Concordance indices are widely popular metrics for assessing the ability of predictive survival models to discriminate underlying risk levels. However, these statistics have also been criticized for using only the rank orderings of the model's predicted risk scores and being insensitive to important model features, such as the addition of strong predictor variables into the model. In this paper, we address these limitations by developing smooth concordance metrics that model the underlying risk discrimination probabilities as continuous functions of the predicted risk score differences, where the shapes of these functions are estimated from the observed data. As a result, these smooth concordance metrics assess model performance across the entire range of possible risk score differences, allowing one to identify specific scenarios where the candidate model performs especially well or better than other models. Simulations show that the proposed smooth concordance metrics provide more detailed information about risk discrimination performance and are much more sensitive to the addition of meaningful predictors. We apply these methods to compare predictive survival models for cancer recurrence.

翻译：一致性指数是评估预测性生存模型区分潜在风险能力广泛使用的度量指标。然而，这些统计量因仅使用模型预测风险得分的排序次序，且对模型重要特征（如加入强预测变量）不敏感而受到批评。本文通过开发平滑一致性度量来解决这些局限性，该度量将潜在风险区分概率建模为预测风险得分差的连续函数，这些函数形状从观测数据中估计得出。因此，这些平滑一致性度量能在全部风险得分差异范围内评估模型性能，从而识别候选模型表现特别优异或优于其他模型的具体场景。模拟表明，所提出的平滑一致性度量能提供关于风险区分性能的更详细信息，且对加入有意义预测变量的敏感度显著提高。我们将这些方法应用于比较癌症复发的预测性生存模型。