[R] A couple of questions regarding the survival:::cch function

[Ryung Kim]

Above, I posted what I find may be errors in survival:::Prentice and survival:::LinYing.

Today, I found (what I believe is) another discrepancy/error in survival:::SelfPrentice.

The variance estimator is slightly different from codes of Therneau & Li (1999).

When extracting dfbeta, 

Therneau & Li uses db <- db[subcoh == 1,] But the survival:::SelfPrentice uses db <- db[gp == 0,]

In other words, Therneau & Li uses the real subcohort index (including duplicate observations that are internally created) but survival:::SelfPrentice uses the dummy index.

This may very well be intentional by the authors of the program. I am just reporting the discrepancy between the program and the article they cite (Therneau & Li, 1999)

 

-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf Of Ryung Kim
Sent: Thursday, August 22, 2013 9:26 PM
To: r-help at r-project.org
Subject: [R] A couple of questions regarding the survival:::cch function

Dear all,

I have  a couple of questions regarding the survival:::cch function.


1)      I notice that Prentice and Self-Prentice functions are giving identical standard errors (not by chance but by programming design) while their beta estimates are different. My guess is they are both using the standard error form from Self and Prentice (1986). I understand that standard errors for both methods are asymptotically identical, but in my simulation study I need to distinguish between two standard errors evaluated at different beta coefficients. My guess is changing the option iter.max=35 in Prentice function to iter.max=0 should do the trick. But I wanted to hear from the experts (or the author of the program) on this issue.



The fact that SE's are identical can be found by the R help example codes of CCH.  I'm copying and pasting them.



     subcoh <- nwtco$in.subcohort

     selccoh <- with(nwtco, rel==1|subcoh==1)

     ccoh.data <- nwtco[selccoh,]

     ccoh.data$subcohort <- subcoh[selccoh]

     ## central-lab histology

     ccoh.data$histol <- factor(ccoh.data$histol,labels=c("FH","UH"))

     ## tumour stage

     ccoh.data$stage <- factor(ccoh.data$stage,labels=c("I","II","III","IV"))

     ccoh.data$age <- ccoh.data$age/12 # Age in years



    cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data, subcoh = ~subcohort, id=~seqno, cohort.size=4028)

    cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data,  subcoh = ~subcohort, id=~seqno, cohort.size=4028, method="SelfPren")



2)      I also notice that Lin-Ying beta estimates are quite different from Self-Prentice estimates. My expectation was that the beta estimates should be the same (or at least very close) and only the variance estimates are supposed to be different. This is because Lin and Ying (1993) 's state  "the estimating equation... reduces to the pseduolikelihood score function of Self and Prentice" and Therneau and Li (1999, Lifetime Data Analysis) also state that " [Lin and Ying's] proposed [beta] estimates ... are identical to those of Self and Prentice.".  Can someone shed light on why the beta estimates in survival:::cch are different between two methods (by design, it seems)?



This also can be seen by the data in the example codes in R help.



      subcoh <- nwtco$in.subcohort

     selccoh <- with(nwtco, rel==1|subcoh==1)

     ccoh.data <- nwtco[selccoh,]

     ccoh.data$subcohort <- subcoh[selccoh]

     ## central-lab histology

     ccoh.data$histol <- factor(ccoh.data$histol,labels=c("FH","UH"))

     ## tumour stage

     ccoh.data$stage <- factor(ccoh.data$stage,labels=c("I","II","III","IV"))

     ccoh.data$age <- ccoh.data$age/12 # Age in years



     cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data,  subcoh = ~subcohort, id=~seqno, cohort.size=4028, method="SelfPren")

     cch(Surv(edrel, rel) ~ stage + histol + age, data =ccoh.data,  subcoh = ~subcohort, id=~seqno, cohort.size=4028, method="LinYing")

Ryung Kim
Department of Epidemiology and Population Health Albert Einstein College of Medicine

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