15 Jun Survival Probability St = pt*St-1
uestion
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:
Alive:
1.2, 2.5, 4.3, 5.6, 6.7, 7.3 and 8.1 years
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
FollowUp,
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
0
1.2
2.5
3.4
4.1
Number at
Risk
Nt
Number of
Deaths
Dt
Number
Censored
Ct
Survival Probability
St+1 = St*((Nt-Dt)/Nt)
25
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