Survival Probability (St)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 involved 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 table shows times to death, or the time to last contact (at which time participant was known to be alive), in years.
Time Event (1 = death, 0 = last contact)
1.2 1
2.5 1
4.3 1
5.6 1
6.7 1
7.3 1
8.1 1
3.4 0
4.1 0
4.2 0
5.7 0
5.9 0
6.3 0
6.4 0
6.5 0
7.3 0
8.2 0
8.6 0
8.9 0
9.4 0
9.5 0
10 0
10 0
10 0
10 0
A) The following table (via the life table approach) estimates the survival function over 2 year intervals. It includes columns for number at risk (Nt), number of deaths (Dt), number censored (Ct), and columns for the average at risk, probability of death, probability of survival, and the cumulative survival. What can you conclude from this table?
Interval_Start Interval_End At_Risk_Start Deaths Censored Average_At_Risk Probability_of_Death Probability_of_Survival Cumulative_Survival
0 2 25 1 0 25.0 0.0400 0.9600 0.9600
2 4 24 1 1 23.5 0.0426 0.9574 0.9191
4 6 22 2 4 20.0 0.1000 0.9000 0.8272
6 8 16 2 4 14.0 0.1429 0.8571 0.7091
8 10 10 1 9 5.5 0.1818 0.8182 0.5801
B) The graph below shows the survival function based on estimates via the Kaplan-Meier approach. What can you conclude from the survival function? How, if at all, does this differ from your conclusions from the life table approach?
Survival Probability (St)
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0 0
2
6
8
10
12
Time (years)