GLM, GLMM, GEE for Correlated Discrete Data with Over-dispersion, Zero-inflation, Measurement Error and Misspecification

我的研究的主要领域是统计程序的方法发展在生物统计学的一般领域，其中纵向或集群相关数据出现在计数，比例或生存时间的形式。例如，纵向数据出现在医学研究中，在医学研究中，随着时间的推移观察患者在医疗程序后的生存情况。在许多情况下，重复数据作为响应组出现。例如，在家庭研究中，家庭成员（母亲和她的孩子或同一家庭的兄弟姐妹）会有类似的医疗问题。因此，同一家庭成员的反应将是相关的。此类研究的一个目的是建立响应变量（疾病状态）和协变量或回归变量（患者的年龄、种族、是否存在其他疾病）之间的关系。然而，在实践中出现的数据往往有很多并发症。例如，计数数据或比例形式的数据通常显示过度分散（方差大于平均值），零通货膨胀（比数据分析的简单模型所预测的零更多）。此外，解释（回归）变量的测量误差和响应和解释变量的缺失值在许多科学领域都很普遍。这些类型的数据出现在生物学，流行病学，社会科学和工程学等不同领域。我的研究目的是为上述类型的数据开发新的，新颖的（具有最佳统计特性）和易于使用的方法。这些方法将有助于许多加拿大公司的数据分析，如加拿大制药研究公司、银行、加拿大安大略水电公司和克莱斯勒公司以及加拿大统计局等政府机构。

The main area of my research is methodological development of statistical procedures in the general area of biostatistics where longitudinal or clustered correlated data arise in the form of counts, proportions or survival times. Longitudinal data arise, for example, in medical studies, where patients are observed over time for survival after a medical procedure. Clustered data arise in many situations as groups of responses. For example, in family studies, family members (mother and her children or siblings in the same family) will have similar medical problems. So, the responses of members of the same family will be correlated. One aim in such studies is to establish the relationship between a response variable (disease status) and covariates or regression variables (age, ethnicity, presence of other disease of the patient). However, data that arise in practice often have a lot of complications. For example, count data or data in the form of proportions often show over-dispersion (variance is greater than the mean), zero-inflation (more zeros than what can be predicted by a simple model for the analysis of the data). Further, measurement error in explanatory (regression) variables and missing values in both response and explanatory variables are prevalent in many scientific fields. Data of these types arise in fields as diverse as biology, epidemiology, social science and engineering.The purpose of my research is to develop new, novel (having best statistical properties) and easy to use methodologies for data of the type described above. These methodologies will be useful for data analysis in many Canadian companies, such as Canadian pharmaceutical research firms, banks, Ontario Hydro and Chrysler Canada and government agencies, such as Statistics Canada.