A full model approach based on the covariance matrix of parameters and covariates
Mats O Karlsson
Dept Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden
Background: A full covariate model approach has been presented [1,2] where all parameter-covariate relations of interest to characterise are added into the model as fixed effects and the posterior distribution of these effects are used for decision-making. The approach has several advantages including no bias based on data-driven model selection and rapid model building. However, there are also disadvantages, including: (i) sensitivity to correlated covariates, (ii) non-included parameter-covariate relations may bias estimates of included relations [3], and (iii) model stability may be an issue when parameter-covariate relations to be characterized are many.
Objective: To propose a new approach to a full model characterization that addresses the above-mentioned disadvantages.
Methods: In the proposed approach, selection of covariates of interest to characterize is made without concern regarding their correlation. Covariates are entered into the data set as observed variables, and their distribution are modelled as random effects. A full covariance matrix between random effects for parameters and covariates is estimated together with the other model components. The method was assessed using simulated data where covariate-parameters were defined as fixed effects in a one-compartment pharmacokinetic simulation model. Analyses were made using covariate-parameter relations either as fixed effects (“traditional” full fixed effects model - FFEM) or as a full covariance matrix of random effects (full random effects model -FREM) including both continuous and binary covariates.
Results: The two approaches described data equally well and the decrease in the objective function value was equally large compared to a base model without parameter-covariate relations for models with or without any true relations, and for both continuous and binary covariates. For a 2-parameter (CL, V) and 3 covariate model (modestly correlated covariates, r=0.4), the imprecision in the estimates of the true parameter-covariate relations were typically higher for the FFEM compared to the FFRM by a factor 1.16. This factor increased as the number of covariates and/or correlation increased.
Discussion: The FREM is a promising approach which improves on some shortcomings of the FFEM. It may also serve as a first step in an exploratory analysis as it provides the maximal benefit of the considered covariates to goodness-of-fit.
Acknowledgement: This work was part of the DDMoRe project.
References:
[1] Gastonguay The AAPS Journal. 2004 (6), S1, W4354.
[2] Gastonguay PAGE 20 (2011) Abstr 2229 [www.page-meeting.org/?abstract=2229]
[3] Ivaturi et al. PAGE 20 (2011) Abstr 2228 [www.page-meeting.org/?abstract=2228]
