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Section 15.4 Exercises

Checkpoint 15.4.1.

This exercise deals with a comparison between Mediterranean diet and low-fat diet recommended by the American Heart Association in the context of risks for illness or death among patients that survived a heart attack
 1 
De Lorgeril, M., Salen, P., Martin, J., Monjaud, I., Boucher, P., Mamelle, N. (1998). Mediterranean Dietary pattern in a Randomized Trial. Archives of Internal Medicine, 158, 1181-1187.
. This case study is taken from the Rice Virtual Lab in Statistics. More details on this case study can be found in the case study Mediterranean Diet and Health that is presented in that site.
The subjects, 605 survivors of a heart attack, were randomly assigned follow either (1) a diet close to the β€œprudent diet step 1” of the American Heart Association (AHA) or (2) a Mediterranean-type diet consisting of more bread and cereals, more fresh fruit and vegetables, more grains, more fish, fewer delicatessen food, less meat.
The subjects’ diet and health condition were monitored over a period of four-year. Information regarding deaths, development of cancer or the development of non-fatal illnesses was collected. The information from this study is stored in the file diet.csv. The file diet.csv contains two factors: health that describes the condition of the subject, either healthy, suffering from a non-fatal illness, suffering from cancer, or dead; and the type that describes the type of diet, either Mediterranean or the diet recommended by the AHA. The file can be found on the internet at http://pluto.huji.ac.il/~msby/StatThink/Datasets/diet.csv. Answer the following questions based on the data in the file:
  1. Produce a frequency table of the two variable. Read off from the table the number of healthy subjects that are using the Mediterranean diet and the number of healthy subjects that are using the diet recommended by the AHA.
  2. Test the null hypothesis that the probability of keeping healthy following an heart attack is the same for those that use the Mediterranean diet and for those that use the diet recommended by the AHA. Use a two-sided alternative and a 5% significance level.
  3. Compute a 95% confidence interval for the difference between the two probabilities of keeping healthy.

Checkpoint 15.4.2.

Cushing’s syndrome disorder results from a tumor (adenoma) in the pituitary gland that causes the production of high levels of cortisol. The symptoms of the syndrome are the consequence of the elevated levels of this steroid hormone in the blood. The syndrome was first described by Harvey Cushing in 1932.
The file coshings.csv contains information on 27 patients that suffer from Cushing’s syndrome
 2 
The source of the data is the data file Cushings from the package MASS in R.
. The three variables in the file are tetra, pregn, and type. The factor type describes the underlying type of syndrome, coded as a, (adenoma), b (bilateral hyperplasia), c (carcinoma) or u for unknown. The variable tetra describe the level of urinary excretion rate (mg/24hr) of Tetrahydrocortisone, a type of steroid, and the variable pregn describes urinary excretion rate (mg/24hr) of Pregnanetriol, another type of steroid. The file can be found on the internet at http://pluto.huji.ac.il/~msby/StatThink/Datasets/coshings.csv. Answer the following questions based on the information in this file:
  1. Plot the histogram of the variable tetra and the mosaic plot that describes the relation between the variable type as a response and the variable tetra. What is the information that is conveyed by the second vertical triangle from the right (the third from the left) in the mosaic plot.
  2. Test the null hypothesis that there is no relation between the variable tetra as an explanatory variable and the indicator of the type being equal to b as a response. Compute a confidence interval for the parameter that describes the relation.
  3. Repeat the analysis from 2 using only the observations for which the type is known. (Hint: you may fit the model to the required subset by the inclusion of the argument subset=(type!=u) in the function that fits the model.) Which of the analysis do you think is more appropriate?