Syllabus of Population Health
800
Quantitative Methods in
Population Health I
Spring
2002
Instructor: 
GuanHua
Huang, Ph.D. 

Office:
703 WARF 

Phone:
6082656176 


Teaching
assistant: 
Rosanne
Scholl 

Office: 

Phone:
6082861586 

Email:
rmscholl@students.wisc.edu 
Class
meetings: 
Lecture:
Tuesday and Thursday 10:0010:50 am at 758
WARF 

Lab:
Thursday 12:302:00 pm at 758 WARF 
Office
hours: 
Instructor:
Tuesday 4:005:00 pm 

TA:
Wednesday 3:004:00 pm 
Course
website: 
The goals of this course are to introduce
regression
analysis for continuous and discrete data, and data analyses that integrate the
methods learned in Stat 541 and PM 650 sec. 2. Topics include measures of
association, simple and multiple linear regressions, inference for regression
coefficients, confounding and interaction, regression diagnostics, logistic
regression, and conditional logistic regression.
The
course consists of lectures and laboratory sessions. The lectures are given on
Tuesday and Thursday mornings. The
lectures will primarily review and reinforce major issues. There is a laboratory
session on Thursday afternoon. The laboratory exercise will be distributed prior
to each class, and students are expected to read each lab exercise at home. Each
student will be assigned to a lab group and discuss the exercise with group
members in the lab. At the end of the lab, there will be a seminartype
discussion. Each group is required to hand in a writeup of laboratory
problems.
The
course uses the SAS software for statistical computing. Students are expected to
be familiar with the usage of the software.
Handouts
corresponding to each lecture will be available on the course website before
each class. The required textbook for this course is
Kleinbaum DG, Kupper LL,
Muller KE and Nizam A: "Applied Regression Analysis and Other Multivariable
Methods" 3rd Edition, Duxbury Press, 1998.
The
course grade will be based on homeworks (25%), writeups of lab problems (20%),
one midterm exam (25%), and one final exam (30%). The midterm exam will be held
on March 14 (12:302:00 pm), and the final exam will be during finals week. Both
exams are open book.
OUTLINE OF
MODULES
Readings refer to
Kleinbaum, Kupper, Muller and Nizam: “Applied Regression Analysis and Other
Multivariable Methods” 3rd Edition, Duxbury Press, 1998
(KKMN).
Module
0 
Revisiting
means and review of fundamentals (KKMN Chapter
3) 

Parameter
versus sample estimator Sampling
distributions and their importance Confidence
interval and pvalue Some
sampling distributions and their relationships 


Module
1 
Measures
of association with emphasis on the difference of
means 

Typical
procedure for analyzing measures of
association 


Module
2 
Basics
of linear regression analysis (KKMN Chapter 5 except
510) 

The
slope as a measure of difference in means Interpretation
of straight line Least
squares principle Variance,
inference on b_{1} Assumptions,
model checking How
assumptions influence estimators 


Module
3 
Correlation
(KKMN Chapter 6 except 63 and 67) 

Pearson
correlation Interpretation
of correlation squared Significance
tests and confidence intervals (Fisher's ztransformation)
Different
names for correlation coefficients depending on data type
Spearman
correlation Equivalence
of test for 0 correlation and ttest for 2 means (c^{2}
for 2 x 2 table) 


Module
4 
The
Analysis of Variance (ANOVA) Table (KKMN Chapter 7) 

Definition
of model and error sums of squares and mean squares Ftest
and its relationship to ttest 


Module
5 
Multiple
regression (KKMN Chapter 8 and 103) 

Interpretation
of multiple regression coefficients as "adjusted" Interpretation
of multiple regression coefficients as averages of simple regression
coefficients Concept
of statistical efficiency in estimation of multiple regression
coefficients R^{2} 


Supplement 
Direct
standardization 

Connection
to adjustment for confounding Comparison
with multiple regression Seeing
multiple regression as the statistically most efficient form of direct
standardization 


Module
6 
Testing
hypotheses in multiple regression (KKMN Chapter 9) 

ttests
and Ftests including partial Ftest 


Module
7 
Polynomial
regression (KKMN131 through 136) 

Adding
quadratic terms to model Interpretation Hierarchical
principle Significance
tests 


Module
8 
Dummy
variables (KKMN 141 through 143) 

Coding
k categories with k1 variables Interpretation
of coefficients as differences of means Testing
singly and jointly 


Module
9 
Confounding
and Interaction (KKMN Chapter 11, 144 to 149) 

Confounding,
definition, detection Understanding
how confounding arises Interaction,
definition, detection Interpreting
interaction as a regression of the slope Extracting
regression coefficients for specific levels and groups
Difference
between confounding and interaction 


Module
10 
Regression
diagnosis (KKMN Chapter 12) 

Leverage,
influence and outliers Residuals,
studentization Residual
plots Remedies
for assumption violations (transformation) 


Module
11 
Model
selection for investigation of associations (KKMN 1653 to
1654) 

Risk
factor analysis versus prediction Structuring
the variable selection 


Module
12 
Rates
and risks 

Differences
between risk and rate Confidence
intervals for risk and rate Instantaneous
rate, cumulative rate 


Module
13 
Some
properties of the odds ratio and the relative risk 

Difference
versus ratio as a measure of association Some
special properties of the odds ratio Cornfield’s
properties of the relative risk 


Module
14 
Significance
testing in 2x2 tables 

c^{2}
tests (Pearson, MantelHaenszel, continuity correction)
(Review
connection to correlation) Fisher's
exact test Review
concepts of confounding and interaction BreslowDay
test of interaction MantelHaenszel
and logit odds ratios for combined relative risk Foundation
of logit estimator as approximately efficiently weighted MantelHaenszel
stratified c^{2} 


Module
15 
Confidence
intervals for the odds ratio and the relative risk 

Logit
(=Woolf) Test
based Cornfield
Exact 


Module
16 
Introduction
to logistic regression (KKMN pages 656660) 

Transformation
to expand range of p Interpretation
of coefficients as odds ratios Solving
for the risk Assumptions 


Module
17 
Maximum
likelihood estimation (KKMN Chapter 22) 

Principal
of maximum likelihood Some
common estimators seen as maximum likelihood based Likelihood
ratio, score and Wald c^{2} Standard
errors, confidence interals Correspondence
of tests to ordinary regression 


Module
18 
Control
of confounding with logistic regression analysis (KKMN page
660) 

Comparison
of regression coefficients with and without controlling for potential
confounders Choice
of continuous confounder or indicator
variables 


Module
19 
Modeling
interaction effects with logistic regression (KKMN pages
661671) 

Constructing
interactions Testing
for interactions Obtaining
odds ratios for subgroups 


Module
20 
Logistic
regression for contingency tables 

Model
for 2x2 table Constructing
models with and without interaction Saturated
models and restrictions Options
and interpretation for dummy variables, continuous and ordinal
Comparison
with contingency table based approach 


Module
21 
Goodnessoffit
for logistic regression 

Comparing
observed and expected numbers Likelihood
ratio and Pearson c^{2} Hosmer
and Lemeshow test Residual
plots 


Module
22 
Logistic
regression of casecontrol data 

Setup
and interpretation Change
in intercept based on sampling fractions of cases and
controls 


Module
23 
Conditional
logistic regression 

Conditional
likelihood Interpretations Advantages
and disadvantages 


Final
Review 
Overview
of data analysis 


WEEKBYWEEK
OUTLINE
Homework data sets are
handed out on Thursdays. Guidelines for assignment preparation should be
followed.
Week
1 
Lecture 
Review
(Modules 0 and 1) 
Jan
22, 24 
Lab 
Lab
group assignment 

Reading 
KKMN
Chapter 3 

Assignment 
NA 



Week
2 
Lecture 
Basics
of linear regression (Module 2) 
Jan
29, 31 
Lab 
Basic
statistics 

Reading 
KKMN
Chapter 5 except 510 

Assignment 
Data
set to analyze with ttest and regression (due in 1
week) 



Week
3 
Lecture 
Correlation
(Module 3) 
Feb
5, 7 
Lab 
Simple
linear regression 

Reading 
KKMN
Chapter 6 except 63 and 6 7 

Assignment 
Data
set to analyze with correlation analysis (due in 1
week) 



Week
4 
Lecture 
The
ANOV A table, multiple regression (Modules 4 and
5) 
Feb
12, 14 
Lab 
Correlation
and linear regression 

Reading 
KKMN
Chapter 7, KKMN Chapter 8 

Assignment 
Data
set to analyze by multiple regression (due in 2
weeks) 



Week
5 Feb
19, 21 
Lecture 
Partial
Ftest (Module 6), polynomial regression (Module 7), indicator variables
(Module 8) 

Lab 
Multiple
linear regression and direct standardization 

Reading 
KKMN
Chapter 9, 131 through 136 and 141 through
143 

Assignment 
NA 



Week
6 
Lecture 
Confounding
and interaction (Module 9) 
Feb
26, 28 
Lab 
Partial
Ftest, polynomial regression and indicator
variables 

Reading 
KKMN
Chapter 11, 144 through 149 

Assignment 
Model
building (due in 2 weeks) 



Week
7 
Lecture 
Regression diagnosis (Module
10) 
Mar
5, 7 
Lab 
Interaction
and confounding 

Reading 
KKMN
Chapter 12 

Assignment 
NA 



Week
8 
Lecture 
Review 
Mar
12, 14 
Lab 
Midterm
exam 

Reading 
NA 

Assignment 
NA 



Week
9 Mar
19, 21 
Lecture 
Review
of exam, properties of relative risk and odds ratio (Module
13) 

Lab 
Model
selection 

Reading 
Supplemental
text 

Assignment 
NA 



Week
10 

Spring
break 
Mar
26, 28 





Week
11 
Lecture 
Significance
testing in 2x2 and 2xk table (Modules 12 and 14), confidence intervals for
odds ratio (Module 15) 
Apr
2, 4 
Lab 
In
class exercise on contingency tables 

Reading 
Supplemental
text 

Assignment 
Analysis
of contingency tables with SAS (due in 2
weeks) 



Week
12 Apr
9, 11 
Lecture 
Introduction
to logistic regression (Module 16), maximum likelihood estimation (Module
17) 

Lab 
In
class exercise on contingency tables and logistic
regression 

Reading 
KKMN
pages 656660, KKMN Chapter 22 

Assignment 
NA 



Week
13 Apr
16, 18 
Lecture 
Control
of confounding with logistic regression (Module 18), interaction effects
in logistic regression (Module 19) 

Lab 
In
class exercise on logistic regression 

Reading 
KKMN
pages 660671, supplemental text 

Assignment 
Analysis
of data set by logistic regression (due in 2
weeks) 



Week
14 
Lecture 
Logistic
regression for contingency tables (Module 20) 
Apr
23, 25 
Lab 
In
class exercise 

Reading 
Supplemental
text 

Assignment 
NA 



Week
15 
Lecture 
Goodness
of fit of logistic regression (Module 21) 
Apr
30, May 2 
Lab 
Model
building 

Reading 
Supplemental
text 

Assignment 
Analysis
of data set by logistic regression (due in 2 weeks) 



Week
16 
Lecture 
Logistic
regression for casecontrol studies (Module 22, 23) 
May
7, 9 
Lab 
Review 

Reading 
KKMN
2352 

Assignment 
NA 



Week
17 

In
class final exam during finals week 


