Statistical infernce for survival data: nonparametric methods and deep learning

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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.