Week 8
Problems—30 points

15 points each.
Place answers within the Word document below.

1. A
study is conducted to estimate survival in patients following kidney
transplant. Key factors that adversely affect success of the transplant include
advanced age and diabetes. This study involves 25
participants who are 65 years of age and older and all have diabetes. Following
transplant, each participant is followed for up to 10 years. The following are
times to death, in years, or the time to last contact (at which time the participant
was known to be alive).

Deaths: 1.2, 2.5, 4.3, 5.6, 6.7, 7.3 and 8.1 years

Alive: 3.4, 4.1, 4.2, 5.7, 5.9, 6.3, 6.4, 6.5,
7.3, 8.2, 8.6, 8.9, 9.4, 9.5, 10, 10, 10, and 10 years

Use the life
table approach to estimate the survival function. Use years intervals of

0–2;
2–4;

Complete
the table below.

Use the
Kaplan-Meier approach to estimate the survival function.

Referring
to the graph above:

What is the probability
of surviving 6.5 years?

A.
None 0.70

B.
0.85

C.
0.60

D.
0.90

Patients have an
85% chance of surviving how many years?

A.
6.0

B.
4.25

C.
3.2

D.
5.5

2. A clinical trial is conducted to
evaluate the efficacy of a new drug for prevention of hypertension in patients
with pre-hypertension (defined as systolic blood pressure between 120–139 mmHg
or diastolic blood pressure between 80–89 mmHg). A total of 20 patients are
randomized to receive the new drug or a currently available drug for treatment
of high blood pressure. Participants are followed for up to 12 months, and time
to progression to hypertension is measured. The experiences of participants in
each arm of the trial are shown below.

New Drug		Currently Available Drug
Hypertension	Free of Hypertension		Hypertension	Free of Hypertension
7	8		6	8
8	8		7	9
10	8		9	11
	9		10	11
	11		11	12
	12
	12

Estimate the
survival (time to progression to hypertension) functions for each treatment
group using the Kaplan-Meier approach.

New Drug

Complete the
table below.

Time, Months	Number at Risk Nt
0	10
7	10
8	9
9	5
10	4
11	3
12	2

Complete the
table below.

Time, Weeks	Number at Risk Nt
0	10
6	10
7	9
8	8
9	7
10	5
11	4
12	1

To
answer the question as to whether or not there is a difference in time to
progression, a Chi square statistic is computed. The critical value for
rejection of the null hypothesis is 3.84. The computed Chi square is 0.335.

Based
on comparing the computed Chi square and the critical Chi square, which of the
following is (are) true?

A.
There
is not statistically significant evidence to show that thetime to progression is different between groups.

B.
There
is statistically significant evidence to show that thetime to progression is different between groups.

C.
The time to progression is
essentially the same for each group.

D.
a and c.

The hazard ratio
risk of progression to hypertension is 0.658. Based on this computation, which
of the following is (are) true?

A. The risk of
progression to hypertension is reduced by 34.2% in patients assigned to the new
drug as compared to the currently available drug.

B.
The risk of progression to
hypertension is 1.52 times higher in patient’s current drug as compared to the
new drug.

C.
The risk of progression to
hypertension is 5.12 times higher in patient’s current drug as compared to the
new drug

D.
A and B

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