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. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
