I am having trouble interpreting the output from a Cox proportion hazard model with a spline term on a continuous exposure.
In the below example (pseudo-code from
R) I see that there is a significant, non-linear relationship between circulating albumin levels and risk of death:
library(pspline) library(survival) ## create the survival object surv.death <- Surv(age_at_death , dead_or_not) ## fit survival model fit.death <- coxph(surv.death ~ pspline(albumin_baseline, df=4) + age_baseline + sex + smokes) ## get predicted values for fitted spline predicted <- predict(fit.death , type = "terms" , se.fit = TRUE , terms = 1) ## plot lines plot( albumin_baseline , exp(predicted$fit) , type="n" ) lines( sm.spline(albumin_baseline , exp(predicted$fit)) , col = "red" , lty = 1 ) lines( sm.spline(albumin_baseline , exp(predicted$fit + 1.96 * predicted$se)) , col = "orange" , lty = 2 ) lines( sm.spline(albumin_baseline , exp(predicted$fit - 1.96 * predicted$se)) , col = "orange" , lty = 2 )
I am struggling to interpret the Hazard Ratio plotted on the y-axis. I can see, of course, that the risk of death is much higher in the follow-up period if you have low albumin.
What I want to know is (for example) what the Hazard Ratio of 2 corresponding with an albumin value of 3.5g/dL is -- 2x the hazard compared to what? I am struggling with the conceptually because it is different to how one would compare a linear hazard ratio (i.e. increased hazard per unit of exposure).
Many thanks for all your inputs, and my apologies if there is a duplicate, I could not find the same question or an answer to my question in a similar topic!