Statistical Methods in Medical Research: Survival Analysis and Clinical Trial Evaluation
This document discusses statistical methods used in medical research, particularly survival analysis and clinical trial evaluation techniques.
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HLTH 501
Page 1 of 7
Statistical Methods in Medical Research: Survival Analysis
and Clinical Trial Evaluation
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: 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 25 25 1 0 0.04 0.96 0.96
2–4 24 23.5 1 0 0.0425531 0.9574468 0.919148936
4–6 23 22.5 2 0 0.08888888 0.91111111 0.837446809
6–8 21 20 2 0 0.1 0.9 0.753702128
8–10 19 18 1 0 0.05555555 0.94444444 0.711829787
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 0 0 1
1.2 25 1 0 0.96
2.5 24 1 0 0.92
3.4 23 0 1 0.92
Page 1 of 7
Statistical Methods in Medical Research: Survival Analysis
and Clinical Trial Evaluation
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: 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 25 25 1 0 0.04 0.96 0.96
2–4 24 23.5 1 0 0.0425531 0.9574468 0.919148936
4–6 23 22.5 2 0 0.08888888 0.91111111 0.837446809
6–8 21 20 2 0 0.1 0.9 0.753702128
8–10 19 18 1 0 0.05555555 0.94444444 0.711829787
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 0 0 1
1.2 25 1 0 0.96
2.5 24 1 0 0.92
3.4 23 0 1 0.92
HLTH 501
Page 2 of 7
4.1 22 0 1 0.92
4.2 21 0 1 0.92
4.3 20 1 0 0.874
5.6 19 1 0 0.828
5.7 18 0 1 0.828
5.9 17 0 1 0.828
6.3 16 0 1 0.828
6.4 15 0 1 0.828
6.5 14 0 1 0.828
6.7 13 1 0 0.7643076
92
7.3 12 1 1 0.7006153
85
8.1 11 1 0 0.6369230
77
8.2 9 0 1 0.6369230
77
8.6 8 0 1 0.6369230
77
8.9 7 0 1 0.6369230
77
9.4 6 0 1 0.6369230
77
9.5 5 0 1 0.6369230
77
10 4 0 4 0.6369230
77
Page 2 of 7
4.1 22 0 1 0.92
4.2 21 0 1 0.92
4.3 20 1 0 0.874
5.6 19 1 0 0.828
5.7 18 0 1 0.828
5.9 17 0 1 0.828
6.3 16 0 1 0.828
6.4 15 0 1 0.828
6.5 14 0 1 0.828
6.7 13 1 0 0.7643076
92
7.3 12 1 1 0.7006153
85
8.1 11 1 0 0.6369230
77
8.2 9 0 1 0.6369230
77
8.6 8 0 1 0.6369230
77
8.9 7 0 1 0.6369230
77
9.4 6 0 1 0.6369230
77
9.5 5 0 1 0.6369230
77
10 4 0 4 0.6369230
77
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Subject
Medicine