The lasso—a novel method for predictive covariate model building in nonlinear mixed effects models

Abstract

Covariate models for population pharmacokinetics and pharmacodynamics are often built with a stepwise covariate modelling procedure (SCM). When analysing a small dataset this method may produce a covariate model that suffers from selection bias and poor predictive performance. The lasso is a method suggested to remedy these problems. It may also be faster than SCM and provide a validation of the covariate model. The aim of this study was to implement the lasso for covariate selection within NONMEM and to compare this method to SCM. In the lasso all covariates must be standardised to have zero mean and standard deviation one. Subsequently, the model containing all potential covariate-parameter relations is fitted with a restriction: the sum of the absolute covariate coefficients must be smaller than a value, t. The restriction will force some coefficients towards zero while the others are estimated with shrinkage. This means in practice that when fitting the model the covariate relations are tested for inclusion at the same time as the included relations are estimated. For a given SCM analysis, the model size depends on the P-value required for selection. In the lasso the model size instead depends on the value of t which can be estimated using cross-validation. The lasso was implemented as an automated tool using PsN. The method was compared to SCM in 16 scenarios with different dataset sizes, number of investigated covariates and starting models for the covariate analysis. Hundred replicate datasets were created by resampling from a PK-dataset consisting of 721 stroke patients. The two methods were compared primarily on the ability to predict external data, estimate their own predictive performance (external validation), and on the computer run-time. In all 16 scenarios the lasso predicted external data better than SCM with any of the studied P-values (5%, 1% and 0.1%), but the benefit was negligible for large datasets. The lasso cross-validation provided a precise and nearly unbiased estimate of the actual prediction error. On a single processor, the lasso was faster than SCM. Further, the lasso could run completely in parallel whereas SCM must run in steps. In conclusion, the lasso is superior to SCM in obtaining a predictive covariate model on a small dataset or on small subgroups (e.g. rare genotype). Run in parallel the lasso could be much faster than SCM. Using cross-validation, the lasso provides a validation of the covariate model and does not require the user to specify a P-value for selection.

Comparison of Nonlinear Mixed Effects Models and Noncompartmental Approaches in Detecting Pharmacogenetic Covariates

“…Lehr et al have suggested an adaptation of the classical stepwise covariate selection on PK phenotype in NLMEM (24), and a method inspired from Lasso has already been used for the selection of non-genetic covariates in NLMEM (40). But this is the first work comparing model-based approach with NCA in this area.…”

Covariate selection in pharmacometric analyses: a review of methods

“…Ribbing et al . use the OFV in their cross‐validation procedure to estimate κ S . It should be noted that the OFV does not necessarily correspond to prediction error in a population.…”

Vertical Integration of Pharmacogenetics in Population PK/PD Modeling: A Novel Information Theoretic Method

“…Previous work from our group suggests that testing saturated parametric interaction models containing as few as 10 predictors may not be feasible on desktop computers 14 . Minimizing bias in covariate effect estimates and model parameters has been previously assessed in population modeling 15 , 16 , 17 , 18 , 19 . Algorithms for building covariate models have also been proposed 15 , 17 .…”

“…Minimizing bias in covariate effect estimates and model parameters has been previously assessed in population modeling 15 , 16 , 17 , 18 , 19 . Algorithms for building covariate models have also been proposed 15 , 17 . For example, Jonsson and Karlsson developed an automated covariate model building strategy within NONMEM 17 that helps to evaluate the effects of adding a covariate on unrelated parameters and tests both linear and nonlinear effects within each run.…”