The logrank test for trend is used when you compare three or more survival curves when the columns are in a natural order (perhaps ages, or stage of cancer). It tests, essentially, whether there is a linear trend between column order and median survival.
Prism will compute the logrank test for trend by default when you have three or more groups. You can turn off this test in the Parameters dialog. In this dialog, you also choose between two methods: an older method used in Prism 5 and a better method available since Prism 6 that matches SAS and SPSS.
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, or go to the parameters dialog and uncheck this option so the results are not shown.
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.
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.
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.
Douglas Altman, Practical Statistics for Medical Research, IBSN:0412276305