Mixed model estimation for discrete longitudinal and/or spatially correlated data from small areas

评估与组成更大群体的许多小群体中的每个个体相关的属性的方法进行了研究。这些小群体可以由一个较大的地理区域中的一个小地理区域来定义，或者根据一些特征（如年龄）对大群体中的个体进行分类。要考虑的属性是计数和每组中具有特定特征的个体的比例。将要调查的方法的部分动机是对不列颠哥伦比亚省各个卫生领域（小群体）的婴儿死亡率进行的一项研究，该研究记录了十年来每个领域每年的死亡人数。这些方法必须承认，数据包括对同一地区的重复观测，以及它们的地理邻近性。特别令人感兴趣的是对未来几年卫生领域死亡率的预测。拟议的方法还将适用于特定地点和时间的疾病病例（例如麻疹）数据，以期预测流行病的趋势和爆发。还将调查研究方法，其中每个小群体的属性是具有特定特征的个体的比例。重要的是，这些方法必须承认一个比例在0和1之间有界限。我过去的研究包括对一项在小学和高中进行的为期七年的预防吸烟研究的评估。目前的兴趣是考虑在特定时间点预测每个学校（小群体）吸烟者比例的方法。要做到这一点，所提出的方法必须承认，这些数据包括随着时间的推移而重复观察，而且同一所学校的学生在吸烟行为方面可能比不同学校的学生更相似。所提出的方法还将应用于癌症研究的数据，以调查促使选择手术类型的因素，以及反映儿童喘息状况的数据。最后，还将制定拟议的方法以适应缺失的数据；换句话说，对于小组的信息不完整的情况。

Approaches for assessing attributes associated with each of a number of small groups of individuals comprising a larger group are investigated.  These small groups may be defined by a small geographic area within a larger one, or by classifying individuals in the large group according to some trait such as age.  Attributes to be considered are counts and the proportion of individuals within each group possessing a particular characteristic.    The approaches to be investigated are motivated in part by a study on infant mortality rates in the various health areas (the small groups) in British Columbia, in which the annual number of deaths in each area were recorded over ten years.  These methods must acknowledge that the data consist of repeated observations on the same area, and their geographic proximity.  Of particular interest is the forecasting of mortality counts for health areas in future years.  The proposed methods will also be applied to data on disease cases (measles, for example) at a specific location and time, with a view towards forecasting trends and outbreaks of epidemics.    Methods for studies where the attribute  for each small group is a proportion of individuals that possess a particular characteristic will also be investigated.  Of importance is that the methods must acknowledge that a proportion is bounded between zero and one.  My past research has included an assessment of a seven year smoking prevention study conducted in elementary and high schools.  Of present interest is to consider methods for forecasting the proportion of smokers at each school (the small groups) at specific time points.  To do so, the proposed approaches must acknowledge that the data comprise repeated observations over time, and that students at the same school will likely be more similar regarding smoking behavior than students attending different schools.  The proposed methods will also be applied to data from a cancer study to investigate the factors that motivate the choice of surgery type, and to data reflecting wheezing status in children.    Finally, the proposed methods will also be developed to accommodate missing data; in other words, for situations where the information for the small group over time is incomplete.