I am familiar with the log-rank test for comparing multiple Kaplan-Meier curves, but I am looking for a test that will compare across ordered groups (an ordinal variable). A significant result from the log rank test indicates that at least one of the groups has a survival curve different than the others. I want a test where a significant test indicates that there is a monotonic trend in the survival curves over the levels of the ordinal grouping variable.
As a more concrete example, consider survival curves for cancer of different stages, and I want to show not just that the curves differ, but that the survival worsens as stage increases.
As a bonus, pointers to implementations of the algorithm in R would be appreciated.
Edit to address
When I tried to find a suitable test, I did find a reference so something that seemed appropriate in the documentation for MedCalc software at http://www.medcalc.org/manual/kaplan-meier.php. Two quotes that sounded like what I wanted from that are
Options: Linear trend for factor levels: Allows testing for a linear trend across levels of the factor. It is appropriate if factor levels have a natural ordering (for example, factor codes represent doses applied to different groups). Kaplan-Meier assumes that the factor levels are equally spaced.
Logrank test for trend: If more than two survival curves are compared, and there is a natural ordering of the groups, then MedCalc can also perform the logrank test for trend. This tests the probability that there is a trend in survival scores across the groups.
But no specific algorithm for this test is stated.