Robust Versus Nonparametric Approaches and Survival Data Analysis

W.Q. Meeker and L.A. Escobar famous book Statistical Methods for Reliability Data [26] is a very well-known reference for all engineers and researchers who are interested in reliability problems. W.Q. Meeker has a long experience in modeling and solving degradation problems with the most complex features, so that it is a pleasure for me to participate in this volume in his honor. For a long time, survival data analysis and reliability studies walked their way parallel without much interpenetration. But nowadays, impulsed by several people among which Bagdonavicius and Nikulin [3, 4], one is aware of the multiple links between reliability and survival analysis, acknowledging still for some specificities. Many parametric models are available, as well as large classes of models like accelerated models, mainly in use in reliability, and extended Cox model [11], that are the favorite for survival data which have parametric as well as semi-parametric versions. In the recent years, there was an increasing interest for purely nonparametric approaches. Their advantage is that they are supposed to be able to adjust any possible data set through a vast class of regular functions. The drawbacks are first that there is generally a lack of easy interpretation for practical purposes and second that proving the required properties of the inference procedures like consistency, for example, is not trivial when censoring and truncation are present (Huber et al. [18], [19]), which is often true in the medical field. The result is that the justification of some proposed procedures is only through some simulations without any theoretical proof of their properties. What I would like to emphasize in this chapter is the need for a robust approach to survival data analysis, which means using robust procedures for flexible parametric models, still valid when the observations follow a model close, but not exactly equal, to the assumed model [22]. This always seemed to me a good compromise between a purely parametric approach and a purely nonparametric one. One of the most interesting chapter on robustness in survival analysis is the one by Kosorok et al. [24], which tackles the case of a possibly misspecified frailty model.