[R] cox.zph vs log-log survival plot

From: Pietro Bulian <pbulian_at_cro.it>
Date: Thu 25 Jan 2007 - 16:21:12 GMT


Hello,
Excuse me for a more methodological than technical question. I'm developing a Cox model with 10 covariates. One of them is age (named "eta"). I've checked proportionality with cox.zph with age continuous:

> cox.zph(coxph(Surv(TTP,CENSOTTP)~eta))

                rho  chisq    p

    eta -0.0154 0.0225 0.88

and categorical (eta<60):

> cox.zph(coxph(Surv(TTP,CENSOTTP)~eta<60))

                                rho  chisq     p
    eta < 60TRUE 0.0168 0.0255 0.873

it seems ok but when I check graphical pattern of log-minus-log Kaplan Meier I see a convergent-divergent pattern, which seems violating proportionality:

> plot(survfit(Surv(TTP,CENSOTTP)~eta<60),fun="cloglog",xlab="log TTP",ylab="log(-log(S))")

also plotting cox.zph of eta<60 (log time) shows a sinusoidal pattern. I' m not experienced with plotting cox.zph or log-minus-log Kaplan Meier, so my question is: should I always rely on significance test from cox.zph or should I look at graphical pattern? Is age in this example violating proportionality? I paste below "eta" (age) "TTP" (time to event) "CENSOTTP" (censor)

Thank you

Pietro Bulian
Clinical and Experimental Hematology Research Unit Centro di Riferimento Oncologico, I.R.C.C.S. Via Pedemontana, 12
I-33081 Aviano (PN) - Italy
phone: +39 0434 659 412
fax: +39 0434 659 409
e-mail: pbulian@cro.it

"eta" "TTP" "CENSOTTP"
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