Methods for parameter-driven and wait time models

我的研究主要是出于医学应用的动机，涉及三个广泛的统计领域：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）是一种越来越受欢迎的工具，用于测量MS临床试验的结果，但很少有研究存在的患者数量，每名患者的扫描次数，以及扫描频率所需的检测感兴趣的治疗效果。考虑到MRI扫描的高成本和围绕这些试验招募患者的伦理问题，这些信息至关重要。 此外，我正在研究一个大的，灵活的模型，随着时间的推移收集一个或多个患者的数据：参数驱动模型（PDM）。如果响应是计数或二进制，则表征此类数据尤其困难。PDM包括几个流行的模型，这可以让我们应用理论开发的一个模型，以其他在这类。我正在调查是否简单的估计方法，这样的一个模型（隐马尔可夫模型）可以用来获得近似估计更复杂的PDM。 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。第一个涉及到建模的等待时间髋关节，膝关节，白内障手术在不列颠哥伦比亚省，制定一个最佳的调度政策的目标。由于等待名单上出现的患者的非随机抽样和该名单上的非随机脱落，这些数据难以描述。第二个问题是当生存时间是离散的，样本量很小时，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.