Stable Survival Extrapolation via Transfer Learning

The mean survival is the key ingredient of the decision process in several applications, notably in health economic evaluations. It is defined as the area under the complete survival curve, thus necessitating extrapolation of the observed data. This may be achieved in a more stable manner by borrowing long term evidence from registry and demographic data. Such borrowing can be seen as an implicit bias-variance trade-off in unseen data. In this article we employ a Bayesian mortality model and transfer its projections in order to construct the baseline population that acts as an anchor of the survival model. We then propose extrapolation methods based on flexible parametric polyhazard models which can naturally accommodate diverse shapes, including non-proportional hazards and crossing survival curves, while typically maintaining a natural interpretation. We estimate the mean survival and related estimands in three cases, namely breast cancer, cardiac arrhythmia and advanced melanoma. Specifically, we evaluate the survival disadvantage of triple-negative breast cancer cases, the efficacy of combining immunotherapy with mRNA cancer therapeutics for melanoma treatment and the suitability of implantable cardioverter defibrilators for cardiac arrhythmia. The latter is conducted in a competing risks context illustrating how working on the cause-specific hazard alone minimizes potential instability. The results suggest that the proposed approach offers a flexible, interpretable and robust approach when survival extrapolation is required.