Recursive Partitioning Methods for Life History Processes

对生命史过程的分析是统计科学的一个重要方面，在许多领域都有应用，包括精算学、经济学、工程学、环境科学、管理学、医学、运筹学、公共卫生以及社会和行为科学。该领域的许多科学问题都集中在各种可能粗糙的事件时间与一组协变量之间的关系上，以进行解释和预测。这种关系通常以回归为特征。比例风险回归是生命周期数据最常用的参数（或半参数）回归。参数回归的一个主要问题是，如果模型假设不满足，统计推断可能会产生误导。递归划分方法是使用机器学习技术的强大的非参数替代方法。它们很有吸引力，因为它们不需要模型结构的说明，并且它们通常会导致具有直观解释的实际友好模型，因此它们具有很大的潜力，易于被实践者接受。现有的递归划分文献大多局限于对完全观察到的反应（分类或连续）或右截尾生存数据的分析，然而，具有多种类型数据粗化的复杂生活史数据仍有待开发。本研究计划的目的是为生命史过程提供一种新的递归划分方法的综合说明。

The analysis of life history processes is an important aspect of statistical science with applications in a wide range of fields including actuarial science, economics, engineering, environmental sciences, management, medicine, operations, public health, and social and behavioural sciences. Many scientific problems in the area focalize interests in the relationship between various possibly coarsened event times and a set of covariates for the purposes of explanation and prediction. Such relationship is conventionally characterized by regression. Proportional hazard regression is the most commonly-used parametric (or semiparametric) regression for lifetime data. One major concern for parametric regression is that statistical inference can be misleading if model assumptions are not satisfied. Recursive partitioning methods are powerful non-parametric alternatives using machine-learning techniques. They are appealing since they require no specification of the model structure and they usually lead to practically friendly models with intuitive interpretation so that they have great potential to be easily accepted by practitioners. Most existing literature of recursive partitioning is restricted to the analysis of completely observed responses (categorical or continuous) or right-censored survival data, however, complex life history data with multiple types of data coarsening remain to be developed. The objective of this research proposal is to provide a comprehensive account of novel recursive partitioning methods for life history processes. Due to the challenging nature of research topic, the research objective will be realized gradually through the following three research stages. The first stage is to better understand life history processes and study complex dependence structure in such processes. I will utilize copula-based models to formulate dependence structure and consider robust inference for marginal analysis to reduce the effect of misspecification of marginal models to the joint analysis of life history processes. The second stage concerns recursive partitioning for various types of coarsened lifetime data including right-censoring and interval-censoring. In the third stage, the recursive partitioning methods will be extended to life history data based on methodologies and algorithms developed in the first two stages. The proposed research is expected to significantly contribute to the study of life history processes and benefit many scientific fields in Canada which deal with life history data and have need to identify risk groups and make prediction. This program will provide excellent training opportunities for graduate students at both the master’s and doctoral level in the fields of stochastic dependence modelling, asymptotic methods, robust inference and computational methods.