Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in medical applications, making survival analysis a key endeavor in biostatistics and machine learning for healthcare, with Cox regression models being amongst the most commonly employed models. We describe a new approach for survival analysis regression models, based on learning mixtures of Cox regressions to model individual survival distributions. We propose an approximation to the Expectation Maximization algorithm for this model that does hard assignments to mixture groups to make optimization efficient. In each group assignment, we fit the hazard ratios within each group using deep neural networks, and the baseline hazard for each mixture component non-parametrically. We perform experiments on multiple real world datasets, and look at the mortality rates of patients across ethnicity and gender. We emphasize the importance of calibration in healthcare settings and demonstrate that our approach outperforms classical and modern survival analysis baselines, both in terms of discriminative performance and calibration, with large gains in performance on the minority demographics.

提出了一种基于混合 Cox 回归模型的新方法，其中硬指派混合组来进行优化，每个组分配使用深度神经网络拟合组内的风险率，并针对每个混合成分进行非参数基线风险拟合。在多个真实数据集上进行了实验，并研究了不同种族和性别的患者的死亡率。结果表明，该方法在医疗保健领域的判别性能和校准性方面都优于经典和现代生存分析，对于少数民族人群的性能优势更为明显。

深度 Cox 混合以实现生存回归