Hatzis, Ph.D.
Nuvera Biosciences, Inc.
400 West Cummings Park
Suite 5350
Woburn, MA 01801
Tel: 781-938-3830
www.nuverabio.com
-----Original Message-----
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Lucke, Joseph F
Sent: Wednesday, March 28, 2007 12:10 PM
To: Eric Elguero; R-help@stat.math.ethz.ch
Subject: Re: [R] what is the difference between survival
analysis and (...)
You can (and I have) fit survival data with logistic
regression. Agresti (1990, pp 189--196) has an introductory
discussion.
The issue is whether the occurrence of the event is of
interest or whether the time-to-event is of interest. If the
study lasts 180 days (as in my case) logistic regression
treats an event at 1 day the same as an event at 179 days.
Similarly, non-occurrence censored at 5 days is treated the
same as non-occurrence censored at 180 days. These
assumptions only make sense if the hazard rate is constant
and (therefore) the time-to-failure distribution is exponential.
One can include exposure time as a offset (non-estimated
covariate) to handle non-constant hazard rates. One can also
model the hazard rate directly as a log-linear model.
Based on what he said (number events/sample size, using
cumulative times), the hostile medical epidemiologist was
implicitly assuming the survival time followed an exponential
distribution. This assumption is often incorrect. His
arrogance was exceeded only by his ignorance.
Joe
@BOOK{Agresti1990,
author = {Agresti, Alan},
title = {Categorical data analysis},
year = {1990},
publisher = {John Wiley \& Sons},
address = {New York, NY},
series = {Wiley Series in Probability and Mathematical Statistics},
keywords = {loglinear; logistic}
}
-----Original Message-----
From: [EMAIL PROTECTED]
[mailto:[EMAIL PROTECTED] On Behalf Of Eric Elguero
Sent: Wednesday, March 28, 2007 8:40 AM
To: R-help@stat.math.ethz.ch
Subject: Re: [R] what is the difference between survival
analysis and (...)
Hi everybody,
recently I had to teach a course on Cox model, of which I am
not a specialist, to an audience of medical epidemiologists.
Not a good idea you might say.. anyway, someone in the
audience was very hostile. At some point, he sayed that Cox
model was useless, since all you have to do is count who dies
and who survives, divide by the sample sizes and compute a
relative risk, and if there was significant censoring, use
cumulated follow-up instead of sample sizes and that's it!
I began arguing that in Cox model you could introduce several
variables, interactions, etc, then I remembered of logistic
models ;-) The only (and poor) argument I could think of was
that if mr Cox took pains to devise his model, there should
be some reason...
but the story doesn't end here. When I came back to my
office, I tried these two methods on a couple of data sets,
and true, crude RRs are very close to those coming from Cox model.
hence this question: could someone provide me with a dataset
(preferably real) where there is a striking difference
between estimated RRs and/or between P-values? and of course
I am interested in theoretical arguments and references.
sorry that this question has nothing to do with R and thank
you in advance for your leniency.
Eric Elguero
GEMI-UMR 2724 IRD-CNRS,
Équipe "Évolution des Systèmes Symbiotiques"
911 avenue Agropolis, BP 64501,
34394 Montpellier cedex 5 FRANCE
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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
--
Brian D. Ripley, [EMAIL PROTECTED]
Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/
University of Oxford, Tel: +44 1865 272861 (self)
1 South Parks Road, +44 1865 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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