Smooth hazards with multiple time scales

TL;DR

This paper introduces a flexible nonparametric hazard model for time-to-event data involving multiple time scales, utilizing P-splines and efficient computation methods, with implementation in an R package.

Contribution

It develops a novel P-spline based hazard model for multiple time scales, extending proportional hazards models, and provides an efficient computational framework with software implementation.

Findings

The model effectively captures joint effects of multiple time scales.

It accommodates standard censoring and truncation schemes.

The R package facilitates practical application of the methodology.

Abstract

Hazard models are the most commonly used tool to analyse time-to-event data. If more than one time scale is relevant for the event under study, models are required that can incorporate the dependence of a hazard along two (or more) time scales. Such models should be flexible to capture the joint influence of several times scales and nonparametric smoothing techniques are obvious candidates. P-splines offer a flexible way to specify such hazard surfaces, and estimation is achieved by maximizing a penalized Poisson likelihood. Standard observations schemes, such as right-censoring and left-truncation, can be accommodated in a straightforward manner. The model can be extended to proportional hazards regression with a baseline hazard varying over two scales. Generalized linear array model (GLAM) algorithms allow efficient computations, which are implemented in a companion R-package.