Advanced Regression and Prediction Methods in Event History Data Analysis

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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.