Poisson Super Learning For Survival And Competing Risks On A Discretized Time Scale
Gabriele Pittarello, Thomas Gerds, Pernille Falberg Rønn, Helene Charlotte Rytgaard
Abstract
We introduce the Poisson Super Learner, a scalable ensemble method for survival and competing risks prediction with right-censored data. The approach exploits the correspondence between the likelihood of piecewise-constant hazard models and the Poisson likelihood. After expanding the data over a chosen time partition, candidate hazard learners are trained under a common Poisson loss, and cross-validated log-hazard predictions are combined by a Poisson meta learner. The resulting ensemble is a geometric combination of candidate hazards, and can be used to estimate survival probabilities and cause-specific absolute risks. The Poisson Super Learner framework is modular and can in principle incorporate any learner that can estimate interval-specific hazards, including parametric, penalised, additive, and other machine-learning hazard models. Training targets the cause-specific hazard directly and does not require explicit modelling of the censoring distribution. For competing risks, separate cause-specific ensembles are fitted and subsequently combined to obtain individualised cumulative incidence predictions. We illustrate the approach using data from the Steno Diabetes Center collected between 2005 and 2022 to predict cardiovascular disease risk in patients with type 1 diabetes from detailed covariate information. The applied analysis is complemented by simulation studies designed to reflect key features of the data and to examine the behaviour of the method under controlled settings. All analyses were implemented using the freely available R software package poissonsuperlearner.