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

["Halla Skuladottir" <halla_skuladottir@hotmail.com>]

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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