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

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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.