[R] 回复: cch() and coxph() for case-cohort

[Peter Dalgaard]

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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>   


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