uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Methodology for Handling Missing Data in Nonlinear Mixed Effects Modelling
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences. (Farmakometri, Pharmacometrics)
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 [en]
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: urn:nbn:se:uu:diva-224098ISBN: 978-91-554-8970-0 (print)OAI: oai:DiVA.org:uu-224098DiVA: diva2:715330
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
List of papers
1. A Population Pharmacokinetic/Pharmacodynamic Model of Methotrexate and Mucositis Scores in Osteosarcoma
Open this publication in new window or tab >>A Population Pharmacokinetic/Pharmacodynamic Model of Methotrexate and Mucositis Scores in Osteosarcoma
Show others...
2011 (English)In: Therapeutic Drug Monitoring, ISSN 0163-4356, E-ISSN 1536-3694, Vol. 33, no 6, 711-718 p.Article in journal (Refereed) Published
Abstract [en]

Methotrexate, when used in high doses (12 g/m(2)) in the treatment of osteosarcoma, shows wide between-subject variability (BSV) in its pharmacokinetics. High-dose methotrexate is associated with severe toxicity; therefore, therapeutic drug monitoring (TDM) is carried out to guide rescue therapy and monitor for nephrotoxicity. Mucositis is a commonly encountered dose-limiting toxicity that often leads to delays in subsequent courses of chemotherapy. This, in turn, results in a reduction in the dosing intensity, which is essential in the treatment of osteosarcoma. The aims of this study were to develop a population pharmacokinetic (PK) model from TDM using physiologically relevant covariates and to investigate the correlation between mucositis scores and methotrexate pharmacokinetics. In total, 46 osteosarcoma patients (30 men and 16 women; age, 4-51 years) were recruited, and blood samples were collected for routine TDM once every 24 hours. Mucositis scores, graded according to the National Cancer Institute Common Toxicity Criteria, were recorded for 28 of the patients (18 men and 10 women; age, 8-51 years) predose and postdose. A population PK model was developed in NONMEM VI. A 2-compartment PK model was chosen, and clearance (CL) was divided into filtration and secretion/metabolism components. All parameters were scaled with body weight, and, in addition, total CL was scaled with age-and sex-adjusted serum creatinine. Between-subject variability was modeled for all parameters, and betweenoccasion variability was included in CL. For a typical 70 kg man of 18 years or older, the parameter estimates for the final model were CL(filt) = 2.69 L/h/70 kg, CL(sec) = 10.9 L/h/70 kg, V(1) = 74.3 L/70 kg, Q = 0.110 L/h/70 kg, and V(2) = 4.10 L/70 kg. Sequential pharmacodynamic modeling consisted of mucositis scores as 5-point ordered categorical data. A significant linear relationship between individual area under the curve (AUC) and mucositis score probability was found, and the probability of having mucositis score >= 1 increased with increasing AUC and was almost 50% at the average cumulative AUC after 2 consecutive methotrexate doses.

Keyword
methotrexate, osteosarcoma, mucositis, NONMEM, pharmacokinetics/pharmacodynamics, therapeutic drug monitoring
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:uu:diva-165678 (URN)10.1097/FTD.0b013e31823615e1 (DOI)000297318200008 ()
Available from: 2012-01-10 Created: 2012-01-09 Last updated: 2017-12-08Bibliographically approved
2. Evaluation of Bias, Precision, Robustness and Runtime for Estimation Methods in NONMEM 7
Open this publication in new window or tab >>Evaluation of Bias, Precision, Robustness and Runtime for Estimation Methods in NONMEM 7
Show others...
2014 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 41, no 3, 223-238 p.Article in journal (Refereed) Published
Abstract [en]

NONMEM is the most widely used software for population pharmacokinetic (PK)-pharmacodynamic (PD) analyses. The latest version, NONMEM 7 (NM7), includes several sampling-based estimation algorithms in addition to the classical algorithms. In this study, performance of the estimation algorithms available in NM7 was investigated with respect to bias, precision, robustness and runtime for a diverse set of PD models. Simulations of 500 data sets from each PD model were reanalyzed with the available estimation algorithms to investigate bias and precision. Simulations of 100 data sets were used to investigate robustness by comparing final estimates obtained after estimations starting from the true parameter values and initial estimates randomly generated using the CHAIN feature in NM7. Average estimation time for each algorithm and each model was calculated from the runtimes reported by NM7.

The algorithm giving the lowest bias and highest precision across models was importance sampling (IMP), closely followed by FOCE/LAPLACE and stochastic approximation expectation-maximization (SAEM). The algorithms relative robustness differed between models, but FOCE/LAPLACE was the most robust algorithm across models, followed by SAEM and IMP. FOCE/LAPLACE was also the algorithm with the shortest runtime for all models, followed by iterative two-stage (ITS). The Bayesian Markov Chain Monte Carlo method, used in this study for point estimation, performed worst in all tested metrics.

Keyword
NONMEM, estimation algorithms
National Category
Pharmaceutical Sciences
Research subject
Pharmaceutical Science
Identifiers
urn:nbn:se:uu:diva-216136 (URN)10.1007/s10928-014-9359-z (DOI)000338496300003 ()24801864 (PubMedID)
Available from: 2014-01-19 Created: 2014-01-19 Last updated: 2017-12-06Bibliographically approved
3. The Impact of Censored Observations on Model Fit and Structural Model Discrimination in Nonlinear Mixed Effects Modelling when using Different Estimation Algorithms
Open this publication in new window or tab >>The Impact of Censored Observations on Model Fit and Structural Model Discrimination in Nonlinear Mixed Effects Modelling when using Different Estimation Algorithms
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Missing data due to censored observations is a common problem in nonlinear mixed effects modelling of clinical data. The aim of this study was to investigate how the estimated model parameters and the discrimination of correct structural model were affected by different patterns of censored observations and to investigate if there were any differences in these statistics when using different estimation algorithms to fit the models. Simulations generated data for 400 individuals with six observations per individual using a one-compartment model. Observations (62%) were censored according to three different missing data mechanisms. A one-compartment and a two-compartment model were fitted to the data using six different estimation algorithms.The performance of the algorithms was evaluated in a stochastic simulations and estimations study where 200 data sets were simulated. The algorithms were compared according to bias and precision of parameter estimates and according to the type I error rate in the evaluation of structural model. The EM algorithms, especially the importance sampling algorithms (IMP and IMPMAP), gave unbiased and precise parameter estimates as long as data were missing completely at random or missing at random, while the gradient based algorithms (especially FO and FOCE) experienced some problems with biased estimates under these missing data mechanisms. The type I error rate was not elevated when using any of the algorithms as long as the missing data mechanism was not missing not at random.

Keyword
missing data, missing dependent variable, missing completely at random (MCAR), missing at random (MAR), missing not at random (MNAR), bias, precision, type I error
National Category
Pharmaceutical Sciences
Identifiers
urn:nbn:se:uu:diva-224097 (URN)
Available from: 2014-05-03 Created: 2014-05-03 Last updated: 2014-06-30
4. Multiple Imputation of Missing Covariates in NONMEM and Evaluation of the Method's Sensitivity to eta-Shrinkage
Open this publication in new window or tab >>Multiple Imputation of Missing Covariates in NONMEM and Evaluation of the Method's Sensitivity to eta-Shrinkage
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.

Keyword
covariates, missing data, multiple imputation, NONMEM
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:uu:diva-210182 (URN)10.1208/s12248-013-9508-0 (DOI)000325126300014 ()
Available from: 2013-11-04 Created: 2013-11-04 Last updated: 2017-12-06Bibliographically approved
5. Comparison of Methods for Handling Missing Covariate Data
Open this publication in new window or tab >>Comparison of Methods for Handling Missing Covariate Data
2013 (English)In: AAPS Journal, ISSN 1550-7416, E-ISSN 1550-7416, Vol. 15, no 4, 1232-1241 p.Article in journal (Refereed) Published
Abstract [en]

Missing covariate data is a common problem in nonlinear mixed effects modelling of clinical data. The aim of this study was to implement and compare methods for handling missing covariate data in nonlinear mixed effects modelling under different missing data mechanisms. Simulations generated data for 200 individuals with a 50% difference in clearance between males and females. Three different types of missing data mechanisms were simulated and information about sex was missing for 50% of the individuals. Six methods for handling the missing covariate were compared in a stochastic simulations and estimations study where 200 data sets were simulated. The methods were compared according to bias and precision of parameter estimates. Multiple imputation based on weight and response, full maximum likelihood modelling using information on weight and full maximum likelihood modelling where the proportion of males among the individuals lacking information about sex was estimated (EST) gave precise and unbiased estimates in the presence of missing data when data were missing completely at random or missing at random. When data were missing not at random, the only method resulting in low bias and high parameter precision was EST.

Keyword
categorical data, covariates, missing data, NONMEM
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:uu:diva-210183 (URN)10.1208/s12248-013-9526-y (DOI)000325126300034 ()
Available from: 2013-11-04 Created: 2013-11-04 Last updated: 2017-12-06Bibliographically approved

Open Access in DiVA

fulltext(7082 kB)808 downloads
File information
File name FULLTEXT01.pdfFile size 7082 kBChecksum SHA-512
0a24496f71e0e363c375ab14b8d5c605b7cae083ba5dd9d35bfdaec30f535b2183bab487ed77367ee35dbc10a768315d2dd1e4ee427e608d5a816dbbd8924c0a
Type fulltextMimetype application/pdf
Buy this publication >>

Authority records BETA

Johansson, Åsa M.

Search in DiVA

By author/editor
Johansson, Åsa M.
By organisation
Department of Pharmaceutical Biosciences
Pharmaceutical Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 808 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 1227 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf