Inverse-Weighted Survival Games
This addresses a practical problem for practitioners in survival analysis who need models optimized for specific evaluation metrics, though it is incremental as it builds on existing inverse-weighting methods.
The paper tackles the mismatch between training survival models via maximum likelihood and evaluating them under criteria like Brier score, which require inverse-weighting by unknown distributions. It introduces Inverse-Weighted Survival Games to jointly optimize these metrics, showing improved performance on simulations and real-world cancer and critically-ill patient data.
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.