Inferences in generalized linear longitudinal mixed models

在社会经济和生物医学研究领域有许多情况，其中在很短的时间内从大量独立家庭的成员那里重复收集二进制和计数响应以及适当的多维依赖时间的协变量。这种类型的家族-纵向二元和计数数据的分析可能并不容易，因为对其潜在的家族-纵向相关结构进行建模存在困难。此外，由于相关模型的复杂性，开发所谓的似然方法来进行适当的推断可能是不可能的，也可能是非常复杂的。最近，基于一类自相关结构，Sutradhar(2003，统计科学)，Sutradhar，Jowaheer和Sneddon(2008，《斯堪的纳维亚统计杂志》)，Sutradhar，Rao和Pandit(2008，Sankhya B，印度统计杂志)等人开发了一种统一的广义准似然(GQL)方法，用于计数和/或二进制数据的纵向和/或家族-纵向模型的推断。然而，这些GQL推论是为标准情况开发的，例如当数据完整时，它们既不包含任何异常值，也不包含任何测量误差。这一建议的主要目的是在三种非标准和高度实用的情况下发展一致和有效的推理技术：(1)家族性纵向数据可能随机缺失的情况；(2)家族性纵向设置中的协变量可能受到污染的情况；(3)家族性纵向设置中的响应或协变量可能包含测量误差的情况。因此，拟议的研究计划将显著推动在二进制和计数数据的家庭纵向设置中分析复杂但重要的社会问题的方法论发展。预计拟议的工作将对未来涉及社会经济和生物医学数据的统计研究产生重大影响，并将有利于政府统计机构、医院和/或临床研究人员以及加拿大和国外的卫生政策制定者。

There are many situations in socio-economic and biomedical research fields, among others, where binary and count responses along with suitable multi-dimensional time-dependent covariates are repeatedly collected over a small period of time, from the members of a large number of independent families. The analysis of this type of familial-longitudinal binary and count data may not be easy, because of the difficulties in modeling their underlying familial-longitudinal correlation structures. Furthermore, due to the complex nature of the correlation models, it may be either impossible or extremely complicated to develop the so-called likelihood approach for suitable inferences. Recently, based on a class of auto-correlation structures, Sutradhar (2003, Statistical Science), Sutradhar, Jowaheer and Sneddon (2008, The Scandinavian Journal of Statistics), and Sutradhar, Rao and Pandit (2008, Sankhya B, The Indian Journal of Statistics), among others, developed a unified generalized quasi-likelihood (GQL) approach for inferences in longitudinal and/or familial-longitudinal models for count and/or binary data. These GQL inferences are, however, developed for standard situations such as when the data are complete, and they neither contain any outliers, nor, any measurement errors. The main objective of this proposal is to develop consistent and efficient inference techniques under three non-standard and highly practical situations: (1) where familial-longitudinal data may be subject to missing at random; (2) where the covariates in the familial-longitudinal set up may be subject to contamination; (3) where the responses or covariates in the familial-longitudinal set up may contain measurement errors. Thus, the proposed research program will significantly advance the methodological developments for the analysis of complex but important societal problems in the familial-longitudinal set up for binary and count data. It is anticipated that the proposed work will have significant impact on future statistical research involving socio-economic and bio-medical data and will be of benefit to goverment statistical agencies, hospital and/or clinical researchers, and health ploicy makers in Canada and abroad.