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 mgcv::cox.ph 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.

You need a gam object created with mgcv::gam(method = “REML”) in R. This procedure is the same that is implemented in Gavin Simpson’s package gratia, available from CRAN.