Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models

  • Elham Haem
  • Kajsa Harling
  • Seyyed Mohammad Taghi Ayatollahi
  • Najaf Zare
  • Mats O. Karlsson
Original Paper


One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.


Lasso Adaptive Lasso Multicollinearity Covariate model building Mixed effects modeling 

Supplementary material

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Supplementary material 1 (DOCX 25 kb)
10928_2017_9504_MOESM2_ESM.docx (24 kb)
Supplementary material 2 (DOCX 24 kb)


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Elham Haem
    • 1
    • 2
  • Kajsa Harling
    • 2
  • Seyyed Mohammad Taghi Ayatollahi
    • 1
  • Najaf Zare
    • 3
  • Mats O. Karlsson
    • 2
  1. 1.Department of BiostatisticsShiraz University of Medical Sciences School of MedicineShirazIran
  2. 2.Department of Pharmaceutical BiosciencesUppsala UniversityUppsalaSweden
  3. 3.Department of Biostatistics, Infertility Research CenterShiraz University of Medical SciencesShirazIran

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