[R] Teasing out logrank differences *between* groups using survdiff or something else?

[David Winsemius]

On Sep 15, 2009, at 9:58 PM, 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.

The column labeled (O-E)^2/V should be distributed (at least if these  
were large
samples) as a chi-square statistic with 1 d.f. each. You've got 3 in  
there that
exceed the nominal 95th%ile of a X^2, but you really ought to be  
looking at the
actual to expected looked along the ordinal scale. "pat.karno" is  
pretty clearly,
(at least to this physician) the Karnofsky Performance score, and  
since that is
ordinal, you probably should be doing a trend test. Perhaps you could  
set up
pat.karno as an ordered variable and see if survdiff gives you a  
meaningful output.

If you are dealing with an analysis that might affect people's lives,  
wouldn't it
be ethically safer to involve a real statistician?

>
--

David Winsemius, MD
Heritage Laboratories
West Hartford, CT