In this paper, we propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. One key technical challenge for directly applying maximum likelihood estimation (MLE) to censored data is that evaluating the objective function and its gradients with respect to model parameters requires the calculation of integrals. To address this challenge, we recognize that the MLE for censored data can be viewed as a differential-equation constrained optimization problem, a novel perspective. Following this connection, we model the distribution of event time through an ordinary differential equation and utilize efficient ODE solvers and adjoint sensitivity analysis to numerically evaluate the likelihood and the gradients. Using this approach, we are able to 1) provide a broad family of continuous-time survival distributions without strong structural assumptions, 2) obtain powerful feature representations using neural networks, and 3) allow efficient estimation of the model in large-scale applications using stochastic gradient descent. Through both simulation studies and real-world data examples, we demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models. The implementation of the proposed SODEN approach has been made publicly available at https://github.com/jiaqima/SODEN.
翻译:在本文中,我们提出了一个使用神经网络和可缩放优化算法进行生存分析的灵活模式; 直接将最大可能性估计(MLE)应用于受审查数据的一个关键技术挑战是,在模型参数方面评估客观功能及其梯度需要计算整体体。为了应对这一挑战,我们认识到,对受审查数据进行的最低限量分析可被视为差异-等分限制优化问题,这是一个新视角。根据这一联系,我们通过普通差异方程式对事件时间的分配进行模拟,并利用高效的 ODE 解答器和联合敏感性分析对可能性和梯度进行数字评估。我们使用这一方法,能够(1) 提供一个广泛的大家庭,在没有强有力的结构假设的情况下,连续时间持续生存分布;(2) 利用神经网络获得强大的特征说明;(3) 利用随机偏差梯度下降对大规模应用中的模型进行有效估计。我们通过模拟研究和现实世界数据实例,展示了拟议方法与现有状态的深层次学习生存分析模型相比较的有效性。我们能够提供拟议的SDEN方法的实施情况,已经在 https://SOIAM/imaq. 上公开提供。