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st: sts test - which is better, A or B


From   Tero T Kivela <tekivela@cc.helsinki.fi>
To   statalist@hsphsun2.harvard.edu
Subject   st: sts test - which is better, A or B
Date   Tue, 18 May 2004 18:50:11 +0300 (EET DST)

Dear Statalisters,

Consider that one has a data set which can be divided into different
classes based on cutpoints of certain variables - which ones and how does
not matter here, but this can be done in two or more different ways.

Say that one way of classifying results in four ordered categories
which give the following result in -sts test-:

Log-rank test for equality of survivor functions

            |   Events         Events
stage1      |  observed       expected
------------+-------------------------
10          |        10          25.70
20          |        73          85.75
31          |        40          24.83
32          |        18           4.71
------------+-------------------------
Total       |       141         141.00

Test for trend of survivor functions

                  chi2(1) =    38.2276
                  Pr>chi2 =     0.0000

Test for trend of survivor functions

The alternative way gives:

Log-rank test for equality of survivor functions

          |   Events         Events
stage2    |  observed       expected
----------+-------------------------
10        |         4          11.05
20        |        58          84.43
31        |        60          41.15
32        |        20           5.37
----------+-------------------------
Total     |       142         142.00

Test for trend of survivor functions

                chi2(1) =    36.8827
                Pr>chi2 =     0.0000

Intuitively, the classification which gives
                  chi2(1) =    38.2276
divides the cases better accoridng to survival than the one which gives
                  chi2(1) =    36.8827

There must be a way to test, statistically, whether orr not it is likely
that the difference in chi-square has occurred by chance (as it may have
in this example, unlike would be the case intuitively had the chi-square
values been, say, 38.2 and 48.2.

And: in this case, both classifications had four categories. What about
comparsion of a classification which has three categories to one that has
four categories.

What would be the method to test for the difference between two
Kaplan-Meier analyses. I have not seen any problems like this in a number
of manuals on survival analysis.

Best regards,

T Kivela
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