I think you do in fact want to just run the analysis for the four groups you
are interested in. The logrank chisquared test would then be of the hypothesis
that these four groups have the same survival and censoring distributions, with
the greatest power for detecting proportional-hazards differences between the
groups.
You are correct in noting that the results you get for comparing these four
groups would change depending on what other groups are in the analysis. This is
a seriously underappreciated property of rank-based analyses. However, because
of this dependence I think you can make a good case that restricting the
analysis to the groups of interest is the best way to run the test.
-thomas
On Tue, 15 Sep 2009, Bryan Hanson wrote:
R Folk:
Please forgive what I'm sure is a fairly naïve question; I hope it's clear.
A colleague and I have been doing a really simple one-off survival analysis,
but this is an area with which we are not very familiar, we just happen to
have gathered some data that needs this type of analysis. We've done quite
a bit of reading, but answers escape us, even though the question below
seems simple.
Considering the following example from ?survdiff:
survdiff(Surv(time, status) ~ pat.karno, data=lung)
Call:
survdiff(formula = Surv(time, status) ~ pat.karno, data = lung)
n=225, 3 observations deleted due to missingness.
N Observed Expected (O-E)^2/E (O-E)^2/V
pat.karno=30 2 1 0.658 0.1774 0.179
pat.karno=40 2 1 1.337 0.0847 0.086
pat.karno=50 4 4 1.079 7.9088 8.013
pat.karno=60 30 27 15.237 9.0808 10.148
pat.karno=70 41 31 26.264 0.8540 1.027
pat.karno=80 51 39 40.881 0.0865 0.117
pat.karno=90 60 38 49.411 2.6354 3.853
pat.karno=100 35 21 27.133 1.3863 1.684
Chisq= 22.6 on 7 degrees of freedom, p= 0.00202
The p value here is for the entire group (right?). How do we go about
determining the p value for the comparison of any four arbitrary groups in
all combinations, say pat.karno = 40, 60, 80, and 100?
We know (we think) that we can't just run the coxph analysis for the only
the groups of interest, as the hazard ratio for any one group in an analysis
with several groups is computed by holding the other groups at their average
value, so the hazard ratio varies by the context.
Seems like we need some sort of t-test or chi-squared test, but being mere
chemists and molecular biologists, we don't quite see it and wouldn't trust
ourselves anyway, given the special nature of survival analysis. Manual
instructions or a function suggestion would be great.
Thanks in Advance, Bryan
*************
Bryan Hanson
Professor of Chemistry & Biochemistry
DePauw University, Greencastle IN USA
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Thomas Lumley Assoc. Professor, Biostatistics
tlum...@u.washington.edu University of Washington, Seattle
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