title: Rapid model exploration for complex hierarchical data: application to pharmacokinetics of insulin aspart.
abstract: We consider situations, which are common in medical statistics, where we have a number of sets of response data, from different individuals, say, potentially under different conditions. A parametric model is defined for each set of data, giving rise to a set of random effects. Our goal here is to efficiently explore a range of possible 'population' models for the random effects, to select the most appropriate model. The range of possible models is potentially vast, because the random effects may depend on observed covariates, and there may be multiple credible ways of partitioning their variability. Here, we consider pharmacokinetic (PK) data on insulin aspart, a fast acting insulin analogue used in the treatment of diabetes. PK models are typically nonlinear (in their parameters), often complex and sometimes only available as a set of differential equations, with no closed-form solution. Fitting such a model for just a single individual can be a challenging task. Fitting a joint model for all individuals can be even harder, even without the complication of an overarching model selection objective. We describe a two-stage approach that decouples the population model for the random effects from the PK model applied to the response data but nevertheless fits the full, joint, hierarchical model, accounting fully for uncertainty. This allows us to repeatedly reuse results from a single analysis of the response data to explore various population models for the random effects. This greatly expedites not only model exploration but also cross-validation for the purposes of model criticism. © 2015 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.
authors.affiliation: MRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge, U.K.
authors.forename: Robert J B
authors.initials: RJ
authors.lastname: Goudie
authors.affiliation: Department of Paediatrics, University of Cambridge, Cambridge, U.K.|Wellcome Trust-MRC Institute of Metabolic Science, Level 4 Metabolic Research Laboratories, University of Cambridge, Cambridge, U.K.|NIHR Cambridge Biomedical Research Centre, Cambridge, U.K.
authors.forename: Roman
authors.initials: R
authors.lastname: Hovorka
authors.affiliation: Department of Paediatrics, University of Cambridge, Cambridge, U.K.|Wellcome Trust-MRC Institute of Metabolic Science, Level 4 Metabolic Research Laboratories, University of Cambridge, Cambridge, U.K.|NIHR Cambridge Biomedical Research Centre, Cambridge, U.K.
authors.forename: Helen R
authors.initials: HR
authors.lastname: Murphy
authors.affiliation: MRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge, U.K.
authors.forename: David
authors.initials: D
authors.lastname: Lunn
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D003922:Diabetes Mellitus, Type 1 / Q000188:drug therapy*; D005260:Female; D006801:Humans; D061267:Insulin Aspart / Q000493:pharmacokinetics* / Q000627:therapeutic use; D008954:Models, Biological; D009010:Monte Carlo Method; D011247:Pregnancy; D011248:Pregnancy Complications / Q000188:drug therapy*; D015203:Reproducibility of Results
chemical_list: D061267:Insulin Aspart
keywords: Bayesian hierarchical models; Markov chain Monte Carlo; insulin; pharmacokinetics; variable selection