Inference for current leukemia free survival

Donor lymphocyte infusion (DLI) for patients who relapse following an allogeneic stem cell transplant has proved remarkably durable. Because of the potential for second remissions with DLI, the current leukemia free survival (CLFS), which is the probability that a patient has not failed the entire course of the treatment, is becoming of interest to clinical investigators. Based on either a multistate Markov model or a linear combination of Kaplan-Meier estimators, we explore regression models for the CLFS. We focus on the two sample problem and we develop confidence bands for the CLFS or for differences in CLFS as well as a Kolmogorov type hypothesis test using a re-sampling technique. We also examine the use of pseudo-values to make inference on the direct effects of covariates on the CLFS function and we develop a score test for the equality of two CLFS. We illustrate these inference methods on a bone marrow transplant dataset.