Smooth Transformation Models for Survival Analysis: A Tutorial Using R

Over the last five decades, we have seen strong methodological advances in survival analysis, mainly in two separate strands: One strand is based on a parametric approach that assumes some response distribution. More prominent, however, is the strand of flexible methods which rely mainly on non-/semi-parametric estimation. As the methodological landscape continues to evolve, the task of navigating through the multitude of methods and identifying corresponding available software resources is becoming increasingly difficult. This task becomes particularly challenging in more complex scenarios, such as when dealing with interval-censored or clustered survival data, non-proportionality, or dependent censoring. In this tutorial, we explore the potential of using smooth transformation models for survival analysis in the R system for statistical computing. These models provide a unified maximum likelihood framework that covers a range of survival models, including well-established ones such as the Weibull model and a fully parameterised version of the famous Cox proportional hazards model, as well as extensions to more complex scenarios. We explore smooth transformation models for non-proportional/crossing hazards, dependent censoring, clustered observations and extensions towards personalised medicine within this framework. By fitting these models to survival data from a two-arm randomised controlled trial on rectal cancer therapy, we demonstrate how survival analysis tasks can be seamlessly navigated within the smooth transformation model framework in R. This is achieved by the implementation provided by the "tram" package and few related packages.