Distributional Regression for Times to Event
There are two types of regression models for the analysis of a mean survival time. Both of them allow for the inclusion of diverse covariates in order to improve the prediction time to event. The Cox proportional hazards model as well as the Accelerated Failure Times (AFT) models comprise semiparametric predictors in order to include information from metric, spatial and categorical variables and add individual-specific random effects. Both model definitions rely on a few assumptions for an operational analysis. In particular for the AFT models we need to specify a family of distributions for the response together with a constant scaling parameter. This reduces the flexibility of the model. For current research questions, such as survival times of patients with different types of cancer, we find that a simple model that is reduced to modelling the mean does not sufficiently assess the effects of the different therapeutical options, specifically in the context of personalised medicine. Within the proposed project we aim to expand modern methods of distributional regression to the framework of time to event analyses. On the one hand, we propose the use of nonparametric methods like quantile and expectile regression including semiparametric mode regression. On the other hand, we will use generalised additive models for location, scale and shape (GAMLSS) that allow for additional predictors for each parameter in a family of distributions. Hence, we will be able to model dependencies between covariates and the time to event also at both tails of the distribution and present the potential differences. All developed models will be evaluated and applied to questions in ongoing research of project partners.