# HW3

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```					                          Applied Statistical Methods
HSRP 734 - Summer 2008
Homework 3 (60 points total)
Due: 6/12/2008
General instructions: 1) you may discuss any and all portions of the assignment with
other members of the class. However, the homework you turn in must be your own. 2)
For problems that require a statistical package you must do your own programming and
work with SAS output. If you give SAS output, clearly indicate your answers to the
questions.

Q1. Give a reasonably detailed explanation of what Maximum Likelihood is (3 points).

*For Questions 2 & 3 use the SAS dataset: mistudy.sas7bdat
(dataset description=mistudy_notes.doc)

Q2. Fit a simple logistic regression model to these data using treatment group as a
predictor for myocardial infarction at 5 years (MI).

a. What is the form of the estimated logistic regression equation (2 points)?

1
b. What is the estimated odds ratio and 95% CI for the OR for the treatment
group effect (3 points)? Interpret the odds ratio (2 points).

c. Add gender to the logistic regression model. Is there possible evidence of
gender confounding on the treatment effects for MI (3 points)? How did
adding gender affect the predictive ability of the model (3 points)?

Q3. Fit a multiple logistic regression model for response with treatment arm, systolic
blood pressure (SBP) at baseline and gender. Use the “centered” version of SBP (which
is centered at its mean value and include this centered variable in your model.

a. What is the form of the estimated logistic regression equation (4 points)?

2
b. What is the estimated odds ratio and 95% CI for the OR for the gender effect
(3 points)? Interpret the odds ratio (2 points).

c. Give and interpret the odds ratio for baseline SBP (3 points).

d. Conduct a Likelihood ratio test and a Wald test to see if there are significant
treatment arm effects (8 points).

3
e. How did adding SBP affect the predictive ability of the model (3 points)?
Give a plot of the corresponding ROC curve which helps summarize this
graphically (1 point).

f. Does the treatment effect depend on gender (in a model with itrt, ifemale,
Csbp)? Conduct an investigation using the data in order to address this

Q4. Answer the following questions by hand (not using SAS). The fitted multiple
logistic regression model for baseline SBP and gender for a subset of the study
participants looks like:

 Pr  mi  
 1  Pr  mi    0.87  0.68* ifemale  0.03  sbp  137.2 
ln                
               

and SE ifemale  0.46 .

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a. Estimate the odds ratio and 95% CI for gender (4 points). Is there evidence of a
gender effect? (2 points).

b. Estimate the probability that a Female with baseline SBP=150 has a MI by 5
years (4 points).

c. Estimate the probability that a Male at the average SBP of the sample (137.2)
will have a MI by 5 years (4 points).

5
B. Explain what quasi-complete separation is and how you would remediate it if you had
it in a multiple logistic regression model with 3 categorical predictor variables. Include
the detailed steps you would take (Bonus up to 2 points).

6

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