The stratified Logrank test

In any study the outcome for patients will often be influenced by the characteristics of the patients themselves as well as by the treatments they receive. For example, for most cancers, patients with a more advanced stage of the disease generally have a shorter expectation of life than patients with less advanced disease. In making comparisons between two groups receiving, for example, different treatments, we need to ensure as much as possible that the differences observed between groups are due to the treatments and not due to the fact that the groups have inherently differing prognoses. In large trials randomization should ensure this, but we may wish to adjust for these prognostic variables when making comparisons between groups, especially in smaller trials. This ensures that 'like' is compared with 'like.' These individual comparisons are then combined to achieve an overall comparison of treatments. This is done by means of the stratified Logrank test.

The extension to equation 9.18 to obtain the stratified logrank statistic for comparing treatments is

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