A weighted Kaplan-Meier estimator for matched data with application to the comparison of chemotherapy and bone-marrow transplant in leukaemia

Studies on the comparison of transplantation with respect to standard therapy present a number of statistical challenges: they are usually not randomized, often retrospective (based on registry data) and the treatment assignment is time dependent (waiting time to transplant). Matching on known prognostic factors and waiting time to transplant can be used to select appropriate samples for the analysis. When a variable number of patients treated with conventional therapy matches each transplanted patient, the standard estimating and testing procedures need to be modified in order to account for the fact that matched data are highly stratified, with strata containing a few, possibly censored, observations. A weighted version of the Kaplan-Meier estimator, which accounts for a variable proportion of matching, is proposed and its statistical properties are studied. The problem of the comparison of the survival experience in the two treatment groups is also considered. Two tests, based on the distance between the survival estimates calculated at a prefixed time point, are examined and their behaviour is evaluated through simulations. The procedures proposed here are applied to data collected from an Italian study whose aim was the evaluation of bone marrow transplant, as compared to intensive chemotherapy, in the cure of paediatric acute lymphoblastic leukaemia.