R help - Jun 2009 - Schoenfeld Residuals with tied data

Dear all,

I am struggling with calculation of Schoenfeld residuals of my Cox Ph
models.

Based on the formula as attached, I calculated the Schoenfeld residuals for
both non tied and tied data, respectively.

And then I validated my results with R using the same data sets. However, I
found that my results for non-tied data was ok but the results for tied data
were different from R's. 

How does R calculate the Schoenfeld Residuals for tied data? Could someone
give me some hints, please?

Thank you so much.

Bessy http://www.nabble.com/file/p24033333/Schoenfeld%2BResiduals.doc
Schoenfeld+Residuals.doc 
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Formally, the Schoenfeld residuals are defined as one residual per event time.

I found that when there are tied events, however, that plots of the residuals 
could be hard to visually interpret: sometimes a residual was large because of a
lack of fit at that point, sometimes because several death happened concurrently
at that point.

Since the Shoenfeld residual is a sum over the events at each time point, coxph 
returns one residual per EVENT, rather than one per event time.  The plots work 
much better (my subjective opinion).  If you sum the returned residuals at a 
given event time, you will get the common result.

	Terry Therneau

-- begin included message ----
Thank you for the reply. I really appreciate it.

I calculated the Scoenfeld residual per event and my results are the
following:

	fin	                       age	race
17	-0.33942334	-2.072218727	0.29024804
20	0.394600944	5.303968774	0.517689472
25	0.488184603	-1.438140647	-0.359535162
25	-0.511815397	-1.438140647	-0.359535162

However, the results from R are shown as below:

	fin	                     age	race
17	-0.3394233	-2.072219	0.290248
20	0.3946009	5.303969	             0.5176895
25	0.4724112	-1.615875	-0.4039688
25	-0.5275888	-1.615875	-0.4039688

--------  end inclusion -------

Bessy,
  By default the coxph function uses the Efron approximation for ties (more 
accurate than the Breslow approx).  You are computing the Schoenfeld residuals 
using the betas from coxph (Efron), and then applying a Breslow formula.  I can 
reproduce your results by forcing the same computation in R:
  
  > fit1 <- coxph(Surv(week, arrest) ~ fin + age + race, bessdata)
  > fit2 <- coxph(Surv(week, arrest) ~ fin + age + race, bessdata,
  	             init=coef(fit1), iter=0, method='breslow')
  > resid(fit2, 'schoen')
    	     fin       age       race
     17 -0.3394233 -2.072219  0.2902480
     20  0.3946009  5.303969  0.5176895
     25  0.4881846 -1.438141 -0.3595352
     25 -0.5118154 -1.438141 -0.3595352

 The Efron approximation is simple for computation of beta, but a bit more 
subtle when doing the residuals from the fit (but still not hard).  You can find
a detailed worked example in E.1.2 of the book by Therneau and Grambsch.
 
  If you had run the phreg procedure in SAS you would not have had this problem:
it contains exactly the same incorrect computation.  (Appendix E of the book 
contains a set of very small data sets where the correct answers can be worked 
out in closed form.  SAS gets all of the Breslow approx computations correct and
about 1/2 of the Efron ones.  R passes all the tests.)
  
  	Terry Therneau