Survival Analysis in Medical Research: Comparing Life Table and Kaplan-Meier Methods
A solved assignment comparing survival analysis techniques, including life table and Kaplan-Meier methods in medical research.
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Survival Analysis in Medical Research: Comparing Life Table and
Kaplan-Meier Methods
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.
Interva
l
In
years
# at
risk
during
interva
l
Averag
e
# at
Risk
during
interval
N1=Nt-
CT/2
# of
deaths
during
interval
,
Dt
Lost
to
Follo
w
Up, Ct
Proportio
n
Dying
Qt=Dt/Nt
Proportio
n
Surviving
pt=1-qt
Survival
Probabilit
y
St=pt*st-1
0-2 25 25 1 0 0.0400 0.9600 0.9600
2-4 24 23.5 1 1 0.0426 0.9574 0.9191
4-6 22 20 2 4 0.1000 0.9000 0.8272
6-8 16 14 2 4 0.1429 0.8571 0.7091
8-10 10 5.5 1 9 0.1818 0.8182 0.5801
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)
Kaplan-Meier Methods
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.
Interva
l
In
years
# at
risk
during
interva
l
Averag
e
# at
Risk
during
interval
N1=Nt-
CT/2
# of
deaths
during
interval
,
Dt
Lost
to
Follo
w
Up, Ct
Proportio
n
Dying
Qt=Dt/Nt
Proportio
n
Surviving
pt=1-qt
Survival
Probabilit
y
St=pt*st-1
0-2 25 25 1 0 0.0400 0.9600 0.9600
2-4 24 23.5 1 1 0.0426 0.9574 0.9191
4-6 22 20 2 4 0.1000 0.9000 0.8272
6-8 16 14 2 4 0.1429 0.8571 0.7091
8-10 10 5.5 1 9 0.1818 0.8182 0.5801
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)
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