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Multiple Imputation of Missing Covariates in NONMEM and Evaluation of the Method's Sensitivity to eta-Shrinkage
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
2013 (English)In: AAPS Journal, ISSN 1550-7416, E-ISSN 1550-7416, Vol. 15, no 4, 1035-1042 p.Article in journal (Refereed) Published
Abstract [en]

Multiple imputation (MI) is an approach widely used in statistical analysis of incomplete data. However, its application to missing data problems in nonlinear mixed-effects modelling is limited. The objective was to implement a four-step MI method for handling missing covariate data in NONMEM and to evaluate the method's sensitivity to eta-shrinkage. Four steps were needed; (1) estimation of empirical Bayes estimates (EBEs) using a base model without the partly missing covariate, (2) a regression model for the covariate values given the EBEs from subjects with covariate information, (3) imputation of covariates using the regression model and (4) estimation of the population model. Steps (3) and (4) were repeated several times. The procedure was automated in PsN and is now available as the mimp functionality (http://psn.sourceforge.net/).. The method's sensitivity to shrinkage in EBEs was evaluated in a simulation study where the covariate was missing according to a missing at random type of missing data mechanism. The eta-shrinkage was increased in steps from 4.5 to 54%. Two hundred datasets were simulated and analysed for each scenario. When shrinkage was low the MI method gave unbiased and precise estimates of all population parameters. With increased shrinkage the estimates became less precise but remained unbiased.

Place, publisher, year, edition, pages
2013. Vol. 15, no 4, 1035-1042 p.
Keyword [en]
covariates, missing data, multiple imputation, NONMEM
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:uu:diva-210182DOI: 10.1208/s12248-013-9508-0ISI: 000325126300014OAI: oai:DiVA.org:uu-210182DiVA: diva2:661557
Available from: 2013-11-04 Created: 2013-11-04 Last updated: 2017-12-06Bibliographically approved
In thesis
1. Methodology for Handling Missing Data in Nonlinear Mixed Effects Modelling
Open this publication in new window or tab >>Methodology for Handling Missing Data in Nonlinear Mixed Effects Modelling
2014 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

To obtain a better understanding of the pharmacokinetic and/or pharmacodynamic characteristics of an investigated treatment, clinical data is often analysed with nonlinear mixed effects modelling. The developed models can be used to design future clinical trials or to guide individualised drug treatment. Missing data is a frequently encountered problem in analyses of clinical data, and to not venture the predictability of the developed model, it is of great importance that the method chosen to handle the missing data is adequate for its purpose. The overall aim of this thesis was to develop methods for handling missing data in the context of nonlinear mixed effects models and to compare strategies for handling missing data in order to provide guidance for efficient handling and consequences of inappropriate handling of missing data.

In accordance with missing data theory, all missing data can be divided into three categories; missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). When data are MCAR, the underlying missing data mechanism does not depend on any observed or unobserved data; when data are MAR, the underlying missing data mechanism depends on observed data but not on unobserved data; when data are MNAR, the underlying missing data mechanism depends on the unobserved data itself.

Strategies and methods for handling missing observation data and missing covariate data were evaluated. These evaluations showed that the most frequently used estimation algorithm in nonlinear mixed effects modelling (first-order conditional estimation), resulted in biased parameter estimates independent on missing data mechanism. However, expectation maximization (EM) algorithms (e.g. importance sampling) resulted in unbiased and precise parameter estimates as long as data were MCAR or MAR. When the observation data are MNAR, a proper method for handling the missing data has to be applied to obtain unbiased and precise parameter estimates, independent on estimation algorithm.

The evaluation of different methods for handling missing covariate data showed that a correctly implemented multiple imputations method and full maximum likelihood modelling methods resulted in unbiased and precise parameter estimates when covariate data were MCAR or MAR. When the covariate data were MNAR, the only method resulting in unbiased and precise parameter estimates was a full maximum likelihood modelling method where an extra parameter was estimated, correcting for the unknown missing data mechanism's dependence on the missing data.

This thesis presents new insight to the dynamics of missing data in nonlinear mixed effects modelling. Strategies for handling different types of missing data have been developed and compared in order to provide guidance for efficient handling and consequences of inappropriate handling of missing data.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2014. 75 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 189
Keyword
Pharmacometrics, population models, censored observations, missing covariates, missing dependent variable, missing data mechanism, missing completely at random (MCAR), missing at random (MAR), missing not at random (MNAR), estimation algorithms
National Category
Pharmaceutical Sciences
Research subject
Pharmaceutical Science
Identifiers
urn:nbn:se:uu:diva-224098 (URN)978-91-554-8970-0 (ISBN)
Public defence
2014-08-29, B41, BMC, Husargatan 3, Uppsala, 09:15 (English)
Opponent
Supervisors
Available from: 2014-05-27 Created: 2014-05-03 Last updated: 2014-06-30Bibliographically approved

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Johansson, Åsa M.Karlsson, Mats O.

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