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.
Highlights
Consider a hierarchical data set, where we have a number of sets of response data, from different patients perhaps
A controlled infusion of insulin enters compartment 1 at a rate Inf(t), supplemented by boluses of insulin, which we model as entering at a rate Bol(t)
Insulin leaves both compartments according to a first-order process, with rate constant−1, where tmax is the time-to-peak insulin concentration in minutes
Summary
Consider a hierarchical data set, where we have a number of sets of response data, from different patients perhaps. The parameters may depend on observed covariates, or there may be different ways of partitioning their variability across levels of the hierarchy Such exploration can be cumbersome and time-consuming, especially when individual-level models are complex. Pharmacokinetic models are typically nonlinear (in their parameters), often have complex functional forms and are sometimes only available as a set of differential equations, with no closed-form solution. Fitting such a aMRC Biostatistics Unit, Cambridge Institute of Public Health, Cambridge, U.K. bDepartment of Paediatrics, University of Cambridge, Cambridge, U.K. cUniversity of Cambridge Wellcome Trust-MRC Institute of Metabolic Science, Level 4 Metabolic Research Laboratories, Cambridge, U.K. dNIHR Cambridge Biomedical Research Centre, Cambridge, U.K
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