Multidimensional penalized splines for survival models: illustration for net survival trend analyses

In descriptive epidemiology, there are strong similarities between incidence and survival analyses. Because of the success of multidimensional penalized splines (MPSs) in incidence analysis, we propose in this pedagogical paper to show that MPSs are also very suitable for survival or net survival studies.

The use of MPSs is illustrated in cancer epidemiology in the context of survival trends studies that require specific statistical modelling. We focus on two examples (cervical and colon cancers) using survival data from the French cancer registries (cases 1990-2015). The dynamic of the excess mortality hazard according to time since diagnosis was modelled using an MPS of time since diagnosis, age at diagnosis and year of diagnosis. Multidimensional splines bring the flexibility necessary to capture any trend patterns while penalization ensures selecting only the complexities necessary to describe the data.

For cervical cancer, the dynamic of the excess mortality hazard changed with the year of diagnosis in opposite ways according to age: this led to a net survival that improved in young women and worsened in older women. For colon cancer, regardless of age, excess mortality decreases with the year of diagnosis but this only concerns mortality at the start of follow-up.

MPSs make it possible to describe the dynamic of the mortality hazard and how this dynamic changes with the year of diagnosis, or more generally with any covariates of interest: this gives essential epidemiological insights for interpreting results. We use the R package survPen to do this type of analysis.