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 <[EMAIL PROTECTED]>:
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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