Inverse-Weighted Survival Games

TL;DR

This paper introduces Inverse-Weighted Survival Games, a novel training framework that directly optimizes survival analysis criteria like Brier score by iteratively estimating and fixing the other distribution, leading to improved model evaluation.

Contribution

It proposes a new game-theoretic approach for survival analysis that jointly estimates failure and censoring distributions without prior knowledge, ensuring convergence to true distributions.

Findings

Optimizes Brier score on simulations

Applies method to cancer and patient data

Ensures stationary points at true distributions

Abstract

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data.