R help - Mar 2007 - 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,
?quipe "?volution des Syst?mes Symbiotiques"
911 avenue Agropolis, BP 64501,
34394 Montpellier cedex 5 FRANCE

Eric Elguero wrote:
> 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...
That is a very ignorant person, concerning statistical 
efficiency/power/precision and how to handle incomplete follow-up 
(variable follow-up duration).  There are papers in the literature (I 
wish I had them at my fingertips) that go into the efficiency loss of 
just counting events.  If the events are very rare, knowing the time 
doesn't help as much, but the Cox model still can handle censoring 
correctly and that person's approach doesn't.

Frank
> 
> 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,
> ?quipe "?volution des Syst?mes Symbiotiques"
> 911 avenue Agropolis, BP 64501,
> 34394 Montpellier cedex 5 FRANCE
> 
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 

-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University

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: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at
stat.math.ethz.ch] On Behalf Of Eric Elguero
Sent: Wednesday, March 28, 2007 8:40 AM
To: R-help at 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,
?quipe "?volution des Syst?mes Symbiotiques"
911 avenue Agropolis, BP 64501,
34394 Montpellier cedex 5 FRANCE

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.