The protective impact of a covariate on competing failures with an example from a bone marrow transplantation study

Starting from an applied Bone Marrow Transplantation (BMT) study, the problem of "unexpected protectivity" in competing risks models is introduced, which occurs when one covariate shows a protective impact not expected from a medical perspective. Current explanations found in the statistical literature suggest that unexpected protectivity might be due to the lack of independence between the competing failures. Actually, in the presence of dependence, the Kaplan-Meier curves are not interpretable. Conversely, the cumulative incidence curves remain interpretable, and therefore seem to be a candidate for solving the problem. We discuss the particular nature of dependence in a competing risks framework and illustrate how this dependence may be created via a common frailty factor. A Monte Carlo experiment is set up which accounts also for the association between the observable covariates and the frailty factor. The aim of the experiment is to understand whether and how the bias showed by the estimates could be related to the omitted frailty variable. The results show that dependence alone does not cause false protectivity, and that the cumulative incidence curves suffer the same bias as the survival curves and therefore do not seem to be a solution to false protectivity. Conversely, false protectivity may occur according to the magnitude and the sign of the dependence between the frailty factor and the covariate. The paper ends with some suggestions for empirical research.