Models for correlated discrete data, with extension and application to small area estimation

拟议的研究方案侧重于制定和评估与组成较大群体的若干小个体群体中的每一个相关的属性的方法。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，也可以通过根据一些特征(如年龄)对大群体中的个体进行分类来定义。要考虑的属性是具有特定特征的每个小群体中的个体的数量和比例。 制定评估这些属性的方法的动机是对以下方面的研究：(1)不列颠哥伦比亚省不同保健区的婴儿死亡率，其中每个保健区的每年死亡人数记录了若干年，以及(2)多年来颗粒物对美国一些县每年哮喘住院病例的影响。对这些激励性研究感兴趣的是希望确定对未来几年婴儿死亡/哮喘住院病例数量的准确预测。制定的方法必须承认，数据包括随时间为每个卫生区/县收集的观察结果，以及它们的地理位置接近程度。将考虑其他关于疾病病例(例如麻疹)的申请，以期预测流行病的趋势和暴发。 在一项在小学和高中进行的为期七年的吸烟预防研究的激励下，还将针对属性是具有特定特征的个人的比例的情况开发方法。将制定方法来预测每所学校在特定时间点的吸烟者比例。这些方法必须承认，这些数据包括随时间的重复观察，以及同一所学校学生吸烟行为的相似性。建议的方法也将应用于癌症研究的数据，以及反映儿童喘息状况的数据。 最后，建议的方法将扩展到这样的情况，即随着时间的推移，小群体的信息可能不完整，一些数据丢失。

The proposed research program focuses on the development and assessment of methods for estimating attributes associated with each of a number of small groups of individuals comprising a larger group. 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 in each of the small groups that possess a particular characteristic. The development of approaches for the assessment of such attributes is motivated by studies on (1) infant mortality rates in various health areas in British Columbia, in which the annual number of deaths in each area are recorded over a number of years, and (2) the effect over a number of years of particulate matter on annual asthma hospitalization cases in a number of United States counties. Of interest in these motivating studies is the desire to determine accurate forecasts of the number of infant mortality/asthma hospitalization cases in future years. The methods developed must acknowledge that the data consist of observations collected over time for each health area/county, as well as their geographic proximity. Other applications on disease cases (measles, for example) will be considered, with a view towards forecasting trends and outbreaks of epidemics. Motivated by a seven year smoking prevention study conducted in elementary and high schools, methods will also be developed for the case where the attribute is a proportion of individuals that possess a particular characteristic. Approaches will be developed to forecast the proportion of smokers at each school at specific time points. These methods must acknowledge that the data comprise repeated observations over time, and the similarity in smoking behaviour of students at the same school. The proposed methods will also be applied to data from a cancer study, and to data reflecting wheezing status in children. Finally, the proposed methods will be extended to situations where information for a small group over time may be incomplete and some data are missing.