Methods for parameter-driven and wait time models

我的研究在很大程度上是由医学应用推动的，涉及三个广泛的统计学领域：多发性硬化症(MS)临床试验的设计，时间序列和纵向数据的模型，以及等待时间模型。特别是，磁共振成像(MRI)是衡量MS临床试验结果的越来越流行的工具，但关于患者数量、每个患者的扫描次数以及检测感兴趣的治疗效果所需的扫描频率的研究很少。考虑到MRI扫描的高昂成本和招募患者参加这些试验的伦理问题，这些信息是至关重要的。此外，我正在研究一大类灵活的模型，这些模型是随着时间的推移收集的一个或多个患者的数据：参数驱动模型(PDMS)。如果响应是计数或二进制，则描述此类数据尤其困难。PDMS包括几个流行的模型，这可以让我们将为一个模型开发的理论应用到这门课的其他模型中。我正在研究一个这样的模型(隐马尔可夫模型)的简单估计方法是否可以用来获得更复杂的PDM的近似估计。最后，我对生存和等待时间数据的分析感兴趣。我在这个领域提出了两个不同的项目。第一个涉及不列颠哥伦比亚省髋关节、膝盖和白内障手术的等待时间的建模，目标是制定最优的调度策略。这些数据很难描述，因为出现在等待名单上的患者是非随机抽样的，从这个名单上掉下来的患者也是非随机的。第二个问题涉及生存时间离散且样本量较小时预测变量的影响的估计。

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.