Comparison of survival times in a transplant study of hematologic disorders

Bone marrow transplantation including autologous, allogeneic and syngeneic has evolved over the past 30 years into an effective therapy for patients with a variety of hematologic malignancies. A total of 51 patients with hematologic disorders were treated with myeloablation and transplantation with either unrelated human leucocyte antigen (HLA) partially matched umbilical cord blood or HLA-matched unrelated donor grafts during 1997-2003. In evaluation of survival of these patients, the log rank and Wilcoxon tests lead to ambiguous results, which also happen in other applications. While the asymptotic properties of these tests are well understood, it is not clear how they behave in a small and specific sample. To resolve the ambiguity and to better understand our patient sample, we compare the power of the two tests by simulation in small samples with piecewise log-logistic and Weibull distributions and with different censoring distributions. Our simulation study confirms the well known fact that when the hazards of underlying survival distributions are non-proportional early on, say t < t(0), but proportional when t> or = t(0), the Wilcoxon test has more power than log rank test. But the importance of our simulation is to gain insight into the time point and impact of t(0) with respect to our transplantation study of leukemia cancer patients. We now conclude that overall survivals of patients with two graft sources are statistically significantly different, in part due to the delay of neutrophil recovery of one patient population immediately after transplantation. Thus, we recommend that Wilcoxon test should be used in future studies of similarly designed clinical trials.