MODELING TIME-DEPENDENT INTERACTION IN A TIME-VARYING COVARIATE AND ITS APPLICATION TO REJECTION EPISODES AND KIDNEY-TRANSPLANT FAILURE

Acute rejection episodes are thought to be prognostic of eventual kidn ey graft failure. The influence of rejection events on the hazard of t ransplant failure appears to be a complex function of how long after t ransplantation the rejection event occurs as well as the time elapsed since the rejection event. To examine the nature of this relationship, we propose a penalized likelihood approach to estimate the parameters of a two-dimensional rectanglewise constant hazard model. The approac h appears to be fairly successful at modelling time dependency in a ti me-varying covariate. The approach is equally applicable for modelling fixed covariates that act in a jointly nonproportional (non-log-linea r) and time-dependent manner.