title: A penalized framework for distributed lag non-linear models.
abstract: Distributed lag non-linear models (DLNMs) are a modelling tool for describing potentially non-linear and delayed dependencies. Here, we illustrate an extension of the DLNM framework through the use of penalized splines within generalized additive models (GAM). This extension offers built-in model selection procedures and the possibility of accommodating assumptions on the shape of the lag structure through specific penalties. In addition, this framework includes, as special cases, simpler models previously proposed for linear relationships (DLMs). Alternative versions of penalized DLNMs are compared with each other and with the standard unpenalized version in a simulation study. Results show that this penalized extension to the DLNM class provides greater flexibility and improved inferential properties. The framework exploits recent theoretical developments of GAMs and is implemented using efficient routines within freely available software. Real-data applications are illustrated through two reproducible examples in time series and survival analysis.
authors.affiliation: Department of Social and Environmental Health Research, London School of Hygiene & Tropical Medicine, 15-17 Tavistock Place, London WC1H 9SH, UK.|Department of Medical Statistics, London School of Hygiene & Tropical Medicine, Keppel Street, London WC1E 7HT, UK.
authors.forename: Antonio
authors.initials: A
authors.lastname: Gasparrini
authors.affiliation: Department of Statistics, Ludwig Maximilians University, Munich, Germany.
authors.forename: Fabian
authors.initials: F
authors.lastname: Scheipl
authors.affiliation: Department of Social and Environmental Health Research, London School of Hygiene & Tropical Medicine, 15-17 Tavistock Place, London WC1H 9SH, UK.
authors.forename: Ben
authors.initials: B
authors.lastname: Armstrong
authors.affiliation: Department of Medical Statistics, London School of Hygiene & Tropical Medicine, Keppel Street, London WC1E 7HT, UK.
authors.forename: Michael G
authors.initials: MG
authors.lastname: Kenward
mesh_terms: D017711:Nonlinear Dynamics; D012984:Software
keywords: Distributed lag; Exposure-lag-response; Generalized additive models; Latency; Penalized splines