Flexible association modelling and prediction with semi-competing risks data

Semi-competing risks data involve a non-terminal event time, such as time to disease progression, and a terminal event time such as time to death. Existing methods for handling semi-competing risks data often assume that the underlying association between the two event times follows a pre-specified copula with unknown association parameters, which often correspond to the strength of association. In this article we propose a flexible association model that does not require pre-specifying a copula. Therefore our methods facilitate a convenient and robust evaluation of the underlying association pattern, as well as the association strength. Furthermore the proposed association model leads to a robust estimator for the conditional survival probability of the terminal event given the non-terminal event. The methods were also extended to handle left-truncation. Both the association and survival estimators were shown to feature desirable asymptotic properties and satisfactory numerical performance. Our methods were successfully applied to a diabetes data set to study the association between time to diabetic nephropathy and time to death, and to predict the mortality rate given the onset time of nephropathy. The Canadian Journal of Statistics xx: 1–14; 2016 © 2016 Statistical Society of Canada Resume Les donnees avec risques semi-concurrents comportent des evenements non terminaux tels qu'une etape de progression de la maladie et des risques terminaux comme la mort. Les modeles pour risques semi-concurrents existants supposent habituellement que l'association entre le temps aux deux evenements suit une copule pre-specifiee avec un parametre inconnu qui represente souvent la force de la dependance. Les auteures proposent un modele flexible pour l'association qui ne necessite pas de preciser une copule, offrant une approche pratique et robuste pour evaluer la structure de l'association et sa force. Ce modele conduit egalement a un estimateur robuste de la probabilite conditionnelle de survie a l’evenement terminal sachant les evenements non terminaux. Les auteures generalisent leur approche aux donnees tronquees a gauche. Elles etablissent aussi que les estimateurs de l'association et de la survie possedent tous deux des proprietes asymptotiques desirables et de bonnes performances numeriques. Elles appliquent finalement leurs methodes a un jeu de donnees sur le diabete qui etudie l'association entre les temps d'apparition d'une nephropathie diabetique et la mort, puis predisent le taux de mortalite sachant la date de debut de la nephropathie. La revue canadienne de statistique xx: 1–14; 2016 © 2016 Societe statistique du Canada