Answer the following.   (5 pts ea) 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, N t Average Number At Risk During Interval, N t* =Nt-C t /2 Number of Deaths During Interval, D t Lost to Follow-Up, C t Proportion Dying q t = D t /N t* Proportion Surviving pt = 1-qt Survival Probability S t  = pt*S t-1 0-2 2-4 4-6 6-8 8-10 1. cont. 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 S t+1 = S t *((N t -D t )/N t ) 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 1. cont. 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. An observational cohort study is conducted to compare time to early failure in patients undergoing joint replacement surgery.  Of specific interest is whether there is a difference in time to early failure between patients who are considered obese versus those who are not.  The study is run for 40 weeks and times to early joint failure, measured in weeks, are shown below for participants classified as obese or not at the time of surgery. Obese Not Obese Failure No Failure Failure No Failure 28 39 27 37 25 41 31 36 31 37 34 39 32 35 40 38 36 36 32 29 39 41 Estimate the survival functions (time to early joint failure) for each group using the Kaplan-Meier approach. Complete the table below. Obese Time, Weeks Number at Risk Nt Number of Events (Joint Failures) Dt Number Censored Ct Survival Probability S t+1 = S t *((N t -D t )/N t ) 0 11 25 28 29 31 32 35 36 37 38 39 41 2. cont. Non-Obese Complete the table below. Time, Weeks Number at Risk Nt Number of Events (Joint Failures) Dt Number Censored Ct Survival Probability S t+1 = S t *((N t -D t )/N t ) 0 11 27 31 32 34 36 37 39 40 41 To answer t.

1. Answer the following. (5 pts ea)
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,
N
t
Average Number At Risk During Interval,
N
t*
=Nt-C
t
/2
Number of Deaths During Interval,
D
t

2. Lost to Follow-Up,
C
t
Proportion Dying
q
t
= D
t
/N
t*
Proportion Surviving
pt = 1-qt
Survival Probability
S
t
= pt*S
t-1
0-2
2-4
4-6

3. 6-8
8-10
1.
cont.
Use the Kaplan-Meier approach to estimate the survival
function.
Complete the table below
Time, Years
Number at Risk
Nt

4. Number of Deaths
Dt
Number Censored
Ct
Survival Probability
S
t+1
= S
t
*((N
t
-D
t
)/N
t
)
0
25
1.2
2.5
3.4

5. 4.1
4.2
4.3
5.6
5.7
5.9
6.3
6.4

6. 6.5
6.7
7.3
8.1
8.2
8.6
8.9

7. 9.4
9.5
10.0
1.
cont.
Referring to the graph above –
What is the probability of surviving 6.5 years?
A.
None
B.
0.85
C.

8. 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.
An observational cohort study is conducted to compare time to
early failure in patients undergoing joint replacement surgery.
Of specific interest is whether there is a difference in time to
early failure between patients who are considered obese versus
those who are not. The study is run for 40 weeks and times to
early joint failure, measured in weeks, are shown below for
participants classified as obese or not at the time of surgery.
Obese

9. Not Obese
Failure
No Failure
Failure
No Failure
28
39
27
37
25
41
31
36
31
37
34
39
32
35
40
38
36
36
32

10. 29
39
41
Estimate the survival functions (time to early joint failure) for
each group using the Kaplan-Meier approach.
Complete the table below.
Obese
Time, Weeks
Number at Risk
Nt
Number of Events (Joint Failures)
Dt
Number Censored
Ct
Survival Probability
S
t+1
= S
t
*((N
t
-D
t
)/N
t
)

11. 0
11
25
28
29
31
32
35
36

12. 37
38
39
41
2.
cont.
Non-Obese
Complete the table below.
Time, Weeks
Number at Risk
Nt
Number of Events (Joint Failures)
Dt

13. Number Censored
Ct
Survival Probability
S
t+1
= S
t
*((N
t
-D
t
)/N
t
)
0
11
27
31
32
34

14. 36
37
39
40
41
To answer the question as to whether or not there is a difference
in time to early joint failure between obese and non-obese
patients undergoing joint replacement surgery – a Chi square
statistic is computed. The critical value for rejection of the null
hypothesis is 3.84. The computed Chi square is 0.339.
Based on comparing the computed Chi square and the critical

15. Chi square which of the following is (are) true?
A.
There is
not
statistically significant evidence to show that the time to early
joint failure between obese and non-obese patients undergoing
joint replacement surgery is different between groups.
B.
There
is
statistically significant evidence to show that the time to early
joint failure between obese and non-obese patients undergoing
joint replacement surgery is different between groups.
C.
The time to early joint failure is essentially the same for each
group.
D.
a and c.
2.
cont.
The hazard ratio for early joint failure between obese and non-
obese patients undergoing joint replacement surgery is 1.555.
Based on this computation which of the following is (are) true?
A.
The risk of early joint failure is 1.55 times higher in obese

16. patients as compared to non obese patients.
B.
The risk of early joint failure is 0.643 times as high for non-
obese patients as compared to obese patients.
C.
The risk of early joint failure is 1.55 times higher in obese
patients as compared to non obese patients.
D.
a and b
3.
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

17. Hypertension
Free of Hypertension
7
8
6
8
8
8
7
9
10
8
9
11
9
10
11
11
11
12
12
12

18. Estimate the survival (time to progression to hypertension)
functions for each treatment group using the Kaplan-Meier
approach.
3.
cont.
New Drug
Complete the table below.
Time, Months
Number at Risk
Nt
Number of Events (Hypertension)
Dt
Number Censored
Ct
Survival Probability
S
t+1
= S
t
*((N
t
-D
t
)/N
t
)
0
10

19. 7
8
9
10
11
12

20. Currently Available Drug
Complete the table below.
Time, Weeks
Number at Risk
Nt
Number of Events (Hypertension)
Dt
Number Censored
Ct
Survival Probability
S
t+1
= S
t
*((N
t
-D
t
)/N
t
)
0
10
6
7

21. 8
9
10
11
12
3.
cont.
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.

22. 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.
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.

23. 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
Total Points for Chapter Problems 8: /15