We next turn to the issue of correlated data which has drawn a good deal of attention among the statistical community during the past 15 years. Here the notion of correlated data refers to the situation where the conventional independent assumption among observations may be violated. Examples of these kinds from real studies are provided and characterized in terms of underlying scientific objectives. Before addressing the issue of correlated data analysis, we first review methods that have been instrumental when the independent assumption is indeed valid. This includes as special cases generalized linear models, quasi-likelihood and the estimating function approaches. In so doing, we focus on the statistical reasoning that has led one approach to another and on the theoretical underpinning of each approach. Second, we discuss in detail the analysis of discrete data which are commonly observed in biomedical research. Here, examples (e.g., teratological studies) and issues considered lead naturally to the arena of correlated data analysis.

　　Finally, we discuss some recent methodological developments for analyzing correlated data. First, three modeling approaches for correlated data, all of which represent multivariate versions of generalized linear models of different flavor, are introduced and contrasted. The emphasis is on the relative merit of interpretations of regression coefficients from these three models. Second, we discuss the pros and cons of the likelihood and semi-parametric inferential procedures along with their connections. Third, we visit the topic of multivariate survival data analysis, which has lately seen considerable renewed interest. Theoretical development and applications of the pseudo-likelihood method to this topic and others will be discussed.

Throughout, a variety of data examples for which we have been directly or indirectly involved will be used for illustrations. For the sake of time, technical derivations will be kept to a minimum. Rather, we focus on the constant feedback between motivation leading to methodological developments and their theoretical justifications on an intuitive ground, whenever possible.

• Motivating examples and their characteristics
• Generalized linear models: origins and key properties
• Estimating functions: historical perspectives and theoretical underpinning
• Some recent developments in regression analysis

• Historical developments
• Analysis of teratological data: a precursor to correlated data analysis
• Retrospective sampling

• Nominal versus ordinal
• Proportional odds versus log-linear models
• Log-linear models: pros and cons

• Marginal models
• Random effects models
• Conditional models

• Likelihood inference
• Semi-parametric inference
• Connections between two approaches

• Motivating examples
• Statistical modeling for multivariate survival data
• Pseudo-likelihood: theory and applications