R help - Feb 2009 - C-index for models fitted using start, stop in Surv?

Dear R-users,

One can use the rcorr.cens function in Design to compute the C index when only
the stop time is indicated (I think implicitely start=0 in that case). When the
start and stop times are used in a Surv object, e.g.

library(Design)
S=with(heart, Surv(start,stop,event))

the object returned is no longer a single number vector, so none of the
following ways to compare a model fit to S makes sense:

rcorr.cens(-cph(S~ age+transplant+surgery, heart)$linear.predictors, with(heart,
Surv(start,stop,event)))
#       C Index            Dxy           S.D.              n        missing 
#      4.95e-01      -9.66e-03       7.15e-02       1.72e+02       0.00e+00 
#this seems bad because it compares the fit to a different Surv than the one
used to fit it (S, above)

rcorr.cens(-cph(S~ age+transplant+surgery, heart)$linear.predictors, with(heart,
Surv(stop-start,event)))
#       C Index            Dxy           S.D.              n        missing 
#      6.02e-01       2.03e-01       7.54e-02       1.72e+02       0.00e+00 

Is there some way I can compute the correlation for this type of survival time
specification in R? If not, does anybody have some tips on how to go about
computing it myself?

Many Thanks

Eleni Rapsomaniki
Research Associate
Strangeways Research Laboratory
Department of Public Health and Primary Care
University of Cambridge
?

Eleni Rapsomaniki wrote:
> Dear R-users,
> 
> One can use the rcorr.cens function in Design to compute the C index when
only the stop time is indicated (I think implicitely start=0 in that case). When
the start and stop times are used in a Surv object, e.g.
> 
> library(Design)
> S=with(heart, Surv(start,stop,event))
> 
> the object returned is no longer a single number vector, so none of the
following ways to compare a model fit to S makes sense:
> 
> rcorr.cens(-cph(S~ age+transplant+surgery, heart)$linear.predictors,
with(heart, Surv(start,stop,event)))
> #       C Index            Dxy           S.D.              n        missing
> #      4.95e-01      -9.66e-03       7.15e-02       1.72e+02       0.00e+00
> #this seems bad because it compares the fit to a different Surv than the
one used to fit it (S, above)
> 
> rcorr.cens(-cph(S~ age+transplant+surgery, heart)$linear.predictors,
with(heart, Surv(stop-start,event)))
> #       C Index            Dxy           S.D.              n        missing
> #      6.02e-01       2.03e-01       7.54e-02       1.72e+02       0.00e+00
> 
> Is there some way I can compute the correlation for this type of survival
time specification in R? If not, does anybody have some tips on how to go about
computing it myself?
> 
> Many Thanks
> 
> Eleni Rapsomaniki
> Research Associate
> Strangeways Research Laboratory
> Department of Public Health and Primary Care
> University of Cambridge
>  
> 
rcorr.cens is not meant for that.
Frank

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

> rcorr.cens is not meant for that.
Thank you for the clarification. On a second thought, I think (hope) a
time-dependent AUC index should be more appropriate in this case, such
as survivalROC. 

Many many thanks for all your help!

Eleni Rapsomaniki
 
Research Associate
Tel:     +44 (0) 1223 740273
Strangeways Research Laboratory
Department of Public Health and Primary Care
University of Cambridge
 

-----Original Message-----
From: Frank E Harrell Jr [mailto:f.harrell at vanderbilt.edu] 
Sent: 25 February 2009 17:50
To: Eleni Rapsomaniki
Cc: r-help at r-project.org
Subject: Re: [R] C-index for models fitted using start, stop in Surv?

Eleni Rapsomaniki wrote:
> Dear R-users,
> 
> One can use the rcorr.cens function in Design to compute the C index
when only the stop time is indicated (I think implicitely start=0 in
that case). When the start and stop times are used in a Surv object,
e.g. 
> 
> library(Design)
> S=with(heart, Surv(start,stop,event))
> 
> the object returned is no longer a single number vector, so none of
the following ways to compare a model fit to S makes
sense:
> 
> rcorr.cens(-cph(S~ age+transplant+surgery, heart)$linear.predictors,
with(heart, Surv(start,stop,event)))
> #       C Index            Dxy           S.D.              n
missing 
> #      4.95e-01      -9.66e-03       7.15e-02       1.72e+02
0.00e+00 
> #this seems bad because it compares the fit to a different Surv than
the one used to fit it (S, above)
> 
> rcorr.cens(-cph(S~ age+transplant+surgery, heart)$linear.predictors,
with(heart, Surv(stop-start,event)))
> #       C Index            Dxy           S.D.              n
missing 
> #      6.02e-01       2.03e-01       7.54e-02       1.72e+02
0.00e+00 
> 
> Is there some way I can compute the correlation for this type of
survival time specification in R? If not, does anybody have some tips on
how to go about computing it myself?
> 
> Many Thanks
> 
> Eleni Rapsomaniki
> Research Associate
> Strangeways Research Laboratory
> Department of Public Health and Primary Care
> University of Cambridge
>  
> 
rcorr.cens is not meant for that.
Frank

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

One of my colleagues has written a technical report on how to do this, but I 
have not yet implemented it in the survival package.  

	Terry Therneau
	
http://mayoresearch.mayo.edu/mayo/research/biostat/techreports.cfm
  #80
  Concordance for Survival Time Data: Fixed and Time-Dependent Covariates and 
Possible Ties in Predictor and Time
Concordance, or synonymously the C-statistic, is a valuable measure of model 
discrimination in analyses involving survival time data. This report provides a 
definition of concordance in the case of survival data, allowing for 
time-dependent covariates with the counting process data representation and 
accounting for ties in the covariates and times.
Walter K Kremers and The William J. von Liebig Transplant Center [April 2007]