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I am learning the Cox model following following helpful advice from Therneau, Crowson and Atkinson. I am having some trouble interpreting the hazard ratios. In the "Using Time Dependent Covariates and Time Dependent Coefficients in the Cox Mode", a flexible fit by using nature spline was set as the time-transform functionality. I am using the Survival package version 3.4_0 and R version 4.1.0.

> vfit4 <- coxph(Surv(time, status) ~ trt + prior + karno + tt(karno),
data=veteran,
tt = function(x, t, ...) x* nsk(t, knots=c(5, 100, 200, 400),
Boundary.knots = FALSE))
>vfit4
Call:
coxph(formula = Surv(time, status) ~ trt + prior + karno + tt(karno),
data = veteran, tt = function(x, t, ...) x * nsk(t, knots = c(5,
100, 200, 400), Boundary.knots = FALSE))
          coef      exp(coef) se(coef)     z      p
trt       -0.025937 0.974397 0.191034 -0.136 0.892003
prior     -0.005787 0.994229 0.020299 -0.285 0.775556
karno     -0.059583 0.942157 0.009414 -6.329 2.46e-10
tt(karno)1 0.048253 1.049436 0.016281 2.964 0.003039
tt(karno)2 0.062323 1.064306 0.016736 3.724 0.000196
tt(karno)3 0.040798 1.041642 0.020558 1.985 0.047197
Likelihood ratio test=59.02 on 6 df, p=7.111e-11
n= 137, number of events= 128

I do not know what is the interpretation of the HR of karno.

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Nov 9, 2022 at 8:48
  • $\begingroup$ I tried reproducing your code with Survival package version 3.3_1 and R version 4.2.0 and got different results. In particular, I only got a single coefficient for tt(karno), not 3 coefficients. Please edit the question to specify what software versions you are using. $\endgroup$
    – EdM
    Commented Nov 10, 2022 at 17:39
  • $\begingroup$ @EdM Thank you for your reply. I am using the Survival package version 3.4_0 and R version 4.1.0. The code above were available in the vignette of Terry Therneau (cran.r-project.org/web/packages/survival/vignettes/timedep.pdf) (Page 23). $\endgroup$
    – Hanjew
    Commented Nov 12, 2022 at 1:51
  • $\begingroup$ Thanks. I wasn't aware that there was an update to the vignette since the last version I had downloaded. $\endgroup$
    – EdM
    Commented Nov 14, 2022 at 15:53

1 Answer 1

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The HR for karno represents what might be considered the linear part of the association between karno and outcome. In this type of model you need to interpret it together with the additional terms from the tt() function.

More precisely, the coefficient for karno is a time-independent change in log-hazard per unit change in karno, to which you add the corrections from the time-dependent tt() function to get the full association of karno with outcome.

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