Logrank test

The Kaplan-Meier curves do not of themselves provide a formal, p-value, comparison of the treatments. This comparison of the survival curves is undertaken using either the logrank test or the Gehan-Wilcoxon test. We will look at these two test procedures in turn. 

In the Packer et al. (2001) trial in Figure 13.1 we see longer-term differences displayed over the 21 month follow-up period and the logrank test is entirely appropriate here. The p-value from the logrank test was 0.00013, a highly significant result. 

The proportional hazards model, as the name suggests, assumes that the hazard ratio is a constant. As such it provides a direct extension of the logrank test, which is a simple two treatment group comparison. Indeed if the proportional hazards model is fitted to data without the inclusion of baseline factors then the p-value for the test Hg c = 0 will be essentially the same as the p-value arising out of the logrank test. 

The sample size methodology above depends upon the assumption of proportional hazards and is based around the logrank test as the method of analysis. If this assumption is not appropriate and we do not expect proportional hazards then the accelerated failure time model may provide an alternative framework for the... 

Hypothesis test of the equality of survival distributions Logrank test... 

In Chapter 10 the use of this method was discussed in terms of estimating the median survival time for participants in a clinical trial. The median survival time can be helpful as a single summary statistic that defines a typical survival time. However, survival distributions may deviate at various points in time. In this section we present the logrank test, which can be used to test the equality of two or more survival distributions. This is not the only test that can be used for this purpose, but it is a natural extension of a method that we have already described and so we have chosen to discuss it. 

Royston P, Parmar MK (2016) Augmenting the logrank test in the design of clinical trials in which non-proportional hazards of the treatment effect may be anticipated. BMC Med Res Methodol 16 16... 

In the next section we will discuss Kaplan-Meier curves, which are used both to display the data and also to enable the calculation of summary statistics. We will then cover the logrank and Gehan-Wilcoxon tests which are simple two group comparisons for censored survival data (akin to the unpaired t-test), and then extend these ideas to incorporate centre effects and also allow the inclusion of baseline covariates. 

The two tests mentioned earlier are designed to look for these different patterns. The logrank is best able to pick up the longer-term differences as seen in Figure 13.2 a) while the Gehan—WUcoxon test focuses on short-term effects or a delay as seen in Figure 13.2 b). The appropriate test to use depends upon what kind of differences you are expecting to see. 

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