Covariate Model Building Using Linear Approximations
Akash Khandelwal, Kajsa Harling, E Niclas Jonsson, Andrew C Hooker, Mats O Karlsson
Dept of Pharmaceutical Biosciences, Uppsala University, Box 591, 75124, Uppsala Sweden
Background: Methods for exploratory covariate model building that rely on individual, empirical Bayes, parameter estimates are not appropriate whenever data per individual are sparse or when covariates are varying in time. Screening that is based on multiple analyses of non-linear mixed effects models are routinely used, but such model building is time-consuming especially when a large number of parameter-covariate relations are to be explored. A method utilizing a first-order (FO) linearization of covariate relations and variability terms, where derivatives and typical subject predictions arise from a nonlinear mixed effects base model, has previously been presented [1]. In covariate model building, it performed similarly to non-linear mixed effects modeling.
Aim: To implement and evaluate existing and new linearization methods for covariate model building.
Methods: The published method is based on a FO approximation for interindividual variability and covariate relations. Here also methods based on conditional first- (FOCE) and second-order (SOCE) approximations, with or without interaction between random effects are developed and evaluated. Both simulated data and real data examples, including studies with phenobarbital, moxonidine and dofetilide, have been explored. .
Results: The FO linearization method performed similarly to previous reports [1]. The conditional linearization methods (utilizing FOCE- and SOCE-derivatives) improved on the FO method and agreed well with estimation with nonlinear mixed effects models for both real and simulated data sets. For covariate relations of weak to moderate strength, where the decrease in the objective function (OFV) was <15 units, there was good agreement between nonlinear and linearized models. For strong covariate relations, OFV differences between the linear and nonlionear models were in general larger, but both methods identified similar covariate effects as significant.
Discussion: Linearized models can provide information on covariate effects that is very similar to that of nonlinear models but with run-times that seldom will exceed a few seconds. Such rapid runtimes allow explorative covariate model building to utilize computer-intensive techniques (variation of initial estimates for each model, randomization tests, cross-validation and case-deletion diagnostics) that can provide important information but are often impossible when nonlinear mixed effects models are analyzed. .
References:
[1] Jonsson EN, Karlsson MO. Automated covariate model building within NONMEM. Pharm Res. 15:1463-8 (1998)