Methods for parameter-driven and wait time models

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My research is largely motivated by medical applications, and involves three broad areas of statistics: designs for multiple sclerosis (MS) clinical trials, models for time series and longitudinal data, and wait time models. In particular, magnetic resonance imaging (MRI) is an increasingly popular tool for measuring outcomes in MS clinical trials, but little research exists on the number of patients, number of scans per patient, and frequency of scanning required to detect the treatment effect of interest. Such information is critical given the high cost of MRI scans and the ethical issues surrounding the recruitment of patients to these trials. In addition, I am investigating a large, flexible class of models for data that are collected over time on one or more patients: parameter-driven models (PDMs). Characterizing such data is especially difficult if the response is a count or is binary. PDMs encompass several popular models, which can allow us to apply theory developed for one model to others in this class. I am investigating whether simple estimation methods for one such model (the hidden Markov model) can be used to obtain approximate estimators of more complex PDMs. Finally, I am interested in the analysis of survival and wait time data. I am proposing two different projects in this field. The first involves the modelling of wait times for hip, knee, and cataract surgery in British Columbia, with the goal of developing an optimal scheduling policy. These data are challenging to describe due to non-random sampling of patients appearing on the wait list and non-random drop-offs from this list. The second concerns the estimation of the effects of predictor variables when survival times are discrete and the sample size is small.