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.

Interval in Years	Number At Risk During Interval, Nt	Average Number At Risk During Interval, Nt* =Nt-Ct /2	Number of Deaths During Interval, Dt	Lost to Follow-Up, Ct	Proportion Dying qt = Dt/Nt*	Proportion Surviving pt = 1-qt	Survival Probability St = pt*St-1
0–2
2–4
4–6
6–8
8–10

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

Complete the table below

Time, Years	Number at Risk Nt	Number of Deaths Dt	Number Censored Ct	Survival Probability St+1= St*((Nt-Dt)/Nt)
0	25
1.2
2.5
3.4
4.1
4.2
4.3
5.6
5.7
5.9
6.3
6.4
6.5
6.7
7.3
8.1
8.2
8.6
8.9
9.4
9.5
10.0

Referring
to the graph above:

What is the probability of surviving 6.5
years?

A. None

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	Number of Events (Hypertension) Dt	Number Censored Ct	Survival Probability St+1= St*((Nt-Dt)/Nt)
0	10
7
8
9
10
11
12

Currently Available Drug

Complete the table below.

Time, Weeks	Number at Risk Nt	Number of Events (Hypertension) Dt	Number Censored Ct	Survival Probability St+1= St*((Nt-Dt)/Nt)
0	10
6
7
8
9
10
11
12

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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