Comparison of covariate selection methods with correlated covariates: prior information versus data information, or a mixture of both?
The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection method...
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| Published in | Journal of pharmacokinetics and pharmacodynamics Vol. 47; no. 5; pp. 485 - 492 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.10.2020
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 1567-567X 1573-8744 1573-8744 |
| DOI | 10.1007/s10928-020-09700-5 |
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| Abstract | The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant:
2
∗
ln
Pr
X
/
1
-
Pr
X
, Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates (
r
=
0.9
), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is < 80%, PACS when > 80% but < 100%, and SCM when the expected power is 100%. |
|---|---|
| AbstractList | The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: [Formula: see text], Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates ([Formula: see text]), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is < 80%, PACS when > 80% but < 100%, and SCM when the expected power is 100%. The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: 2 ∗ ln Pr X / 1 - Pr X , Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates ( r = 0.9 ), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is < 80%, PACS when > 80% but < 100%, and SCM when the expected power is 100%. The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: $$2*{\kern 1pt} \,{\ln}\left( {{\Pr}\left( X \right)/\left( {1 - {\Pr}\left( X \right)} \right)} \right)$$ 2 ∗ ln Pr X / 1 - Pr X , Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates ( $$r=0.9$$ r = 0.9 ), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is < 80%, PACS when > 80% but < 100%, and SCM when the expected power is 100%. The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: 2(*) ln(Pr(X)/(1 - Pr(X))), Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates (r = 0.9), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is < 80%, PACS when > 80% but < 100%, and SCM when the expected power is 100%. The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2*{\kern 1pt} \,{\ln}\left( {{\Pr}\left( X \right)/\left( {1 - {\Pr}\left( X \right)} \right)} \right)$$\end{document} 2 ∗ ln Pr X / 1 - Pr X , Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r=0.9$$\end{document} r = 0.9 ), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is < 80%, PACS when > 80% but < 100%, and SCM when the expected power is 100%. The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: [Formula: see text], Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates ([Formula: see text]), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is < 80%, PACS when > 80% but < 100%, and SCM when the expected power is 100%.The inclusion of covariates in population models during drug development is a key step to understanding drug variability and support dosage regimen proposal, but high correlation among covariates often complicates the identification of the true covariate. We compared three covariate selection methods balancing data information and prior knowledge: (1) full fixed effect modelling (FFEM), with covariate selection prior to data analysis, (2) simplified stepwise covariate modelling (sSCM), data driven selection only, and (3) Prior-Adjusted Covariate Selection (PACS) mixing both. PACS penalizes the a priori less likely covariate model by adding to its objective function value (OFV) a prior probability-derived constant: [Formula: see text], Pr(X) being the probability of the more likely covariate. Simulations were performed to compare their external performance (average OFV in a validation dataset of 10,000 subjects) in selecting the true covariate between two highly correlated covariates: 0.5, 0.7, or 0.9, after a training step on datasets of 12, 25 or 100 subjects (increasing power). With low power data no method was superior, except FFEM when associated with highly correlated covariates ([Formula: see text]), sSCM and PACS suffering both from selection bias. For high power data, PACS and sSCM performed similarly, both superior to FFEM. PACS is an alternative for covariate selection considering both the expected power to identify an anticipated covariate relation and the probability of prior information being correct. A proposed strategy is to use FFEM whenever the expected power to distinguish between contending models is < 80%, PACS when > 80% but < 100%, and SCM when the expected power is 100%. |
| Author | Chasseloup, Estelle Yngman, Gunnar Karlsson, Mats O. |
| Author_xml | – sequence: 1 givenname: Estelle surname: Chasseloup fullname: Chasseloup, Estelle organization: Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University – sequence: 2 givenname: Gunnar surname: Yngman fullname: Yngman, Gunnar organization: Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University – sequence: 3 givenname: Mats O. orcidid: 0000-0003-1258-8297 surname: Karlsson fullname: Karlsson, Mats O. email: mats.karlsson@farmbio.uu.se organization: Department of Pharmaceutical Biosciences, Faculty of Pharmacy, Uppsala University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/32661654$$D View this record in MEDLINE/PubMed https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-439275$$DView record from Swedish Publication Index |
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| Cites_doi | 10.1007/BF01061662 10.1023/A:1011970125687 10.1023/A:1011579109640 10.1002/pst.1776 10.1111/j.1365-2125.2007.02975.x 10.1023/A:1022972420004 10.1023/A:1018828709196 10.1007/BF01061469 10.1111/bcp.12451 10.1038/psp.2013.24 |
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| Issue | 5 |
| Keywords | Stepwise covariate modelling Prior-adjusted covariate selection Correlation Full fixed effects modelling Covariates Prior |
| Language | English |
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| PublicationTitle | Journal of pharmacokinetics and pharmacodynamics |
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| References_xml | – year: 1989 ident: CR14 publication-title: NONMEM 7.3.0 Users Guides – volume: 19 start-page: 377 year: 1991 end-page: 384 ident: CR3 article-title: A three-step approach combining Bayesian regression and NONMEM population analysis: application to midazolam publication-title: J Pharmacokinet Biopharm doi: 10.1007/BF01061662 – volume: 15 start-page: 1463 year: 1998 end-page: 1468 ident: CR5 article-title: Automated covariate model building within NONMEM publication-title: Pharm Res doi: 10.1023/A:1011970125687 – volume: 28 start-page: 253 year: 2001 end-page: 275 ident: CR6 article-title: Efficient screening of covariates in population models using Wald’s approximation to the likelihood ratio test publication-title: J Pharmacokinet Pharmacodyn doi: 10.1023/A:1011579109640 – year: 2017 ident: CR15 publication-title: R: a language and environment for statistical computing – volume: 16 start-page: 45 year: 2017 end-page: 54 ident: CR17 article-title: Effect of correlation on covariate selection in linear and nonlinear mixed effect models publication-title: Pharm Stat doi: 10.1002/pst.1776 – volume: 64 start-page: 603 year: 2007 end-page: 612 ident: CR2 article-title: Overview of model-building strategies in population PK/PD analyses: 2002–2004 literature survey publication-title: Br J Clin Pharmacol doi: 10.1111/j.1365-2125.2007.02975.x – volume: 29 start-page: 473 year: 2002 end-page: 505 ident: CR18 article-title: Use of prior information to stabilize a population data analysis publication-title: J Pharmacokinet Pharmacodyn doi: 10.1023/A:1022972420004 – ident: CR11 – volume: 6 start-page: W4354 year: 2004 ident: CR7 article-title: A full model estimation approach for covariate effects: inference based on clinical importance and estimation precision publication-title: AAPS J – ident: CR9 – volume: 16 start-page: 709 year: 1999 end-page: 717 ident: CR12 article-title: The effect of collinearity on parameter estimates in nonlinear mixed effect models publication-title: Pharm Res doi: 10.1023/A:1018828709196 – volume: 20 start-page: 511 year: 1992 end-page: 528 ident: CR4 article-title: Building population pharmacokinetic-pharmacodynamic models. I. Models for covariate effects publication-title: J Pharmacokinet Biopharm doi: 10.1007/BF01061469 – volume: 8750 start-page: 27 year: 2018 ident: CR10 article-title: Linearization of full random effects modeling (FREM) for time-efficient automatic covariate assessment publication-title: InAbstr – ident: CR8 – volume: 79 start-page: 132 year: 2015 end-page: 147 ident: CR1 article-title: Covariate selection in pharmacometric analyses: a review of methods publication-title: Br J Clin Pharmacol doi: 10.1111/bcp.12451 – volume: 2 start-page: e50 year: 2013 ident: CR13 article-title: Modeling and simulation workbench for NONMEM: tutorial on Pirana, PsN, and Xpose publication-title: CPT Pharmacomet Syst Pharmacol doi: 10.1038/psp.2013.24 – volume: 2220 start-page: 20 year: 2011 ident: CR16 article-title: Influence of Correlated Covariates on Predictive Performance for Different Models publication-title: InAbstr – volume: 19 start-page: 377 year: 1991 ident: 9700_CR3 publication-title: J Pharmacokinet Biopharm doi: 10.1007/BF01061662 – volume: 20 start-page: 511 year: 1992 ident: 9700_CR4 publication-title: J Pharmacokinet Biopharm doi: 10.1007/BF01061469 – ident: 9700_CR8 – volume: 16 start-page: 45 year: 2017 ident: 9700_CR17 publication-title: Pharm Stat doi: 10.1002/pst.1776 – volume: 28 start-page: 253 year: 2001 ident: 9700_CR6 publication-title: J Pharmacokinet Pharmacodyn doi: 10.1023/A:1011579109640 – ident: 9700_CR9 – volume: 79 start-page: 132 year: 2015 ident: 9700_CR1 publication-title: Br J Clin Pharmacol doi: 10.1111/bcp.12451 – volume: 6 start-page: W4354 year: 2004 ident: 9700_CR7 publication-title: AAPS J – volume: 2220 start-page: 20 year: 2011 ident: 9700_CR16 publication-title: InAbstr – volume-title: NONMEM 7.3.0 Users Guides year: 1989 ident: 9700_CR14 – volume: 8750 start-page: 27 year: 2018 ident: 9700_CR10 publication-title: InAbstr – volume-title: R: a language and environment for statistical computing year: 2017 ident: 9700_CR15 – volume: 64 start-page: 603 year: 2007 ident: 9700_CR2 publication-title: Br J Clin Pharmacol doi: 10.1111/j.1365-2125.2007.02975.x – ident: 9700_CR11 – volume: 29 start-page: 473 year: 2002 ident: 9700_CR18 publication-title: J Pharmacokinet Pharmacodyn doi: 10.1023/A:1022972420004 – volume: 16 start-page: 709 year: 1999 ident: 9700_CR12 publication-title: Pharm Res doi: 10.1023/A:1018828709196 – volume: 2 start-page: e50 year: 2013 ident: 9700_CR13 publication-title: CPT Pharmacomet Syst Pharmacol doi: 10.1038/psp.2013.24 – volume: 15 start-page: 1463 year: 1998 ident: 9700_CR5 publication-title: Pharm Res doi: 10.1023/A:1011970125687 |
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| SubjectTerms | Biochemistry Biomedical and Life Sciences Biomedical Engineering and Bioengineering Biomedicine Correlation Covariates Full fixed effects modelling Original Paper Pharmacology/Toxicology Pharmacy Prior Prior-adjusted covariate selection Stepwise covariate modelling Veterinary Medicine/Veterinary Science |
| Title | Comparison of covariate selection methods with correlated covariates: prior information versus data information, or a mixture of both? |
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