Question

The times are shown below only for the 3-drug arm, with "+" indicating censored subjects:

22; 2; 48; 85; 160; 238; 56+; 94+; 51+; 12; 171; 80; 180; 4; 90; 180+; 3

(a) Using the above data (and assuming non-informative censoring as necessary), calculate the Kaplan-Meier estimate of the survival function, ^ S(t), by hand. Summarize your calculations in a table with columns for events (dj), censoring (cj), and risk sets (rj) at each time tj .

Answer 1

Solution: I have used a table to solve s(t) so that there wont be any confusion.

	Time points	Number of censoring at each point	Number of events at each times points(reverse 0 and 1)	Number of risk at time 0	Survival in each interval	Survival probability
	tj	cj	dj	rj=(rj-1)-dj-cj	Sj=1-(dj/rj)	s(t)=sj*sj+i
1	22	0	1	17	1-(1/17)=0.941	0.941
2	2	0	1	17-1-0=16	1-(1/16)=0.938	0.941*0.938=0.882
3	48	0	1	16-1-0=15	1-(1/15)=0.933	0.882*0.933=0.823
4	85	0	1	14	0.929	0.765
5	160	0	1	13	0.923	0.706
6	238	0	1	12	0.917	0.647
7	56	1	0	11	1.000	0.647
8	94	1	0	10	1.000	0.647
9	51	1	0	9	1.000	0.647
10	12	0	1	8	0.875	0.566
11	171	0	1	7	0.857	0.485
12	80	0	1	6	0.833	0.404
13	180	0	1	5	0.800	0.323
14	4	0	1	4	0.750	0.243
15	90	0	1	3	0.667	0.162
16	180	1	0	2	1.000	0.162
17	3	0	1	1	0.000	0.000

While calculating rj, r1=17 is the total number of sample. So we will start with 17.

Next, r2=r1-d2-c2=17-1-0=16

This is how s(t) is calculated.