Advanced Regression and Prediction Methods in Event History Data Analysis

事件风险预测在许多领域都很重要，它有助于早期预防、决策和资源规划。例如，首次缓解后白血病复发的风险预测有助于在临床症状出现之前指导治疗；保险索赔可能性的预测有助于评估成本和估计保费。 到达事件终点的时间通常作为经济学、金融学、工程学、医学、社会科学和环境科学的结果来研究，例如癌症复发的时间、产品失败的时间、发起汽车保险索赔的时间等。与事件结束时间相关的风险因素的纵向数据创建了一个动态的数据环境，其中预后信息随着时间的推移而更新，以适应不断变化的风险集。例如，在长期的疾病管理中，患者经常被反复的门诊随访，在那里进行医生评估和实验室测试，并收集数据。这种随时间变化的信息提供了与疾病活动、治疗反应和其他临床病史相关的个体特征，这些特征可能会随着时间的推移而显著变化，从而促进动态预后模型的发展。 在这一应用中，我将讨论利用纵向预测变量对事件风险进行动态预测，并提出相应的统计方法。使用纵向生物标记物预测临床事件的风险(例如，疾病复发、进展到终末期)将被用作说明。实践中出现的众所周知的挑战是由于患者不遵守预定的就诊时间而导致的纵向生物标记物的间歇性测量、多个标记物的不同步测量方案、疾病进展期间的多状态转换等。我的最终目标是开发新的统计方法来解决多样化和复杂的真实数据问题，并实现对单个事件风险的良好预测。与此同时，将寻求广泛的合作网络，将拟议的方法应用于现实生活中的各个领域。 研究计划中提出了具体的研究目标作为短期目标。笔者提出的方法跨越生存数据分析、纵向数据分析、功能数据分析等。预后模型主要通过界标或联合建模来构建。非常需要计算高效且易于实现的方法，以便处理日益庞大和复杂的数据集，这些数据集可能包括电子健康记录、基因组数据、成像数据、基于互联网的数据源、以及由数字监控设备提供的数据。 虽然在本提案中重点讨论了临床事件，但所解决的问题在自然科学和工程中的许多领域都存在，所提出的方法适用于各种实际问题。

Event risk prediction is important in many fields, which facilitates early prevention, decision making and resource planning. For example, risk prediction of the relapse of leukemia after first remission is helpful to guide treatment before clinical symptoms appear; prediction of the likelihood of insurance claims can aid assessing cost and estimating premium. Time to an event endpoint is often studied as the outcome in economics, finance, engineering, medical science, social science and environmental science, e.g. time to cancer relapse, time to the failure of a product, time to the initiation of an auto insurance claim, etc. Longitudinal data on risk factors associated with time-to-event outcomes create a dynamic data environment in which prognostic information is updated over time with adapting to the changing risk sets. For example, in long-term disease management, patients are often followed up by recurrent clinic visits where physician evaluation and lab tests are performed and data are collected. This time-varying information provides individual characteristics related to disease activity, responses to therapies, and other clinical history that could notably change over time, and thus promotes the development of dynamic prognostic models. In this application, I will discuss the dynamic prediction of event risks by using longitudinal predictor variables and propose statistical methodologies accordingly. Prediction of the risk of a clinical event (e.g. disease relapse, progression to end stage) using longitudinal biomarkers will be used as an illustration. The well-known challenges arising from practice are intermittent measurements of longitudinal biomarkers due to patients' non-adherence to scheduled visit times, unsynchronized measurement schemes of multiple markers, multistate transition during disease progression, etc. My ultimate goal is to develop novel statistical methodologies to solve diverse and complex real data problems and accomplish well-performing prediction of individual event risks. Broad collaboration networks will be sought in the meantime to apply the proposed methods to various areas in real life. Specific research aims are proposed in the research plan as short-term goals. The methodologies I propose across survival data analysis, longitudinal data analysis, and functional data analysis, etc. Prognostic models are mainly constructed by landmarking or joint modeling. Computationally efficient and easily implementable methods are highly desirable so as to handle increasingly big and complicated data sets that may include electronic health records, genomic data, imaging data, internet-based data sources, and data provided by digital monitoring devices. Although the discussion about clinical events is focused in this proposal for illustration, the addressed problems exist in many areas in natural science and engineering and the proposed methods are applicable to a variety of practical problems.