[R] 回复: cch() and coxph() for case-cohort
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Mon Jun 16 22:16:28 CEST 2008
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
>>
>>
>>
>>
>
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--
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
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