1. The original dataset and descriptive statistics summary:
Untreated Controls Group (n = 20)
Mouse I.D.
No. Weeks Alive
1013
104
Alive
1014
21
Dead
1015
54
Dead
1016
21
Dead
1017
31
Dead
1018
57
Dead
1019
44
Dead
1020
69
Dead
1021
55
Dead
1022
86
Dead
1023
87
Dead
1024
34
Dead
1025
43
Dead
1026
104
Dead
1027
79
Dead
1028
55
Dead
1029
104
Alive
1030
104
Alive
1031
55
Dead
1032
104
Alive
Endpoint
7 Week-old donors Group (n = 21)
Mouse I.D.
No. Weeks Alive
989
30
Dead
990
43
Dead
991
47
Dead
992
25
Dead
993
23
Dead
994
45
Dead
995
19
Dead
996
20
Dead
997
19
Dead
998
17
Dead
999
15
Dead
1000
49
Dead
1001
43
Dead
1002
49
Dead
1003
49
Dead
1004
45
Dead
1005
49
Dead
1006
32
Dead
Endpoint
1007
17
Dead
1008
40
Dead
1009
20
Dead
27 Month-old Donors Group (n = 23)
Mouse I.D.
No. Weeks Alive
816
20
Dead
817
23
Dead
818
16
Dead
819
21
Dead
820
23
Dead
821
11
Dead
822
17
Dead
823
21
Dead
824
22
Dead
825
21
Dead
826
19
Dead
827
19
Dead
828
19
Dead
829
23
Dead
830
27
Dead
831
25
Dead
832
24
Dead
833
20
Dead
834
20
Dead
835
17
Dead
836
25
Dead
837
25
Dead
838
12
Dead
Endpoint
Based on these datasets, we summarize the basic descriptive statistics information, including number of observations,
failed, censored, quantiles, mean, and standard error.
Summary of the Number of Censored and Uncensored Values
Group
Total Failed Censored Percent Censored
Untreated controls
20
16
4
20
7 Week-old donors
21
21
0
0
27 Week-old donors
23
23
0
0
Total
64
60
4
6.25
Summary of Quantiles, Means, and Standard Errors
Group
First Quantile Median Third Quantile Mean Standard Error
Untreated controls
43.5
56
95.5 65.55
6.559
7 Week-old donors
20
32
45 33.143
2.885
27 Week-old donors
19
21
23 20.435
0.834
2. The Kaplan-Meier Survival Plot
The survival curve for three groups together:
The separate survival curves for each group:
3. The Log-rank test
We conduct the log-rank test in SAS to compare the survival distributions of these datasets. Firstly, we compute the
corresponding log-rank values and check the equality over the groups. The procedure output is shown as following:
Rank Statistics
Group
Log-Rank
Untreated controls
-18.767
7 Week-old donors
4.522
27 Week-old donors
14.245
Test of Equality over Strata
Test
Chi-Square DF Pr > Chi-Square
Log-Rank
48.0374
2 <.0001
Since the probability larger than Chi-square is less than 0.0001, the log-rank test shows that the numbers of week alive for
these three groups are significantly different.
Then, we continue to apply the pairwise Sidak multiple-comparison to check if there is significant difference between
these groups. The procedure output is shown as following:
Adjustment for Multiple Comparisons for the Log-rank Test
Strata Comparison
p-Values
Group
Group
Chi-Square Raw
Sidak
Untreated controls 7 Week-old donors
14.9482 0.0001 0.0003
Untreated controls 27 Week-old donors
47.3571 <.0001 <.0001
7 Week-old donors 27 Week-old donors
4.3816 0.0363 0.1051
There is significant difference between the untreated controls group and the 7 week-old donors group. And the difference
between the untreated controls group and the 27 week-old donors group is significant as well. However, the difference
between the 7 week-old donors group and the 27 week-old donors group is nonsignificant.
4. Conclusion
According to our analysis, there are highly significant differences between the untreated controls group and the 7 weekold donors group, as well as the untreated controls group and the 27 week-old donors group. But, the difference between
the 7 week-old donors group and the 27 week-old donors group is nonsignificant.