The Nurses’ Health Study wanted to show that hormone replacement therapy (HRT) reduces the risk of heart attack for post-menopausal women. The investigators found out whether each woman experienced a heart attack during the study period, and her HRT usage: 6,224 subjects were on HRT and 27,034 were not. For each subject, baseline measurements were made on potential confounders: age, height, weight, cigarette smoking (yes or no), hypertension (yes or no), and high cholesterol level (yes or no).

(a) If the investigators asked you whether to use OLS or logistic regression to explain the risk of heart attack in terms of HRT usage

(yes/no) and the confounders, what would be your advice? Why?

(b) State the model explicitly. What is the design matrix X? n? p?

How will the yes/no variables be represented in the design matrix?

What is Y ? What is the response schedule?

(c) Which parameter is the crucial one?

(d) Would the investigators hope to see a positive estimate or a negative estimate for the crucial parameter? How can they determine whether the estimate is statistically significant?

(e) What are the key assumptions in the model?

(f) Why is a model needed in the first place? a response schedule?

(g) To what extent would you find the argument convincing? Discuss briefly.

Comment. Details of the study have been changed a little for purposes of this question; see chapter end notes.