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 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) 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) 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 ...

1. 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

2. Survival Probability
St= pt*St-1
0–2
2–4
4–6
6–8
8–10

3. Use the Kaplan-Meier approach to estimate the survival
function.
Complete the table below

6. 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

7. 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

8. 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

9. Ct
Survival Probability
St+1 = St*((Nt-Dt)/Nt)

10. 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)

11. 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
the time to progression is different between groups.
B. There is statistically significant evidence to show that the
time to progression is different between groups.
C. The time to progression is essentially the same for each
group.
D. a and c.

12. 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
51.
McBurger’s fast-food restaurant has a drive-through window
with a single server who takes orders from an intercom and also
is the cashier. The window operator is assisted by other
employees who prepare the orders. Customers arrive at the
ordering station prior to the drive-through window every 3.6
minutes (exponentially distributed) and the service time is 2.4
minutes (exponentially distributed). Determine the average
length of the waiting line and the waiting time. Discuss the
quality implications of your results. If you decide that the
quality of the service could be improved, indicate what things
you might do to improve quality.
65.
Patricia Zell, a dollmaker from Olney, Maryland, is interested
in the mass marketing and production of a ceramic doll of her
own design called Tiny Trisha. The initial investment required
for plant and equipment is estimated at $25,000. Labor and
material costs are approximately $10 per doll. If the dolls can
be sold for $50 each, what volume of demand is necessary for

13. the Tiny Trisha doll to break even?
66.
Although it will fulfill her lifelong dream, Patricia is not
confident that demand for her Tiny Trisha doll will exceed the
breakeven point computed in Problem 6-5. If she chooses a less
appealing site and does more of the work by hand, her initial
investment cost can be reduced to $5000, but her per-unit cost
of manufacture will rise to $15 per doll.
a. What is the breakeven point for this new process?
b. Compare this process to the process proposed in the previous
problem. For what volume of demand should Patricia choose
this process?
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