title: Boosting multi-state models.
abstract: One important goal in multi-state modelling is to explore information about conditional transition-type-specific hazard rate functions by estimating influencing effects of explanatory variables. This may be performed using single transition-type-specific models if these covariate effects are assumed to be different across transition-types. To investigate whether this assumption holds or whether one of the effects is equal across several transition-types (cross-transition-type effect), a combined model has to be applied, for instance with the use of a stratified partial likelihood formulation. Here, prior knowledge about the underlying covariate effect mechanisms is often sparse, especially about ineffectivenesses of transition-type-specific or cross-transition-type effects. As a consequence, data-driven variable selection is an important task: a large number of estimable effects has to be taken into account if joint modelling of all transition-types is performed. A related but subsequent task is model choice: is an effect satisfactory estimated assuming linearity, or is the true underlying nature strongly deviating from linearity? This article introduces component-wise Functional Gradient Descent Boosting (short boosting) for multi-state models, an approach performing unsupervised variable selection and model choice simultaneously within a single estimation run. We demonstrate that features and advantages in the application of boosting introduced and illustrated in classical regression scenarios remain present in the transfer to multi-state models. As a consequence, boosting provides an effective means to answer questions about ineffectiveness and non-linearity of single transition-type-specific or cross-transition-type effects.
authors.affiliation: University of Göttingen, Göttingen, Germany. hreulen@uni-goettingen.de.
authors.forename: Holger
authors.initials: H
authors.lastname: Reulen
authors.affiliation: University of Göttingen, Göttingen, Germany.
authors.forename: Thomas
authors.initials: T
authors.lastname: Kneib
mesh_terms: D000465:Algorithms; D016026:Bone Marrow Transplantation / Q000706:statistics & numerical data; D003198:Computer Simulation; D003422:Critical Care / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D016016:Proportional Hazards Models; D012121:Respiration, Artificial / Q000706:statistics & numerical data; D012984:Software
keywords: Boosting; Cross-transition-type effects; Model choice; Multi-state models; Non-linear effects; Variable selection