Tests Between Groups
|This is the section that tells us whether there
are differences in the survival patterns of the various groups. The
null hypotheses of these two tests are the same:
H0: Each group has the same survival function. There are
no differences in the survival rates over time between the various groups.
Large chi-square* values and their correspondingly small p values
indicate that the null hypothesis should be rejected and that the survival
patterns of the various groups do differ. The log-rank test puts more
emphasis on differences that show up later in time, whereas the Wilcoxon test
puts more emphasis on differences that occur at earlier failure times. The
log-rank test is the more powerful test when the groups have proportional
It also has been found to work well when the hazard rate is constant.
In this example, using the 5% level of significance (alpha) the log-rank
test indicates that there are differences among the three groups, while the
Wilcoxon test does not detect differences. This is not surprising since
the largest differences occured after 300 days. (The hazards do not
seem to be proportional. Group B has its largest hazard around 200 days,
while Group A has its largest hazard around 650 days.) Also, the hazard
rate is not constant. My conclusion in this case is that these is insufficient
evidence to say that there are differences among the groups' survival functions.
*Chi is a Greek letter which is written like an X (it is the
first letter in the Greek word for christ, hence the abreviation X-mas for
Chritsmas). English speakers would do well to pronounce it like "kai"
-- not like "chee" nor like "chai" It should rhyme with pie.