This data set is from the Duke University Cardiovascular Disease Databank and consists of 2258 patients and 6 variables. The patients were referred to Duke University Medical Center for chest pain. The variables included in the data set acath2.csv are the following:
- sex: sex of the patient (0=male, 1=female)
- age: age of the patient
- cad.dur: duration of symptoms of coronary artery disease
- cholest: cholesterol (in mg)
- sigdz: significant coronary disease by cardiac catheterization (definied as ≥ 75$ diameter narrowing in
at least one important coronry artery – 1 = yes, 0 = no)
- tvdm: severe coronary disease (definied as three vessel or left main disease by cardiac catheterization –
1 = yes, 0 = no))
- (a) [3 points] In R create a new vector that dichotomizes cholest into high and low, where the cutoff is the median of cholest. Calculate the odds ratio for significant coronary disease based on high/low cholesterol. Interpret the odds ratio.
- (b) [3 points] Do the same as part (a), but use severe coronary disease instead of significant coronary disease.
- (c) [2 points] Do you think you could estimate the risk ratio for significant or severe coronary disease in this example? If yes, then estimate the risk ratios for the relationships investigated in part (a) and (b). If not, say why. In either case justify your answer.
Question 2
Use the same data set as in Question 1. Run a linear regression model to investigate the joint effect of age and sex on cholesterol (mg).
(a) [3 points] Write out the fitted regression model based on the R output. Interpret all the estimated β parameters in the model.
(b) [2 points] Calculate and report 95% confidence intervals for the coefficients of age and sex. Interpret. (c) [2 points] Predict the cholesterol of a 50-year-old female.
(d) [2 points] Predict the cholesterol of a 10-year-old male. Are you less confident in this prediction than the one you made in part (c)? Why?
