New methods for predictive models for univariate and multivariate longitudinal response data

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Accurate prediction of future outcomes is a common goal in many areas of science (e.g., climate, biology, medical, etc.). The goal in my research program is to develop new methods for predicting not simply binary events but instead trajectories of longitudinal outcomes, including for problems where there is more than one such outcome (i.e., multivariate longitudinal responses). These efforts will be for problems containing univariate or multivariate longitudinal responses which may be collected either sparsely or intensively, and, in the multivariate case, possibly asynchronously. Our 1st objective is to develop flexible predictive models for univariate longitudinal responses, where the basis of evaluation is improving the accuracy of predicting single response trajectories at the individual level. This is an area that has been studied using dynamical modeling, where the trajectory predictions are updated as more data over time are collected. However, there are problems for which early predictions are necessary (and there is not the luxury of waiting to continue to update predictions dynamically); we will focus on this setting here. Examples of such scenarios include potential urgent situations, such as a river possibly flooding or a heat wave impending. To help improve these early predictions of longitudinal trajectories, I propose incorporating the concept of similarity. This approach uses characteristics of former scenarios (e.g., temperature trajectories in similar climates in the past) to help inform what might happen in a given new setting, instead of considering all possible historical scenarios; essentially, a subset of strategically chosen former scenarios is used, and decisions need to be made on how to both identify and weight suitably similar scenarios to improve predictive accuracy. Part of this objective will continue with the similarity approach investigated in the more complex problem of predicting multivariate longitudinal response trajectories. For the 2nd objective, an entirely distinct context for predicting multivariate longitudinal response trajectories that are assumed driven by latent process(es) will be considered, where we will develop a hidden Markov modeling (HMM) approach; this work will build from previous work with a former trainee in modeling multivariate longitudinal data with mixed HMM's. To accomplish both objectives, we will operate under the Bayesian paradigm, which allows for a direct approach to statistical inference via predictive densities, while overcoming some difficult computational challenges, particularly for the mixed HMM approach. This research program comprises novel contributions in predictive modeling that are relevant to various disciplines, including in statistics and other areas of science (e.g., climate, biology) and could be applied in some practical urgent settings. Hence, the methods that my trainees and I will produce should be valuable for researchers in Canada and beyond.