Statistical infernce for survival data: nonparametric methods and deep learning

在事件数据截短时间的生存分析中，研究干预与其他潜在协变量之间的相互作用是很重要的。我的研究计划是通过非参数方法和深度学习神经网络对生物标志物的生存数据进行统计推断。加速失效时间模型（AFT模型）是广泛使用的Cox比例风险模型的一个有吸引力的替代方案，因为它直接模拟了生存时间，并提供了简单的解释。我将考虑使用现代深度学习技术的非参数和非线性AFT模型。采用多层前馈神经网络对非线性协变量效应进行建模。期望最大化（EM）算法和秩回归可以用于非参数处理截尾生存时间。我将进一步研究所提出的深度学习AFT模型的渐近性质，并为这种新方法提供理论证明。生物标志物阈值模型广泛用于确定连续生物标志物的最佳切割点，通常使用指标函数进行二分类。二分类的缺点是信息丢失和不可微的似然函数。我将研究使用分段线性函数组合的生物标志物阈值模型的替代方法。该连续阈值模型具有生物合理性和计算效率高的优点。我将研究生物标志物阈值参数和回归系数的一致性和渐近分布。该方法可以扩展到处理多个生物标志物变量。提出了许多不同的测量方法来研究治疗效益的时间与事件数据。例如，在Cox模型中，风险比量化了相对收益，而受限平均生存时间比较了生存时间的期望值。这些治疗效果可能随着生物标志物的不同值而变化。通过非参数技术，治疗-生物标志物相互作用效应可以建模为生物标志物的灵活函数，而无需预先指定形式。我将开发非参数方法，基于不同治疗测量设置下生物标志物依赖效应的渐近分布，构建生物标志物-治疗相互作用的同时置信带。本研究将提出新的统计方法和理论来处理生存数据的非参数模型，并为HQP培训提供许多机会。这些方法可以减少估计的偏差，提高统计模型的效率，解决复杂数据结构的计算挑战。从拟议的研究中开发的软件将有利于加拿大的统计科学、工程和可靠性研究以及生物医学研究界。

In survival analysis of censored time to event data, it is important to study the interaction between intervention and other potential covariates. My research plan for this discovery grant is to conduct statistical inference for survival data with biomarkers by nonparametric methods and deep learning neural network. Accelerated failure time model (AFT model) is an appealing alternative to the widely used Cox proportional hazards model because it directly models the survival time and provides a straightforward interpretation. I will consider nonparametric and non-linear AFT models using modern deep learning techniques. A multiple layer feedforward neural network will be used to model the non-linear covariate effects. The Expectation-Maximization (EM) algorithm and rank regression can be applied to deal with censored survival time non-parametrically. I will further study the asymptotic properties of the proposed deep learning AFT model and provide a theoretical justification of this new approach. Biomarker threshold models are widely used in identifying the optimal cut point for a continuous biomarker, which is often dichotomized using an indicator function. Disadvantages of dichotomization are information lost and a non-differentiable likelihood function. I will investigate an alternative method for biomarker threshold models using combinations of piecewise linear functions. This continuous threshold model has the advantages of more biological plausibility and computational efficiency. I will study the consistency and asymptotic distribution of the biomarker threshold parameter and regression coefficients. The proposed method can be extended to deal with multiple biomarker variables. Many different measurements are proposed to study the treatment benefit for time to event data. For example, the hazard ratio quantifies relative benefits in the Cox model and the restricted mean survival time compares the expected value of survival times. These treatment effects may vary with different values of a biomarker. By non-parametric techniques, the treatment-biomarker interaction effects can be modeled as a flexible function of the biomarker without pre-specified forms. I will develop nonparametric methods to construct the simultaneous confidence bands for the biomarker-treatment interactions based on the asymptotic distributions for the biomarker-dependent effects under different treatment measurements settings. The proposed research will advance new statistical methodologies and theories to deal with non-parametric models for survival data and provide many opportunities for HQP training. These methods can reduce bias of the estimation, improve the efficiency of the statistical model and address the computational challenges for complex data structures. Software developed from the proposed research will benefit statistical science, engineering and reliability research and the biomedical research community in Canada.