使用R中的生存包在考克斯比例风险模型中实现非线性关系

Question

I am modeling tree mortality based on tree census data. People go out at various intervals, and record whether trees lived or died. I am using the coxph function to run a cox proportional hazard model to analyze the probability of tree mortality as a function of several predictor variables. The code looks like:

 model <- coxph(S ~ x1 + x2 + x3, data = data)

However, one of my predictors, tree size, is actually expected to have a non-linear relationship with mortality probability. Specifically, trees die a lot when they are small, the probability of death goes down as they reach a 'juvenile' stage and are an intermediate size, and then the mortality probability creeps back up as trees get older and larger in size. This creates a 'inverse J shaped' pattern between mortality probability and tree size. It looks like this:

How can I incorporate this non-linear relationship into the coxph framework? If this is not possible, how else can I analyze the mortality probability in the R environment, using a JAGS model or something else?

Answer 1

Try:

library(mgcv)
fit <- gam(S ~ s(x1, bs = 'cr', k = 10) + s(x2, bs= 'cr', k = 10) +
           s(x3, bs = 'cr', k = 10), family = cox.ph(), data = data)

You can fit an additive Cox proportional hazards model , where all terms are non-linear splines. See ?cox.ph for extensive examples.

If you have not used mgcv before, you may need to look at ?gam and ?s as well. After model fitting, summary.gam() , gam.check() and predict.gam() are your friends.