title: Model checks for Cox-type regression models based  on optimally weighted martingale residuals.
abstract: We introduce directed goodness-of-fit tests for Cox-type regression models in survival analysis. "Directed" means that one may choose against which alternatives the tests are particularly powerful. The tests are based on sums of weighted martingale residuals and their asymptotic distributions.We derive optimal tests against certain competing models which include Cox-type regression models with different covariates and/or a different link function. We report results from several simulation studies and apply our test to a real dataset.
authors.affiliation: Department of Mathematics, Imperial College London, London, UK. a.gandy@imperial.ac.uk
authors.forename: Axel
authors.initials: A
authors.lastname: Gandy
authors.forename: Uwe
authors.initials: U
authors.lastname: Jensen
mesh_terms: D000465:Algorithms; D006801:Humans; D016016:Proportional Hazards Models; D016019:Survival Analysis