Joint Models for Longitudinal and Time-to-Event Data

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The main focus of this proposal is to develop statistical methodologies to quantify the association between a time-dependent covariate and the time until an event of particular interest occurs. For example, investigating the reliability of a critical unit is crucial to guarantee the overall functional capabilities of a system in engineering applications. In such a study, the aim is to evaluate whether the degradation signal of the unit is significantly associated with the risk of failure of the entire system. One common problem encountered in such studies is that the time-dependent covariate (e.g., degradation signal) is often measured with error, and failure to account for such error in the analyses leads to a biased estimate of the association between the covariate and the time to the occurrence of the event. The modern approach to analyze these types of data involves two separate models: a model that takes into account the measurement error in the time-dependent covariate to estimate its true values (longitudinal model), and another model that uses these estimated values to quantify the association between this covariate and the time to the occurrence of the event (time-to-event model). The motivating idea behind the joint modeling techniques is to couple the time-to-event model with the longitudinal model. The standard approach is to consider a linear model for the time-dependent covariate (i.e., the longitudinal response) and a relative risk model for the association analysis. However, there are situations where more flexible techniques are required to appropriately model these two processes. I will emphasize three main topics which the standard approach cannot properly handle, and requires further methodological development. The first topic considers situations where the time-to-event process involves a sequence of events for which a multi-state relative risk model is required to characterize the transitions among the states/events. The second topic considers situations where the longitudinal trajectories exhibit a transition between two linear phases, so that the linearity assumption does not hold. The third topic involves two or more longitudinal binary responses for which the inherent association between them needs to be taken into account to investigate their effects on the time to the occurrence of the event. My long-term goal is to develop methods for joint modeling of longitudinal and time-to-event data. This will be pursued via three short-term objectives, each of which involves novel statistical methods appropriate for PhD students. In fact, my research aims at innovative statistical methods, which involve both theory and computation, and applications in natural sciences. The participation and training of students to help complete the objectives of this proposal is quite important. All students will be trained to get started toward a research career or inspiring employment.**