Please explain using excel worksheet and indicate formulas in the explanation. T
ID: 3253700 • Letter: P
Question
Please explain using excel worksheet and indicate formulas in the explanation. Thank you.
1. An observational study is conducted to compare experiences of men and women between the ages of 50-59 years following coronary artery bypass surgery. Participants undergo the surgery and are followed until the time of death, until they are lost to follow-up or up to 30 years, whichever comes first. The following table details the experiences of participating men and women. The data below are years of death or years of last contact for men and women.
Men
Women
Year of Death
Year of Last Contact
Year of Death
Year of Last Contact
5
8
19
4
12
17
20
9
14
24
21
14
23
26
24
15
29
26
17
27
19
29
21
30
22
30
24
30
25
30
a) Estimate the survival functions for each treatment group using the Kaplan-Meier approach
b) Test if there is a significant difference in survival between treatment groups using the log rank test and a 5% level of significance.
Men
Women
Year of Death
Year of Last Contact
Year of Death
Year of Last Contact
5
8
19
4
12
17
20
9
14
24
21
14
23
26
24
15
29
26
17
27
19
29
21
30
22
30
24
30
25
30
Explanation / Answer
a)We assume that censoring of data is done after the death occurs.
Terminology:
tj = Time of jth death
dj = No. of death at tj
nj = No. of people alive just before jth death.
?j = Probability of death at tj.
MEN
j
tj
dj
nj
?j = dj / nj
1 - ?j
S(t)
1
5
1
15
0.0667
0.9333
0.9333
2
12
1
13
0.0769
0.9231
0.8615
3
14
1
12
0.0833
0.9167
0.7897
4
23
1
10
0.1000
0.9000
0.7108
5
29
1
5
0.2000
0.8000
0.5686
Survival Function =
S(t)
1
0 < t < 5
0.9333
5 < t < 12
0.8615
12 < t < 14
0.7897
14 < t < 23
0.7108
23 < t < 29
0.5686
t > 29
WOMEN
j
tj
dj
nj
?j = dj / nj
1 - ?j
S(t)
1
19
1
10
0.1000
0.9000
0.9000
2
20
1
8
0.1250
0.8750
0.7875
3
21
1
7
0.1429
0.8571
0.6750
4
24
1
4
0.2500
0.7500
0.5063
Survival Function =
S(t)
1
0 < t < 19
0.9
19 < t < 20
0.7875
20 < t < 21
0.675
21 < t < 24
0.5063
t > 24
j
tj
dj
nj
?j = dj / nj
1 - ?j
S(t)
1
5
1
15
0.0667
0.9333
0.9333
2
12
1
13
0.0769
0.9231
0.8615
3
14
1
12
0.0833
0.9167
0.7897
4
23
1
10
0.1000
0.9000
0.7108
5
29
1
5
0.2000
0.8000
0.5686