I. Course Description

This course is the second part of a two-course sequence intended for PhD students in the School of Public Health who need a rigorous approach to probability and statistics and statistical inference with applications to research in public health.

II. Course Prerequisites

This is the second course in a sequence of courses aimed towards doctoral students in Public Health and other Health Science fields other than Biostatistics. Background in matrix algebra and calculus required. The SAS software will be used extensively due to the nature of the theoretical materials.

III. Course Goals and Objectives

Upon completion of this course, the student should understand the fundamentals of generalized linear models. This means comprehending the concepts of model construction, applying these concepts to actual datasets, and implementing the appropriate model in standard statistical software. Students will learn to apply generalized linear models to continuous, discrete, ordinal, and survival outcomes as well as account for correlated data collected over time.

IV. Methods of Instruction and Work Expectations

Instruction will be by in-class lecture. The lecture notes are available in Coffman Union as a course packet. They can also be individually downloaded and printed from the class website http://www.biostat.umn.edu/~tracyb/ph7402.html. Examples and applications will come from Public Health and other Health Science fields. SAS software and the R language will be used extensively throughout the course. Students are expected to complete assigned homework and exams.

V. Course Text and Readings

Required:

--"Statistical Analysis and Data Display: An Intermediate Course with Examples in S-PLUS, R, and SAS" by Heiberger, R.M. and Holland, B.

--Lecture Notes are compiled in a course packet available at the University Bookstore in Coffman Union.

Optional (these are on reserve in the Biostat reading room and the Biomed library):

(1) "An Introduction to Generalized Linear Models" by Dobson, A.J.

(2) "Biostatistical Methods: The Assessment of relative risks", by Lachin, J.M.

(3) "Biostatistics: A Methodology for the Health Sciences", 2^nd Ed. by van Belle, G., Heagerty, P.J., Fisher, L.D., and Lumley, T.S.

(4) "Regression Methods in Biostatistics: Linear Logistic, Survival, and Repeated Measures Models", by Vittinghoff, E., Glidden, D.V., Shiboski, S.C., and McCulloch, C.E.

VI. Course Outline/Weekly Schedule

1. Introduction to general(ized) linear models - as overview for rest of course (1 week)

2. Linear regression (3 weeks)

a. Simple linear – OLS

b. Multiple regression including dummy variables (general linear model, line to ANOVA)

c. Diagnostics, model selection, heteroskedasticity, measurement error

3. Categorical and count data modeling (4 weeks)

a. Binary models - logistic regression

b. Multinomial response models - proportional odds models, generalized logistic regression (i.e. discrete choice models), diagnostics

c. Poisson regression, overdispersion, diagnostics

4. Correlated data modeling: (continuous and discrete, GEE), otherwise known as mixed effects modeling, hierarchical modeling (4 weeks)

a. clustered data (e.g. patients within clinics, clinics within health plans)

b. longitudinal data – repeated measures, lagged dependent variables, time varying covariates, autocorrelation

5. Survival models (2 weeks) - life tables, exponential, Weibull models

Homework

There will be eight homework assignments during the semester. We encourage you to work together in computing and discussing the problems. However, each student is expected to independently write up the submitted assignment using her or his own computing and giving explanations in her or his own words. All assignments will involve computing; please attach only relevant computer output to what you turn in. Some assignments may also include reading, writing, and presenting about a related journal article.

You will get 1-2 weeks to work on each homework assignment. One week assignments will be 25 points and two week assignments will be 50 points, for a maximum of 300 points possible over the semester. Late homework will lose four points per day, unless arrangements for an extension have been made with the instructor PRIOR to the due date.

Exam

There will be one midterm exam worth 150 points. A hand calculator with the ln and e functions will be needed.

Project

There will be a final project towards the end of the semester instead of a final exam. The project is worth 150 points. The project has the following structure:

Obtain a data set for analysis; using relevant background information, determine several scientific questions to be answered by the data. Carry out a full analysis that addresses these scientific questions using any appropriate modeling strategies covered in class and discuss the results. A written report is required.

More details will be handed out in April. Each student must write a <1 page project proposal (by e-mail is fine) and get approval from the instructor. We will have a few data sets available if you do not already have something you would like to work on.

VII. Evaluation and Grading

1. Homework: 50%

2. Midterm Exam: 25%

3. Final project: 25%

A letter grade will be determined from the percentage of (600 possible) points each student receives as follows:

B+ 87-89% C+ 77-79% D+ 67-69%

A 93-100% B 83-86% C 73-76% D 63-66%

A- 90-92% B- 80-82% C- 70-72% F 0-62%

For those enrolled S/N, a letter grade of C- or better must be achieved to receive an S. The University Senate has established a uniform grading policy for all letter grades: http://www1.umn.edu/usenate/usen/policies.html. If you would like to switch grading options (e.g., A/F to S/N), it must be done within the first two weeks of the semester.

Incomplete Grade

A grade of incomplete “I” shall be assigned at the discretion of the instructor when, due to extraordinary circumstances, the student was prevented from completing the work of the course on time. The assignment of an incomplete requires a written agreement between the instructor and student specifying the time and manner in which the student will complete the course requirements. In no event may any such written agreement allow a

period of longer than one year to complete the course requirements.

University of Minnesota Uniform Grading and Transcript Policy

A link to the policy can be found at onestop.umn.edu.

VIII. Other Course Information and Policies

Grade Option Change (if applicable)

For full-semester courses, students may change their grad option, if applicable, through the second week of the semester. Grade option change deadlines for other terms (i.e. summer and half-semester) can be found at onestop.umn.edu.

Course Withdrawal

Students should refer to the Refund and Drop/Add Deadlines for the particular term at onestop.umn.edu for information and deadlines for withdrawing from a course. As a courtesy, students should notify their instructor and, if applicable, advisor of their intent to withdraw.

Students wishing to withdraw from a course after the noted final deadline for a particular term must contact the School of Public Health Student Services Center at sph-ssc@umn.edu for further information

Student Conduct, Scholastic Dishonesty and Sexual Harassment Policies

Students are responsible for knowing the University of Minnesota, Board of Regents' policy on Student Conduct and Sexual Harassment found at www.umn.edu/regents/polindex.html.

Students are responsible for maintaining scholastic honesty in their work at all times. Students engaged in scholastic dishonesty will be penalized, and offenses will be reported to the Office of Student Academic Integrity (OSAI, www.osai.umn.edu).

The University’s Student Conduct Code defines scholastic dishonesty as “plagiarizing; cheating on assignments or examinations; engaging in unauthorized collaboration on academic work; taking, acquiring, or using test materials without faculty permission; submitting false or incomplete records of academic achievement; acting alone or in cooperation with another to falsify records or to obtain dishonestly grades, honors, awards, or professional endorsement; or altering, forging, or misusing a University academic record; or fabricating or falsifying of data, research procedures, or data analysis.”

Plagiarism is an important element of this policy. It is defined as the presentation of another's writing or ideas as your own. Serious, intentional plagiarism will result in a grade of "F" or "N" for the entire course. For more information on this policy and for a helpful discussion of preventing plagiarism, please consult University policies and procedures regarding academic integrity: http://writing.umn.edu/tww/plagiarism/.

Students are urged to be careful that they properly attribute and cite others' work in their own writing. For guidelines for correctly citing sources, go to http://tutorial.lib.umn.edu/ and click on “Citing Sources”.

In addition, original work is expected in this course. It is unacceptable to hand in assignments for this course for which you receive credit in another course unless by prior agreement with the instructor. Building on a line of work begun in another course or leading to a thesis, dissertation, or final project is acceptable.

If you have any questions, consult the instructor.

Disability Statement

It is University policy to provide, on a flexible and individualized basis, reasonable accommodations to students who have a documented disability (e.g., physical, learning, psychiatric, vision, hearing, or systemic) that may affect their ability to participate in course activities or to meet course requirements. Students with disabilities are encouraged to contact Disability Services to have a confidential discussion of their individual needs for accommodations. Disability Services is located in Suite180 McNamara Alumni Center, 200 Oak Street. Staff can be reached by calling 612/626-1333 (voice or TTY).