Poisson Super Learning For Survival And Competing Risks On A Discretized Time Scale

Gabriele Pittarello, Thomas Gerds, Pernille Falberg Rønn, Helene Charlotte Rytgaard

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…