A penalised power-generalised Weibull distributional regression model

In medical applications, non-proportional hazards are often encountered, and, in these scenarios, standard survival modelling techniques are not appropriate. Such non-proportional hazards are observed, for instance, in cases where the risk of death changes during the treatment period. Distributional regression is an approach whereby covariates enter the hazard function via multiple distributional parameters (e.g., scale and shape) simultaneously and allows for varying hazard shapes to be detected. We develop the adapted power-generalised Weibull (APGW) distributional regression model, which, with three parameters (one scale, two shapes), encompasses various common survival models and hazard shapes. Variable selection is challenging in this setting (and distributional regression more generally) since covariates can enter the model in various ways. Thus, we propose the use of a computationally feasible adaptive lasso penalised estimation procedure for variable selection and explore its performance using numerical studies and real-world data application.