Generalised linear models for flexible parametric modelling of the hazard function

Abstract

Background: Parametric modelling of survival data is important and reimbursement decisions may depend on the selected distribution. Accurate predictions require sufficiently flexible models to describe adequately the temporal evolution of the hazard function. A rich class of models is available among the framework of generalised linear models (GLMs) and its extensions, but these models are rarely applied to survival data. This manuscript describes the theoretical properties of these more flexible models, and compares their performance to standard survival models in a reproducible case-study. Methods: We describe how survival data may be analysed with GLMs and its extensions: fractional polynomials, spline models, generalised additive models, generalised linear mixed (frailty) models and dynamic survival models. For each, we provide a comparison of the strengths and limitations of these approaches. For the case-study we compare within-sample t, the plausibility of extrapolations and extrapolation performance based on data-splitting. Results: Viewing standard survival models as GLMs shows that many impose a restrictive assumption of linearity. For the case-study, GLMs provided better within-sample t and more plausible extrapolations. However, they did not improve extrapolation performance. We also provide guidance to aid in choosing between the different approaches based on GLMs and its extensions. Conclusions: The use of GLMs for parametric survival analysis can out-perform standard parametric survival models, although the improvements were modest in our case-study. This approach is currently seldom used. We provide guidance on both implementing these models and choosing between them. The reproducible case-study will help to increase uptake of these models