Question

Data from a study investigating the relationship between smoking and aortic stenosis, a narrowing or stricture of the aorta that impedes the flow of blood to the body are available below. It is known that gender is associated with both of these variables and it is suspected that it might influence the observed relationship between them. Smoking status is saved under the variable name SMOKE, the presence of aortic stenosis under the name DISEASE, and gender under the name SEX. Data set is below.

a. Using the presence of aortic stenosis as the response, fit a logistic regression model with smoking status as the single explanatory variable. Interpret the estimated coefficients of smoking status.

b. What are the estimated odds of suffering from aortic stenosis for individuals who smoke relative to those who do not?

c. Construct a 95% confidence interval for the population odds ratio. Does this interval contain the value 1? What does this tell you?

d. Add the explanatory variable gender to the model that already contains smoking status. What is the odds ratio for aortic stenosis for smokers versus nonsmokers, adjusting for gender?

e. Construct a 95% confidence interval for the population odds ratio that adjusts for gender. What do you conclude?

f. Do you believe that the relationship between the presence of aortic stenosis and smoking status differs for males and females? Explain.

Data set stenosis Variables: smoke disease and sex (this dataset consists of many repeated observations; rather than list them all, we summarize the outcomes.)

37 yes and yes and male

24 yes and no and male

25 no and yes and male

20 no and no and male

14 yes and yes and female

19 yes and no and female

29 no and yes and female

47 no and no and female

Please answer question f, e, d, c showing all work.

If you would also list the STATA commands that could be used to solve this problem, that would be awesome. Thank you

Answer 1

(c) For the total population two individual (male, female ) data are summed and the results are as shown in the table below,

Aortic Atenosis	Smoker
	Yes	No
Yes	51	54
No	43	67

The estimated odds ratio(OR) of suffering from aortic stenosis for individuals who smoke relative to those who do not, for population

=(51×67)/(43×54) = 1.47

From the odd ratio the 95% CI formula is given by

e^{(log(OR)±[1.96×SE(log(OR))])}

So, 95% CI for the population odd ratio =(0.86, 2.53)

(d) The odds ratio for aortic stenosis for smokers versus nonsmokers with gender adjustment = 2.2

(e) The 95% confidence interval for the population odds ratio that adjusts for gender = (1.17, 3.61)

From the calculated CI we can conclude that for aortic stenosis gender is a significant predictor.

(f) Yes the relationship between the presence of aortic stenosis and smoking status differs for males and females, because the gender adjusted odd ratio is statistically different from 1.