From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>

Date: Mon, 16 Jun 2008 22:16:28 +0200

Date: Mon, 16 Jun 2008 22:16:28 +0200

Jin Wang wrote:

> I tried to compare if cch() and coxph() can generate same result for

*> same case cohort data
**>
**> Use the standard data in cch(): nwtco
**>
**> Since in cch contains the cohort size=4028, while ccoh.data size =1154
**> after selection, but coxph does not contain info of cohort size=4028.
**>
**> The rough estimate between coxph() and cch() is same, but the lower
**> and upper CI and P-value are a little different. Can we exactly use
**> coxph() to repeat cch() using with appropriate configuration in
**> coxph()? Is SAS a better way(PHREG,CASECOH.SAS) to implement
**> time-dependent case-cohort?
**>
**>
**>
*

I think you need to read the literature, in particular the paper by
Therneau (!) and Li, which among other things details the implementation
of the Self-Prentice estimator. With that in mind, it should not be
surprising that it is non-trivial how to get correct SE's out of coxph.
What _is_ surprising (at least somewhat) is how close the robust SE are
to those of the Self-Prentice method -- if I understand correctly, the
connection is that Self-Prentice uses jackknifing for the contribution
from subcohort sampling plus the standard Cox asymptotic variance and
the robust method effectively uses jackknifing for both.

(I'm a bit puzzled about why cch() insists on having unique id's, though. Doesn't _look_ like it would be too hard to get rid of that restriction, at least for S-P, which admittedly is the only method I spent enough time studying. And that was a some years ago.)

>> summary(fit2.ccP)

*>>
**> Call:
**> coxph(formula = Surv(edrel, rel) ~ stage + histol + age + offset(-100 *
**> (1 - subcohort)) + cluster(seqno), data = ccoh.data)
**>
**> n= 1154
**> coef exp(coef) se(coef) robust se z p
**> stageII 0.7363 2.09 0.1213 0.1699 4.33 1.5e-05
**> stageIII 0.5976 1.82 0.1233 0.1753 3.41 6.5e-04
**> stageIV 1.3921 4.02 0.1339 0.2081 6.69 2.2e-11
**> histolUH 1.5059 4.51 0.0911 0.1644 9.16 0.0e+00
**> age 0.0432 1.04 0.0146 0.0243 1.78 7.6e-02
**>
**> exp(coef) exp(-coef) lower .95 upper .95
**> stageII 2.09 0.479 1.497 2.91
**> stageIII 1.82 0.550 1.289 2.56
**> stageIV 4.02 0.249 2.676 6.05
**> histolUH 4.51 0.222 3.267 6.22
**> age 1.04 0.958 0.996 1.09
**>
**> Rsquare= 0.273 (max possible= 1 )
**> Likelihood ratio test= 368 on 5 df, p=0
**> Wald test = 134 on 5 df, p=0
**> Score (logrank) test = 490 on 5 df, p=0, Robust = 165 p=0
**>
**> (Note: the likelihood ratio and score tests assume independence of
**> observations within a cluster, the Wald and robust score tests do not).
**>
**>
**>
**>> summary(fit.ccSP)
**>>
**> Case-cohort analysis,x$method, SelfPrentice
**> with subcohort of 668 from cohort of 4028
**>
**> Call: cch(formula = Surv(edrel, rel) ~ stage + histol + age, data = ccoh.data,
**> subcoh = ~subcohort, id = ~seqno, cohort.size = 4028, method = "SelfPren")
**>
**> Coefficients:
**> Coef HR (95% CI) p
**> stageII 0.736 2.088 1.491 2.925 0.000
**> stageIII 0.597 1.818 1.285 2.571 0.001
**> stageIV 1.392 4.021 2.670 6.057 0.000
**> histolUH 1.506 4.507 3.274 6.203 0.000
**> age 0.043 1.044 0.996 1.095 0.069
**>
**>
**> 2008/6/12, Terry Therneau <therneau_at_mayo.edu>:
**>
**>> Jin Wang had an error. My original note specified a variable that was 1 for
**>> subjects NOT in the subcohort, so the correct coxph call is
**>>
**>> coxph(Surv(edrel, rel) ~ stage + histol + age +
**>> offset(-100*(subcohort==0)) + cluster(seqno), data =ccoh.data)
**>>
**>> This gives the same coefficients as the cch example, along with the
**>> infinitesimal jackknife or "robust" variance estimate.
**>>
**>> Terry Therneau
**>>
**>>
**>>
**>>
**>
**> ______________________________________________
**> R-help_at_r-project.org 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.
**>
*

-- O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard_at_biostat.ku.dk) FAX: (+45) 35327907 ______________________________________________ R-help_at_r-project.org 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.Received on Mon 16 Jun 2008 - 20:20:14 GMT

Archive maintained by Robert King, hosted by
the discipline of
statistics at the
University of Newcastle,
Australia.

Archive generated by hypermail 2.2.0, at Tue 17 Jun 2008 - 15:30:40 GMT.

*
Mailing list information is available at https://stat.ethz.ch/mailman/listinfo/r-help.
Please read the posting
guide before posting to the list.
*