Coxph predictions don't match the coefficients

Question

Good afternoon,

I could post reproducible code and certainly will if everyone agrees that something is wrong, but right now I think my question is quite simple and someo

Answer 1

The Details section in ?predict.coxph reads:

The Cox model is a relative risk model; predictions of type "linear predictor", "risk", and "terms" are all relative to the sample from which they came. By default, the reference value for each of these is the mean covariate within strata.

To illustrate what this means, we can look at a simple example. Some fake data:

test1 <- list(time=c(4,3,1,1,1), 
             status=c(1,1,1,0,0), 
             x=c(0,2,1,1,0)) 

We fit a model and view predictions:

fit <- coxph(Surv(time, status) ~ x, test1) 
predict(fit, type = "lp")
# [1] -0.6976630  1.0464945  0.1744157  0.1744157 -0.6976630

The predictions are the same as:

(test1$x - mean(test1$x)) * coef(fit)
# [1] -0.6976630  1.0464945  0.1744157  0.1744157 -0.6976630

(Using this logic and some arithmetic we can back out from your results that you have 8849 "trues" out of 9000 observations for your created_as_free_user variable.)