Logrank and Gehan-Breslow-Wilcoxon tests

The P value tests the null hypothesis that the survival curves are identical in the overall populations. In other words, the null hypothesis is that the treatment did not change survival.

The P value answers this question:

If the null hypothesis is true, what is the probability of randomly selecting subjects whose survival curves are as different (or more so) than was actually observed?

The difference between the logrank and the Gehan-Breslow-Wilcoxon tests is that the latter places more weight on deaths at early time points.

Note that Prism lets you choose one of two algorithms for computing the P value when comparing three or more groups. The results will show "(conservative)" or "(recommended)", to document your choice.

Logrank test for trend

If you compare three or more survival curves with Prism, it will show results for the overall logrank test, and also show results for the logrank test for trend.

When should you look at the results for the test for trend?

The test for trend is only relevant when the order of groups (defined by data set columns in Prism) is logical. Examples would be if the groups are different age groups, different disease severities, or different doses of a drug. The left-to-right order of data sets in Prism must correspond to equally spaced ordered categories.

If the data sets are not ordered (or not equally spaced), then you should ignore the results of the logrank test for trend.

Results of the logrank test for trend

The logrank test for trend reports a chi-square value, which is always associated with one degree of freedom (no matter how many data sets are being compared). It uses that chi-square value to compute a P value testing the null hypothesis that there is no linear trend between column order and median survival. If the P value is low, you can conclude that there is a significant trend.

Prism assumes the groups are equally spaced  

Computing the logrank test for trend requires assigning each group a code number. The test then looks at the trend between these group codes and survival. With some programs, you could assign these codes, and thus deal with ordered groups that are not equally spaced. Prism uses the column number as the code, so it can only perform the test for trend assuming equally spaced ordered groups. Even if you enter numbers as column titles, Prism does not use these when performing the test for trend.

How it works

The test looks at the linear trend between group code (column number in Prism) and survival. But it doesn't look at median survival, or five-year survival, or any other summary measure. It first computes expected survival assuming the null hypothesis that all the groups are sampled from population with the same survival experience. Then it quantifies the overall discrepancy between the observed survival and the expected survival for each group. Finally it looks at the trend between that discrepancy and group code. For details, see the text by Marchin.

Multiple comparison tests

After comparing three or more treatment groups, you may want to go back and compare two at a time. Prism does not do this automatically, but it is easy to duplicate the analysis, and change the copy to only compare two groups. Then repeat with a different two data sets. If you do this, you need to manually adjust the definition of 'significance' to account for multiple comparisons. Or place all the P values into a new column table, and then analyze that stack of P values.

Reference

Survival Analysis: A Practical Approach, Second edition, by David Machin, Yin Bun Cheung, Mahesh Parmar, IBSN:0470870400.