title: Model building in nonproportional hazard regression.
abstract: Recent developments of statistical methods allow for a very flexible modeling of covariates affecting survival times via the hazard rate, including also the inspection of possible time-dependent associations. Despite their immediate appeal in terms of flexibility, these models typically introduce additional difficulties when a subset of covariates and the corresponding modeling alternatives have to be chosen, that is, for building the most suitable model for given data. This is particularly true when potentially time-varying associations are given. We propose to conduct a piecewise exponential representation of the original survival data to link hazard regression with estimation schemes based on of the Poisson likelihood to make recent advances for model building in exponential family regression accessible also in the nonproportional hazard regression context. A two-stage stepwise selection approach, an approach based on doubly penalized likelihood, and a componentwise functional gradient descent approach are adapted to the piecewise exponential regression problem. These three techniques were compared via an intensive simulation study. An application to prognosis after discharge for patients who suffered a myocardial infarction supplements the simulation to demonstrate the pros and cons of the approaches in real data analyses.
authors.affiliation: SiDOR Research Group, University of Vigo, Spain; Unit of Biostatistics, Department of Statistics, University of Santiago de Compostela, Spain.
authors.forename: Mar
authors.initials: M
authors.lastname: Rodríguez-Girondo
authors.forename: Thomas
authors.initials: T
authors.lastname: Kneib
authors.forename: Carmen
authors.initials: C
authors.lastname: Cadarso-Suárez
authors.forename: Emad
authors.initials: E
authors.lastname: Abu-Assi
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D009203:Myocardial Infarction / Q000401:mortality; D011379:Prognosis; D012044:Regression Analysis; D016019:Survival Analysis
keywords: boosting; generalized additive models; model choice; penalized likelihood; piecewise exponential model; survival analysis; variable selection