Case study: Fitting a penalized one-dimensional spline as random effect in coxme

A colleague recently asked me how to fit a spline with a point constraint in a Cox proportional hazards (PH) model. After realizing that his response was interval censored I found that couldn't be used, as the right censoring is specified as a 0-weight in the syntax (event as 1). I quickly looked into other ways to estimate a penalized spline from the mgcv framework, and since a penalized spline can be rewritten as a random effect I needed to find another package that could estimate mixed Cox PH models, with a Surv object describing the response (which allows for interval censoring). One package fulfilling those criteria is coxme, which also support a ridge regression shrinkage for variables, which we will see is especially well suited for estimating penalized splines in a random effect setting.

Read More