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st: Confidence intervals for Kaplan-Meier get narrower with fewer patients?


From   "Halla Skuladottir" <halla_skuladottir@hotmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Confidence intervals for Kaplan-Meier get narrower with fewer patients?
Date   Wed, 23 Jun 2004 16:26:41 +0000

Dear stata-listers,

I use STATA7 and I am doing some simple Kaplan-Meier analyses on the survival of cancer patients. I am wondering why the confidence intervals get narrower with time. I would expect the confidence intervals to get broader the fewer patients I have left under observation.

Here is an example of some of my results:

xi: sts list if aa==1 & sex==0 & bb==1, by(operation) at(1/10)

Beg. Survivor Std.
Time Total Fail Function Error [95% Conf. Int.]
-------------------------------------------------------------------------------
operation=0
1 77 87 0.4663 0.0391 0.3882 0.5405
2 46 31 0.2761 0.0350 0.2099 0.3461
3 30 16 0.1779 0.0300 0.1237 0.2402
4 22 4 0.1534 0.0282 0.1030 0.2129
5 16 3 0.1299 0.0270 0.0828 0.1879
6 14 1 0.1206 0.0266 0.0747 0.1783
7 14 0 0.1206 0.0266 0.0747 0.1783
8 14 0 0.1206 0.0266 0.0747 0.1783
9 13 1 0.1114 0.0261 0.0668 0.1686
10 13 0 0.1114 0.0261 0.0668 0.1686
operation=1
1 327 346 0.4851 0.0193 0.4468 0.5223
2 191 136 0.2827 0.0174 0.2492 0.3172
3 148 43 0.2188 0.0159 0.1883 0.2507
4 119 15 0.1956 0.0153 0.1665 0.2266
5 93 12 0.1743 0.0149 0.1462 0.2044
6 76 8 0.1581 0.0145 0.1308 0.1877
7 67 0 0.1581 0.0145 0.1308 0.1877
8 60 2 0.1532 0.0145 0.1261 0.1828
9 49 2 0.1474 0.0145 0.1203 0.1771
10 42 4 0.1347 0.0146 0.1077 0.1648


Although it says in the column “Beg. Total =77” I start out with 163 patients in the first group and 672 in the second group.

If I take the first table of output as an example (operation=0): In the beginning the confidence interval ranges from 0.3882-0.5405 (width=0.1523) but at 10 years it is 0.0668-0.1686 (width =0.1018).

Is there someone who can explain why this is so? Am I doing something wrong?

I hope someone has time to answer my mail.

Looking forward to your answer, with my best regards,

Halla Skuladottir
Research Fellow


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