title: A flexible approach to the crossing hazards problem.
abstract: We propose a simple and flexible framework for the crossing hazards problem. The method is not confined to two-sample problems, but may also work with continuous exposure variables whose effect changes its sign at some time-point of the observed follow-up time. Penalized partial likelihood estimation relies upon the assumption of a smooth hazard ratio via low-rank basis splines with a conventional difference penalty to ensure smoothness, and additional ad hoc penalties to obtain restricted estimates useful in the context of crossing hazards. The framework naturally also leads to a statistical test that has good power for revealing a global effect under several alternatives, including crossing hazards. We provide the results from a real-data analysis and from some simulations to illustrate empirically the performance of the proposed approach as compared with the possible alternatives.
authors.affiliation: Dipartimento di Scienze Statistiche e Matematiche S. Vianelli, Università di Palermo, viale delle Scienze, ed. 13, 90128 Palermo, Italy. vito.muggeo@unipa.it
authors.forename: Vito M R
authors.initials: VM
authors.lastname: Muggeo
authors.forename: Miriam
authors.initials: M
authors.lastname: Tagliavia
mesh_terms: D000465:Algorithms; D001699:Biometry; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D008297:Male; D016016:Proportional Hazards Models; D016019:Survival Analysis