Comparing treatments in the presence of crossing survival curves: An application to bone marrow transplantation

In some clinical studies comparing treatments in terms of their survival curves, researchers may anticipate that the survival curves will cross at some point, leading to interest in a long-term survival comparison. However, simple comparison of the survival curves at a fixed point may be inefficient, and use of a weighted log-rank test may be overly sensitive to early differences in survival. We formulate the problem as one of testing for differences in survival curves after a prespecified time point, and propose a variety of techniques for testing this hypothesis. We study these methods using simulation and illustrate them on a study comparing survival for autologous and allogeneic bone marrow transplants.