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 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.
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