A study involves 25 participants who are age 65 years or older | Complete Solution

1.     A study involves 25 participants who are age 65 years or older and all of them have diabetes. Each participant is followed for 10 years after a transplant.  Times to death are listed below in years, or the time to last contact of which the participant is 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 the years intervals of 0-2, 2-4.

Complete the table below.

Interval
In
years

    # at risk
during
interval    Average
# at Risk during
interval
N1=Nt-CT/2    # 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
Probablility
St+1=St*((Nt-D1)/Nt)    
0                    
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                    

2.   20 randomized patients are to receive a new drug or currently available drug for prevention of hypertension in patients with pre-hypertension. Patients 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    New Drug
Hypertension    Prehypertension
7    8
8    8
10    8
    9
    11

    12

12

Currently Available Drug    
Hypertension    Free of Hypertension
6    8
7    9
9    11
10    11
11    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    # at risk
Nt    # of events
hypertension
Dt    Number
Censored
Ct    Survival
Probablility
St+1=St*((nt-Dt)/Nt)
0    10            
6                
7                
8                
9                
10                
11
12                

Currently Available Drug
Complete Table Below
Time, months    # at risk
Nt    # of events
hypertension
Dt    Number
Censored
Ct    Survival
Probablility
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.

Which of the following is true?

A.    there is not a 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.    Time to progression is essentially the same for each group.
D.     A and C

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

A.    The risk of progression to hypertension is reduced by 34.2% in patients assisgned 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