Qe E Ee2 E Qc E Ec292

where denotes the sum over strata. More than two groups

We have described how two groups may be compared using the logrank test. There are also situations where we may wish to compare more than two treatment groups in a clinical trial or compare outcomes for patients with differing characteristics. For example, we may wish to compare the survival times of patients with different stages of disease. Here we describe how the Logrank test can be extended to three or more group comparisons.

The general expression corresponding to equation 9.18 but for G groups is given by


with G groups the degrees of freedom is G — 1.

This test is a general test and does not identify where any differences occur. This information may be sought in an informal way from the Kaplan-Meier plots, or by making further, usually pairwise, statistical tests in subgroups of the G groups. However, we need to take some care, when comparing more than two groups, because as pointed out below in Section 9.5 as the number of tests performed increases, the probability of finding a spurious 'positive' result increases. One practical solution to this is to use what is called a 'closed' analysis, which helps protect against this. In this 'closed' analysis, a single logrank analysis is performed across all the groups to assess whether there is overall evidence of differences between groups. Only if this analysis is significant at a pre-specified level (for example, if the observed p-value is less than 0.05), are further pairwise comparisons performed between groups. If the initial overall p-value is not significant at this level then the conclusion is reached that there is no good evidence of a difference anywhere between the groups and no further analyses are done.

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