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 The logrank test for trend

The logrank test for trend is used when you compare three or more survival curves. In order for the results of this test to be meaningful, the order of groups (columns in the Survival data table) must be arranged in a natural order. Examples could be age groups, stages of cancer, or dosages of treatments. Moreover, these groups must be equally spaced. This test essentially examines whether there is a linear trend median survival and the column order of each group.

## Choosing the logrank test for trend

Prism will compute the logrank test for trend by default when you include three or more groups (columns) in the data table for survival analysis. If you’d like, you can disable this test in the Parameters dialog for the analysis. In this dialog, you can also choose between two methods for calculation of this test: an older method used in Prism 5, and a newer (and better) method available since Prism 6 that matches SAS and SPSS.

## 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 represent different age ranges, different disease severities, or different doses of a drug. The left-to-right order of these groups in the Survival data table must correspond to ordered and equally spaced categories. If the data are not ordered (or equally spaced), then you should ignore the results of the logrank test for trend (or disable it in the Parameters dialog as noted above).

## 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 groups 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 the order of the groups and the median survival time. If the resulting P value is smaller than a pre-specified threshold (typically 0.05), this null hypothesis can be rejected.

## 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 other programs, you are able to assign these codes manually, 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 that the groups are equally spaced. Even if you enter numbers as column titles to represent code numbers, Prism will not use these to perform the test for trend.

## How it works

The logrank test for trend looks at the linear trend between group code (specified by column number in Prism) and survival. However, it doesn’t simply look at median survival, or five-year survival, or any other specific summary measure. It first computes expected survival assuming that the null hypothesis (subjects in all groups are sampled from a population with the same survival experience) is true. 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 the corresponding group code. For additional details, see the text by Machin (1).

## References

1.David Machin, Yin Bun Cheung, Mahesh Parmar, Survival Analysis: A Practical Approach, 2nd edition, IBSN:0470870400.

2.Douglas Altman, Practical Statistics for Medical Research,  IBSN:0412276305