第二次客座系列專題演講

**Generalized Linear Models, Estimating Functions and Multivariate Extensions**

梁 賡 義 教授 主講

Professor Kung-Yee Liang, Department of Biostatistics

School of Hygiene & Public Health, The Johns Hopkins University

摘 要

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.

地點：中央研究院生物醫學科學研究所地下一樓B1C演講廳

88年7月12日 上午 8：30 - 9：00 報到登記 上午 9：00 - 9：10 開幕致詞

演講場次 日期 時間 講題 Lecture 1 88年7月12日(星期一)
09:10 – 10:30 am
The Interplay between Statistics and Biomedical Science Lecture 2
11:00 – 12:30 am
Correlated Data and Regression Analysis
Lecture 3
02:00 – 03:30 pm
Correlated Data and Regression Analysis
Lecture 4
88年7月13日(星期二)
09:00 – 10:30 am
Analysis of Binary Data
Lecture 5
11:00 – 12:30 am
Analysis of Polytomous and Count Data
Lecture 6
02:00 – 03:30 pm
Multivariate Extension I: Statistical Modeling
Lecture 7
88年7月14日(星期三)
09:00 – 10:30 am
Multivariate Extension II: Statistical Inference
Lecture 8
11:00 – 12:30 am
Multivariate Extension III: Survival Analysis
Lecture 9
02:00 – 03:30 pm
General Discussion

OUTLINES OF THE LECTURE

I. The Interplay between Statistics and Biomedical Science

- The role of statistics in biomedical research
- Some fundamental principles in statistics
- Some basic tools and (mis)-conceptions in statistics

- 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