[R] weighted cox ph model

[Bessy]

Dear all,

I am struggling with the weighted Efron approximation. I really need some
help.

I am confused by the explanation regarding applying weights to Efron
approximation on the paper of “A Package for Survival Analysis in S” (Terry
M. Therneau, Feb 1999).  In the section 3.3.7 Weighted Cox models, it states
that, for a simple example with 5 subjects in time order and 1 and 2 died at
the same time, the second term of the weighted partial likelihood is either
w1r1/ ( w1r1 + w3r3+ w4r4+ w5r5)
or 
w1r1/ (w2r2+ w3r3+ w4r4+ w5r5)

The author suggests that to compute the Efron approximation one can simply
separately replace the numerator with 0.5 (w1r1 + w2r2) and the denominator
with 0.5w1r1 + 0.5w2r2+ w3r3+ w4r4+ w5r5. 

Does this suggestion refer to the second term (stated above) of the
likelihood function only ?

If so should the first term of the likelihood function should still be 
w2r2/ (w1r1 + w2r2+ w3r3+ w4r4+ w5r5)
or 
w1r1/ (w1r1 + w2r2+ w3r3+ w4r4+ w5r5)?

Then to compute the Efron approximation, should the numerator of the this
likelihood function should be 
0.5 (w1r1 + w2r2)* 0.5 (w1r1 + w2r2), 
i.e.
the likelihood function should be
[0.5 (w1r1 + w2r2)/ (w1r1 + w2r2+ w3r3+ w4r4+ w5r5) ]* [0.5 (w1r1 + w2r2)/(
0.5w1r1 + 0.5w2r2+ w3r3+ w4r4+ w5r5)]?

Since we add the probability to the numerator of the second term, we should
add the probability to the numerator of the first term as well. If 1 and 2
each have the probability of 0.5 for the deaths in the second term they
should also have the probability of 0.5 for the deaths in the first term.
That’s my thinking. If it is wrong, please correct it for me. I will really
appreciate it. 

By the way, I tried another weighted Efron approximation, which can yield
the same result with R if and only if the weights for tied data are the
same.  Otherwise it yields the different results but close to the R’s.

The formula has been attached with this message already.
Could someone give me some hints regarding my formula, please? 

Any suggestions will be sincerely appreciated.

Bessy
http://www.nabble.com/file/p24462598/Weighted%2BEfron%2BApproximation_Nabble_R.doc
Weighted+Efron+Approximation_Nabble_R.doc 
-- 
View this message in context: http://www.nabble.com/weighted-cox-ph-model-tp24462598p24462598.html
Sent from the R help mailing list archive at Nabble.com.