Inverse-Weighted Survival Games
Inverse-Weighted Survival Games
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发表时间：
2021-11
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通讯作者：
Xintian Han;Mark Goldstein;A. Puli;Thomas Wies;A. Perotte;R. Ranganath
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作者：
Xintian Han;Mark Goldstein;A. Puli;Thomas Wies;A. Perotte;R. Ranganath
通过最大似然训练的深度模型已经取得了最先进的生存分析结果。尽管有这种训练方案，但从业者在其他标准下评估模型，例如在选定的一组时间范围内的二进制分类损失，例如Brier评分（BS）和Bernoulli对数似然（BLL）。使用最大似然训练的模型可能具有较差的BS或BLL，因为最大似然并不直接优化这些标准。直接优化像BS这样的标准需要通过截尾分布进行逆加权。然而，在这些指标下估计截尾模型需要通过失效分布进行逆加权。每个模型的目标都需要另一个，但都不知道。为了解决这个难题，我们引入了逆加权生存游戏。在这些游戏中，每个模型的目标都是根据另一个模型的重新加权估计来构建的，后者在训练期间保持固定。当损失是适当的，我们表明，游戏总是有真正的失败和删失分布作为一个平稳点。这意味着游戏中的模型一旦达到正确的分布就不会离开。我们构造了一种情形，在这种情形下，这个不动点是唯一的。我们表明，这些游戏优化BS的模拟，然后将这些原则应用于真实的世界癌症和危重病人的数据。
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.