UMDNJ School Of Public Health

Piscataway/New Brunswick Campus

Applied Categorical Data Analysis

Spring 2007

3 Credits

SPH, Room 2A, Wednesdays, 6:10-9:00 p.m.

Course Information

Instructor: Pamela Ohman Strickland, Ph.D.

Division of Biometrics, UMDNJ-SPH

School of Public Health, Room 218, 732-235-9721

ohmanpa@umdnj.edu

TA: Susan Huyck, PhD candidate in Biostatistics

Textbooks

Required:	Agresti, A. (1996) An Introduction to Categorical Data Analysis. John Wiley & Sons.
Highly Recommended:	Stokes, M.E., Davis, C.S. and Koch, G.G. Categorical Data Analysis Using the SAS System, 2^nd Edition. SAS Publishing

Prerequisites: Introduction to Biostatistics, Biostatistics Computing, Regression Methods for Public Health Studies

Course Description

Public health studies, especially those involving questionnaires, contain large amounts of categorical data. This class provides an introduction to descriptive and inferential statistics for univariate and multivariate categorical data with applications to epidemiological and clinical studies. For 2 and 3-way contingency tables, measures of association and tests for homogeneity between populations and independence of variables are presented. Related tests of trend for ordinal data are studied. Loglinear and logistic regression analyses are investigated for data sets with both nominal and ordinal variables.

Computing Language: SAS

Course Objectives

By the end of this course, students will be able to:

1. Formulate appropriate statistical hypotheses for examining cross-classified data from public health and clinical studies

2. Justify the basic theoretical models for categorical data

3. Create and/or actively participate in the design and analysis plan for a study involving categorical data, whether nominal or ordinal in nature

4. Conduct and/or actively participate in the analysis of categorical data

5. Interpret results from contingency tables or generalized linear models that evaluate relationships between categorical variables

Outline

January 17	Introduction, Distributions and Sampling Examples to be Used in the Course of the Semester, Definitions Poisson, Binomial and Multinomial Distributions Inference about univariate proportions
January 24	Two-way Contingency Tables Probability Structures for 2-way tables, Chi-square tests of independence Comparing proportions, risk ratios and odds ratios
January 30	Two-way Contingency Tables with Ordinal Data Continuous or Categorical? Testing independence for ordinal data Measures of Association for ordinal data
February 7	Analyses for Matched Pairs of Categorical Data Defining the hypothesis of interest, Testing independence Three-way Tables Justification for studying three-way relationships, partial association, Cochran-Mantel-Haenszel Methods, Common odds ratios
February 14	Generalized Linear Models Components of a generalized linear model, linear regression, models for binary data and Poisson regression Models for count and rate data, model inference and model fitting
February 21	Logistic Regression Interpreting the logistic regression model, inference for logistic regression, model checking, logit models with qualitative and/or ordinal predictors, multiple logistic regression Project Plan due.
February 28	Logistic Regression, Continued
March 7	Mid-term
March 21	Multi-category Logit Models Logit Models for Nominal Responses, cumulative logit models for ordinal responses, paired-category logits for ordinal responses
March 28	Loglinear Models for Contingency Tables Loglinear models for two- and three-way tables, inference for loglinear models, loglinear models for higher dimensions, the loglinear-logit connection
April 4	Building and Applying Logit and Loglinear Models Association graphs and collapsibility, modeling ordinal associations, tests of conditional independence, effects of sparse data
April 11	Models for Matched Pairs Comparing dependent proportions, logistic regression for matched pairs, symmetry and quasi-symmetry models for square tables, comparing marginal distributions, analyzing rater agreement
April 18	Conditional Logistic Regression (Final Project Reports Due)
April 25	Final Exam
May 1	Revised Final Report Due

Evaluation

1. Homework 25%

2. Class Attendance and Participation 5%

3. Exams 45%

4. Final Project Write-Up 15%

5. Peer Review of Final Project 10%

Homework policies

1. All homework must be turned in at the beginning of the class period on the day on which they are due.
2. On all homework assignments/problem sets, students are encouraged to discuss with one another, but work should be carried out and written up independently. If any two identical write-ups are found, both homework assignments will be given a grade of zero.
3. The homework assignments will involve computer work using SAS. Relevant portions (only) of the output should be cut and pasted into the homework assignment at the appropriate spot, not attached at the end. Failure to comply will result in a reduction of 50% of points for that homework.

Exam policies

Exams will be given on March 7^th and April 25^th. Any unexcused absences for these exams will result in a grade of zero for that exam.

Final Project

There are two options for the final project.

1) Data Analysis

Complete a full analysis of a set of data that contains an ordinal or multinomial response and at least one ordinal covariate. This data set may not be one that you are using for a fieldwork project or dissertation. Present two alternative analyses, one of which must be a generalized linear model. Compare and contrast the two approaches.

2) Report on a Statistical Paper

Report on a statistical paper addressing the analysis of categorical or ordinal data.

1. Describe the problem it addresses
2. Give an original example of data to which the methods would apply
3. Summarize the solution proposed along with advantages and disadvantages of the solution
4. Formulate two or three application or research questions propagated by the research paper. (Try to be as original as possible.)

The emphasis in these final projects should be on the statistical methodology and how it is applied. A “Project Plan” will be due on February 21^st along with any regular homework assignment. The final project report is due on April 18^th. After a feedback and peer review, a revised final report may be submitted by May 1^st.

Final Project Peer Review

Final drafts of the Paper will be due on April 18^th. Each student will be randomly assigned three other students’ papers to review. Using a template, each student will be asked to rate and comment on these three other papers. Statistical methods will be used to combine these ratings and create a final ranking of all papers. 10% of your final grade will be based on these peer reviews. (Please note that if you do not hand in your own peer reviews for other students’ papers, you will get a 0 out of this 10%. If you do not have a paper to hand out to other students for review on April 18^th, you will also get 0 out of this 10%. No exceptions will be made!)

You may use these peer reviews to revise your own paper for a final submission of the project due on May 1^st.