While many survival models have been invented, the Cox model and the proportional odds model are among the most popular ones. Both models are special cases of the linear transformation model. The linear transformation model typically assumes a linear function on covariates, which may not reflect the complex relationship between covariates and survival outcomes. Nonlinear functional form can also be specified in the linear transformation model. Nonetheless, the underlying functional form is unknown and mis-specifying it leads to biased estimates and reduced prediction accuracy of the model. To address this issue, we develop a neural-network transformation model. Similar to neural networks, the neural-network transformation model uses its hierarchical structure to learn complex features from simpler ones and is capable of approximating the underlying functional form of covariates. It also inherits advantages from the linear transformation model, making it applicable to both time-to-event analyses and recurrent event analyses. Simulations demonstrate that the neural-network transformation model outperforms the linear transformation model in terms of estimation and prediction accuracy when the covariate effects are nonlinear. The advantage of the new model over the linear transformation model is also illustrated via two real applications.

中文翻译：

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用于计数过程的神经网络转换模型

虽然已经发明了许多生存模型，但 Cox 模型和比例优势模型是最受欢迎的模型之一。这两种模型都是线性变换模型的特例。线性变换模型通常假设协变量为线性函数，这可能无法反映协变量与生存结果之间的复杂关系。非线性函数形式也可以在线性变换模型中指定。尽管如此，潜在的函数形式是未知的，并且错误地指定它会导致有偏差的估计和模型的预测准确性降低。为了解决这个问题，我们开发了一个神经网络转换模型。类似于神经网络，神经网络转换模型使用其层次结构从简单的特征中学习复杂的特征，并且能够逼近协变量的底层函数形式。它还继承了线性变换模型的优点，使其适用于时间到事件分析和重复事件分析。仿真表明，当协变量效应为非线性时，神经网络变换模型在估计和预测精度方面优于线性变换模型。新模型相对于线性变换模型的优势也通过两个实际应用来说明。仿真表明，当协变量效应为非线性时，神经网络变换模型在估计和预测精度方面优于线性变换模型。新模型相对于线性变换模型的优势也通过两个实际应用来说明。仿真表明，当协变量效应为非线性时，神经网络变换模型在估计和预测精度方面优于线性变换模型。新模型相对于线性变换模型的优势也通过两个实际应用来说明。