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

[Thomas Lumley]

On Mon, 16 Jun 2008, Peter Dalgaard wrote:

> 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.

Yes. The cch() methods all do a model-based analysis of the full cohort and a finite-sampling analysis of the second-phase sampling.

For Cox models the model-based and jackknife variances are usually very close. The nwtco data is actually an unusually bad fit to the Cox model and the differences are larger than usual.

> (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.)

If you have only one event per person the only problem is that the code isn't written that way.   On the other hand, if you do have additional time-varying covariates there will be a (possibly useful) efficiency gain from using more efficient methods than cch() provides, with calibration of weights based on covariates inside and outside the subcohort.

        -thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle