Homework 5 (30 points)
STAT 305
Name(s) _______________________________
Due: Monday October 22ndby 4pm
1. A medical research team wished to evaluate a proposed test for Alzheimer’s disease. The test
was given to a random sample of 450 patients with Alzheimer’s disease and an independent
random sample of 500 patients without symptoms of the disease. The two samples were drawn
from populations of subjects who were 65 years of age or older. The results can be found in the
table below.
Positive Result
Negative Result
Total
Alzheimer’s
436
14
450
No Alzheimer’s
5
495
500
Total
441
509
950
a. Compute the sensitivity of the proposed screening test. (2 points)
b. Compute the specificity of the proposed screening test. (2 points)
c. An estimated 11.3% of the U.S. population aged 65 or older have Alzheimer’s disease.
Use this estimate to compute the positive predictive value of the proposed screening
test. (2 points)
d. An estimated 11.3% of the U.S. population aged 65 or older have Alzheimer’s disease.
Use this estimate to compute the positive negative value of the proposed screening
test. (2 points)
1
2. To investigate whether calorie intake has an effect on the incidence of chronic disease,
researchers divided 120 rhesus monkeys into two groups. Over the span of more than 10 years,
one group ate without limit and the other group consumed only 70% as many calories as the
first group. In the well-fed group, 25 animals experienced some form of chronic disease. In the
low-calorie group, only 13 animals experienced some form of chronic disease. The data from
the study are given in the table below.
Low-calorie
Well-fed
Total
Disease
13
25
38
No Disease
47
35
82
Total
60
60
120
a. Compute the risk of disease for the low-calorie group, i.e. P(Disease | Low-calorie).
(1 point)
b. Compute the risk of disease for the well-fed group, i.e. P(Disease | Well-fed). (1 point)
c. Compute the relative risk (RR) of disease for the Well-fed group compared to the lowcalorie group, i.e.
P(Disease | Well-fed)
. (1 point)
P(Disease | Low-calorie)
d. Interpret the relative risk computed in part c. (3 points)
e. Using JMP, verify the relative risk computed in part c. Paste or provide a detailed sketch
of the JMP output below. (2 points)
2
f.
Looking at the relative risk computed in part c, can it be concluded that there is a
difference/relationship/association between the risk of disease and caloric intake?
Explain. (2 points)
g. Using JMP, compute the odds ratio for this scenario. Paste or provide a detailed sketch
of the JMP output below. (2 points)
h. Interpret the odds ratio computed in part g. (3 points)
3. To study the difference in drug therapy adherence among subjects with depression who
received usual care and those who received care in a collaborative care model was the goal of a
study conducted by Finley et al. (Pharmacotherapy, 2003). The collaborative care model
emphasized the role of clinical pharmacists in providing drug therapy management and
treatment follow-up. Of the 50 subjects receiving usual care, 24 adhered to the prescribed drug
regimen, while 50 of the 75 subjects in the collaborative care model adhered to the drug
regimen.
a. Construct a 99% confidence interval for the difference in proportions. (4 points)
b. Interpret the 99% confidence interval found in part a. (3 points)
3