I read many literatures and try to find variance estimation of Prentice
method in case cohort. Only SelfPrentice variance estimation can be
found. Does the jacknife variance using cluster(id) in coxph() only  applies
to Self Prentice?  I can find using [t-e,t] to estimate Beta for Prentice.
But How can we implement Prentice jacknife variance estimation in R
strictly?
Thanks

2008/6/17 Thomas Lumley <tlumley@u.washington.edu>:

> 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@u.washington.edu        University of Washington, Seattle
>
>
>

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