I hope one and all will allow a stats question:
When running a cox proportional hazards model ,there are two ways to
deal with age,
including age as a covariate, or to include age as part of the
follow-up time, viz,
Age as a covariate:
tetest1 <- list(time= c(4, 3,1,1,2,2,3),
status=c(1,NA,1,0,1,1,0),
age= c(0, 2,1,1,1,0,0),
riskfactor= c(0, 0,0,0,1,1,1))
fitagecovariate<-coxph( Surv(time, status) ~ age +riskfactor, test1)
fitagecovariate
Age included as part of follow-up time:
test2<-test1
test2$timeplusage<-test2$time+test2$age
fitagefollowup<-coxph( Surv(timeplusage, status) ~ riskfactor, test2)
fitagefollowup
I would appreciate any thoughts about the differences in the
interpretation of the two models.
One obvious difference is that in the first model (fitagecovariate) one
can make inferences about age and in the second one cannot. I think a
second
difference may be that in the first model the riskfactor is assumed to
have values measured at the values of age where as in the second model
riskfactor is assumed to have given values throughout the subject's
life.
Your thoughts please.
Thanks,
John
R 2.1.1
windows XP
John Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
Baltimore VA Medical Center GRECC,
University of Maryland School of Medicine Claude D. Pepper OAIC,
University of Maryland Clinical Nutrition Research Unit, and
Baltimore VA Center Stroke of Excellence
University of Maryland School of Medicine
Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)
jsorkin at grecc.umaryland.edu
Confidentiality Statement:
This email message, including any attachments, is for the so...{{dropped}}
John Sorkin wrote:> I hope one and all will allow a stats question: > > When running a cox proportional hazards model ,there are two ways to > deal with age, > including age as a covariate, or to include age as part of the > follow-up time, viz, > > Age as a covariate: > > tetest1 <- list(time= c(4, 3,1,1,2,2,3), > status=c(1,NA,1,0,1,1,0), > age= c(0, 2,1,1,1,0,0), > riskfactor= c(0, 0,0,0,1,1,1)) > fitagecovariate<-coxph( Surv(time, status) ~ age +riskfactor, test1) > fitagecovariate > > Age included as part of follow-up time: > > test2<-test1 > test2$timeplusage<-test2$time+test2$age > fitagefollowup<-coxph( Surv(timeplusage, status) ~ riskfactor, test2) > fitagefollowup > > I would appreciate any thoughts about the differences in the > interpretation of the two models. > One obvious difference is that in the first model (fitagecovariate) one > can make inferences about age and in the second one cannot. I think a > second > difference may be that in the first model the riskfactor is assumed to > have values measured at the values of age where as in the second model > riskfactor is assumed to have given values throughout the subject's > life. > >Model2 is plainly wrong, unless your times can be negative it represents long stretches of immortality (more obvious if all ages are about 80...)! Presumably, age is the age at entry, so a delayed-entry model could be appropriate (Surv(age,timeplusage,status)). If this modification is made, the main difference is that the time-since-entry scale can not (easily) have a separate effect in the delayed-entry model. If time is really is time since diagnosis or operation, then that could be badly wrong.> Your thoughts please. > > Thanks, > John > > R 2.1.1 > windows XP > > John Sorkin M.D., Ph.D. > Chief, Biostatistics and Informatics > Baltimore VA Medical Center GRECC, > University of Maryland School of Medicine Claude D. Pepper OAIC, > University of Maryland Clinical Nutrition Research Unit, and > Baltimore VA Center Stroke of Excellence > > University of Maryland School of Medicine > Division of Gerontology > Baltimore VA Medical Center > 10 North Greene Street > GRECC (BT/18/GR) > Baltimore, MD 21201-1524 > > (Phone) 410-605-7119 > (Fax) 410-605-7913 (Please call phone number above prior to faxing) > jsorkin at grecc.umaryland.edu > > Confidentiality Statement: > This email message, including any attachments, is for the so...{{dropped}} > > ______________________________________________ > R-help at stat.math.ethz.ch 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. >-- O__ ---- Peter Dalgaard ?ster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
On Mon, 5 Feb 2007, John Sorkin wrote:> When running a cox proportional hazards model ,there are two ways to > deal with age, > including age as a covariate, or to include age as part of the > follow-up time, viz,<snip>> I would appreciate any thoughts about the differences in the > interpretation of the two models. > One obvious difference is that in the first model (fitagecovariate) one > can make inferences about age and in the second one cannot. I think a > second > difference may be that in the first model the riskfactor is assumed to > have values measured at the values of age where as in the second model > riskfactor is assumed to have given values throughout the subject's > life.There are even more possibilities (a nice example and discussion is in Breslow & Day, the example being occupational exposure to nickel and later cancer). The Cox model works by comparing covariates for the observation that failed and other observations at risk at the same time, so the comparisons are entirely within time-point. If you use time since start of study you are comparing people with different covariates at the same time since start of study. If you use calendar time you are comparing people with different covariates at the same calendar time If you use age you are comparing people with different covariates at the same age. In an observational study it often is more important to control for age or for calendar time than for time since the study started, so these might be better time scales. A disadvantage in some studies with longitudinal data is that on the study time scale everyone may have measurements at the same time but on other time scales everyone may have measurements at different times. -thomas