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I have run Cox regression using the survival package to calculate mortality hazard ratio of an exposure A. I have found that the age variable violated the proportional hazard assumption (with cox.zph) and used strata(age)to stratify age in further models.

I need a parameter estimate of the age variable, as well as the variance and the matrix of covariance (to calculate Rate Advancement Periods)... And I don't know where to find them!

Am I missing something or am I misunderstanding what strata is doing?

Here is a reproducible example, using the lung data from the survival package.

library(survival)

I create the survival object and do a first Cox regression with non-stratified age variable.

lung$SurvObj <- with(lung, Surv(time, status == 2))
coxreg1 <- coxph(SurvObj ~ age + sex, data =  lung)

So, I get coefficients, variance, and covariance matrix for the parameter estimates.

>   coxreg1$coefficients
        age         sex 
 0.01704533 -0.51321852 

> vcov(coxreg1)
             age          sex
age 8.506877e-05 8.510634e-05
sex 8.510634e-05 2.804217e-02

Now, if do a second regression with the stratified age variable, I don't get any coefficient estimates, variance or covariance. 

coxreg2 <- coxph(SurvObj ~ strata(age) + sex, data =  lung)

> coxreg2$coefficients
     sex 
-0.64471 

> vcov(coxreg2)
          sex
sex 0.0449369

Thanks for the help!

jeanphikri
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  • As I read material about "age advancement periods" it appears that age (possibly represented as a functional other than the identity function) and a target exposure risks must be estimated jointly in a statistical model. Using `strata` prevents such an estimate, so your question is basically answered by saying "don't do that". The `survival::coxph`-function supports the use of a `tt` argument where age is represented as as a functional whose coefficient would be reported. We would need to see data to support a proper choice of the functional representation of age. – IRTFM Aug 27 '17 at 14:14
  • Or if you need a worked example to follow, perhaps you can present the data used in this article in a form that R users might assimilate. This article appears to be extremely similar to the one cited above : http://www.sascommunity.org/seugi/SEUGI1994/Point%20and%20Interval%20Estimation%20of%20Risk%20and%20Rate%20Advancement%20Periods%20in%20Epidemiologic%20Studies%20Using%20SAS%20Software.pdf – IRTFM Aug 27 '17 at 16:03
  • Nevermind. That second paper just has a macro with no demonstration of its use. – IRTFM Aug 27 '17 at 16:13

1 Answers1

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When you use a variable for stratification you don't get any coefficient estimate for it. Instead separate baseline hazards are estimated for the different age groups. The essence of a stratified cox regression is to fit a model that has a different baseline hazard in each stratum.

sjakw
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  • Thanks for the explanation. So, with `strata`, I have different baseline hazards h for each age group and only one coefficient B for sex. That makes sense. However, I see articles in which rate advancement periods (RAPs) were calculated on age-stratified Cox regressions, although RAPs calculation is supposed to be B[exposure] / B[age]. Any idea how this is possible? – jeanphikri Aug 25 '17 at 15:52
  • Perhaps you should cite such articles. It's possible you mis-understood the methods or it's also possible the authors and reviewers didn't know what they were doing. I'm looking at : https://academic.oup.com/ije/article-lookup/doi/10.1093/ije/dyv320 where it's pointed out that many misinterpretations of this notion are present in hte published literature. – IRTFM Aug 27 '17 at 14:20