It is a close book test. Read the Academic Integrity section of the syllabus.

Q1. (5 pts) True or false

No. Statement
1. T F We can use the logistic model whenever all the independent variables in the model are continuous.
2. T F The range of the logistic function lies between 0 and 1.
3. T F The logistic model describes the probability of disease development, e.g., risk for the disease, for a given set of independent variables.
4. T F The logistic model can only be applied to analyze a prospective (or follow-up) study.
5. T F In prospective (follow-up) studies, we can use a fitted logistic model to estimate a risk ratio comparing two groups whenever all the independent variables in the model are specified for both groups.

Q2. (20 pts) Bernoulli model

Following table lists the coefficients of a fitted logistic regression. The outcome is HPT (hypertension, binary \(\{0, 1\}\)).

Variable Type Coefficient
INTERCEPT -4.3200
AGE continuous 0.0274
SMK binary, \(\{0,1\}\) 0.5859
SEX binary, \(\{0,1\}\) 1.1523
CHOL cholesterol, continuous 0.0087
OCC occupation, \(\{0,1\}\) -0.5309

  1. Write down the logistic model that was fit to the data, in terms of the unknown population parameters and the predictors being considered.

  2. Write down the estimated logistic model, in terms of the fitted coefficients.

  3. Write down the estimated logistic model in logit form.

  4. Assuming the study design used was a prospective (follow-up) design, compute the estimated risk for a 40-years-old, male (SEX=1) smoker (SMK=1) with CHOL=200 and OCC=1.

  5. Again assuming a prospective (follow-up) design, compute the estimated risk for a 40-years-old, male (SEX=1) nonsmoker (SMK=0) with CHOL=200 and OCC=1.

  6. Compute and interpret the estimated risk ratio (or relative risk) that compares the risk of a 40-year-old male smoker to a 40-year-old male nonsmoker, both of whom have CHOL=200 and OCC=1.

  7. Would the risk ratio computation in the last question be appropriate if the study design had been retrospective (case-control)? Explain.

  8. Compute and interpret the estimated odds ratio for the effect of SMK controlling for AGE, SEX, CHOL and OCC.

  9. What assumption will allow us to conclude that the estimate obtained in the last question is approximately a risk ratio estimate?

  10. Compute and interpret the estimated odds ratio for the effect of OCC controlling for AGE, SMK, SEX, and CHOL.