Analysis of time to death after transplantation when transplants are only given to patients in remission

The analysis in nonrandomized studies of the potential benefit to a patient which is derived from organ transplantation has been an important topic in survival analysis, having served as a key motivation for the development of such methods as the Mantel-Byar test and the Cox regression model with time-dependent covariates. This paper discusses an additional complication in the analysis of survival after transplantation that arises in cases when organ transplantation is only given to patients who are currently in remission from their illness after a first application of some other initial treatment. We show that the time-dependent covariates methods available in current survival analysis statistical programs are inadequate to properly handle the comparison of subsequent survival from transplant in this case, and propose a modification of the Mantel-Byar test specifically designed to deal with this difficulty The proposed method is contrasted with other approaches using data from studies of bone marrow transplantation in the treatment of childhood cancer.