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Optimal (Adaptive) Design and Estimation Performance in Pharmacometric Modelling
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The pharmaceutical industry now recognises the importance of the newly defined discipline of pharmacometrics. Pharmacometrics uses mathematical models to describe and then predict the performance of new drugs in clinical development. To ensure these models are useful, the clinical studies need to be designed such that the data generated allows the model predictions to be sufficiently accurate and precise. The capability of the available software to reliably estimate the model parameters must also be well understood. 

This thesis investigated two important areas in pharmacometrics: optimal design and software estimation performance. The three optimal design papers progressed significant areas of optimal design research, especially relevant to phase II dose response designs. The use of exposure, rather than dose, was investigated within an optimal design framework. In addition to using both optimal design and clinical trial simulation, this work employed a wide range of metrics for assessing design performance, and was illustrative of how optimal designs for exposure response models may yield dose selections quite different to those based on standard dose response models. The investigation of the optimal designs for Poisson dose response models demonstrated a novel mathematical approach to the necessary matrix calculations for non-linear mixed effects models. Finally, the enormous potential of using optimal adaptive designs over fixed optimal designs was demonstrated. The results showed how the adaptive designs were robust to initial parameter misspecification, with the capability to "learn" the true dose response using the accruing subject data. The two estimation performance papers investigated the relative performance of a number of different algorithms and software programs for two complex pharmacometric models.

In conclusion these papers, in combination, cover a wide spectrum of study designs for non-linear dose/exposure response models, covering: normal/non-normal data, fixed/mixed effect models, single/multiple design criteria metrics, optimal design/clinical trial simulation, and adaptive/fixed designs. 

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2012. , 76 p.
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 166
Keyword [en]
Phase II, dose response, optimal design, adaptive design, exposure response, count data
National Category
Pharmaceutical Sciences
URN: urn:nbn:se:uu:diva-182284ISBN: 978-91-554-8491-0 (print)OAI: diva2:559324
Public defence
2012-11-30, B41, Biomedicinskt Centrum, Husargatan 3, Uppsala, 09:15 (English)
Available from: 2012-11-02 Created: 2012-10-08 Last updated: 2013-01-23Bibliographically approved
List of papers
1. Optimal adaptive design in clinical drug development: a simulation example
Open this publication in new window or tab >>Optimal adaptive design in clinical drug development: a simulation example
2007 (English)In: Journal of clinical pharmacology, ISSN 0091-2700, E-ISSN 1552-4604, Vol. 47, no 10, 1231-1243 p.Article in journal (Refereed) Published
Abstract [en]

The objective of this article is to demonstrate optimal adaptive design as a methodology for improving the performance of phase II dose-response studies. Optimal adaptive design uses both information prior to the study and data accrued during the study to continuously update and refine the study design. Dose-response models include linear, log-linear, 4-parameter sigmoidal E-max, and exponential models. Where the response has both a placebo effect and plateau at higher doses, only the 4-parameter sigmoidal E-max model behaves acceptably and hence is used to illustrate the methodology. Across 13 hypothetical dose-response scenarios considered, it was shown that the capability of the adaptive designs to "learn" the true dose response resulted in performances up to 180% more efficient than the best fixed optimal designs, This work exposes the common misconception that adaptive designs are somehow "risky." As shown in this simple simulation example, the converse is true. Adaptive designs perform extremely well both when prior information is accurate and inaccurate. This leads to improved dose-response models and dose selection in phase III. This benefits sponsors, regulators, and subjects alike by reducing sample size, increasing information, and providing better dose guidance.

adaptive, optimal, E-max, phase II, dose response
National Category
Pharmaceutical Sciences
urn:nbn:se:uu:diva-13503 (URN)10.1177/0091270007308033 (DOI)000249872700002 ()17906158 (PubMedID)
Available from: 2008-01-23 Created: 2008-01-23 Last updated: 2017-12-11Bibliographically approved
2. Performance in population models for count data, part I: maximum likelihood approximations.
Open this publication in new window or tab >>Performance in population models for count data, part I: maximum likelihood approximations.
2009 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 36, no 4, 353-366 p.Article in journal (Refereed) Published
Abstract [en]

There has been little evaluation of maximum likelihood approximation methods for non-linear mixed effects modelling of count data. The aim of this study was to explore the estimation accuracy of population parameters from six count models, using two different methods and programs. Simulations of 100 data sets were performed in NONMEM for each probability distribution with parameter values derived from a real case study on 551 epileptic patients. Models investigated were: Poisson (PS), Poisson with Markov elements (PMAK), Poisson with a mixture distribution for individual observations (PMIX), Zero Inflated Poisson (ZIP), Generalized Poisson (GP) and Negative Binomial (NB). Estimations of simulated datasets were completed with Laplacian approximation (LAPLACE) in NONMEM and LAPLACE/Gaussian Quadrature (GQ) in SAS. With LAPLACE, the average absolute value of the bias (AVB) in all models was 1.02% for fixed effects, and ranged 0.32-8.24% for the estimation of the random effect of the mean count (lambda). The random effect of the overdispersion parameter present in ZIP, GP and NB was underestimated (-25.87, -15.73 and -21.93% of relative bias, respectively). Analysis with GQ 9 points resulted in an improvement in these parameters (3.80% average AVB). Methods implemented in SAS had a lower fraction of successful minimizations, and GQ 9 points was considerably slower than 1 point. Simulations showed that parameter estimates, even when biased, resulted in data that were only marginally different from data simulated from the true model. Thus all methods investigated appear to provide useful results for the investigated count data models.

NONMEM, LAPLACE, Laplacian approximation, SAS, Gaussian quadrature, Maximum likelihood approximation, Count data, Poisson model
National Category
Pharmaceutical Sciences
urn:nbn:se:uu:diva-122145 (URN)10.1007/s10928-009-9126-8 (DOI)000269079600004 ()19653080 (PubMedID)
Available from: 2010-04-06 Created: 2010-04-06 Last updated: 2013-08-20Bibliographically approved
3. An example of optimal phase II design for exposure response modelling
Open this publication in new window or tab >>An example of optimal phase II design for exposure response modelling
Show others...
2010 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 37, no 5, 475-491 p.Article in journal (Refereed) Published
Abstract [en]

This paper presents an example of how optimal design methodology was used to help design a phase II clinical study. The planned analysis would relate the clinical endpoint to exposure (measured via the area under the curve (AUC)), rather than dose. Optimal design methodology was used to compare a number of candidate phase II designs, and an algorithm for finding optimal designs was employed. The sigmoidal E-max with baseline (E-0) model was used to relate the clinical endpoint to individual subject AUCs, and the primary metrics were D optimality and the standard error (SE) of the AUC required to yield a clinically relevant change in the clinical endpoint. The performance of the candidate designs were compared across four different 'true' exposure response relationships (determined from the analysis of an earlier proof of concept (PoC) study). The results suggested the total sample size should be increased from the planned 540 individuals, and that the optimal design with 700 individuals would be equivalent to 812 individuals with the reference design (a 16% gain). The performance with this design was considered acceptable, although all designs performed poorly if the true exposure response relationship was very flat. This work allowed a prospective assessment of the likely performance and precision from the exposure response modelling prior to the start of the phase II study, and hence allowed the design to be revised to ensure the subsequent analysis would be of most value.

Exposure response, Optimal design, E-max model, Phase II clinical trial
National Category
Pharmaceutical Sciences
urn:nbn:se:uu:diva-134140 (URN)10.1007/s10928-010-9168-y (DOI)000282873500002 ()20872056 (PubMedID)
Available from: 2010-11-24 Created: 2010-11-22 Last updated: 2017-12-12Bibliographically approved
4. Performance comparison of various maximum likelihood nonlinear mixed-effects estimation methods for dose-response models
Open this publication in new window or tab >>Performance comparison of various maximum likelihood nonlinear mixed-effects estimation methods for dose-response models
Show others...
2012 (English)In: AAPS Journal, ISSN 1550-7416, E-ISSN 1550-7416, Vol. 14, no 3, 420-432 p.Article in journal (Refereed) Published
Abstract [en]

Estimation methods for nonlinear mixed-effects modelling have considerably improved over the last decades. Nowadays, several algorithms implemented in different software are used. The present study aimed at comparing their performance for dose–response models. Eight scenarios were considered using a sigmoid E max model, with varying sigmoidicity and residual error models. One hundred simulated datasets for each scenario were generated. One hundred individuals with observations at four doses constituted the rich design and at two doses, the sparse design. Nine parametric approaches for maximum likelihood estimation were studied: first-order conditional estimation (FOCE) in NONMEM and R, LAPLACE in NONMEM and SAS, adaptive Gaussian quadrature (AGQ) in SAS, and stochastic approximation expectation maximization (SAEM) in NONMEM and MONOLIX (both SAEM approaches with default and modified settings). All approaches started first from initial estimates set to the true values and second, using altered values. Results were examined through relative root mean squared error (RRMSE) of the estimates. With true initial conditions, full completion rate was obtained with all approaches except FOCE in R. Runtimes were shortest with FOCE and LAPLACE and longest with AGQ. Under the rich design, all approaches performed well except FOCE in R. When starting from altered initial conditions, AGQ, and then FOCE in NONMEM, LAPLACE in SAS, and SAEM in NONMEM and MONOLIX with tuned settings, consistently displayed lower RRMSE than the other approaches. For standard dose–response models analyzed through mixed-effects models, differences were identified in the performance of estimation methods available in current software, giving material to modellers to identify suitable approaches based on an accuracy-versus-runtime trade-off.

Nonlinear Mixed Effects Models, Maximum Likelihood Estimation, FOCE, Laplace, adaptive gaussian quadrature, SAEM
National Category
Medical and Health Sciences
urn:nbn:se:uu:diva-150925 (URN)10.1208/s12248-012-9349-2 (DOI)000305519900006 ()
Available from: 2011-04-07 Created: 2011-04-07 Last updated: 2017-12-11Bibliographically approved
5. D Optimal Designs for Three Poisson Dose-Response Models
Open this publication in new window or tab >>D Optimal Designs for Three Poisson Dose-Response Models
2013 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 40, no 2, 201-211 p.Article in journal (Refereed) Published
Abstract [en]

The objective of this paper was to find and investigate the performance of the D optimal designs for three Poisson dose-response models. Phase II dose ranging studies are pivotal in the drug development program, being used to select dose(s) for phase III. Count data is encountered in a number of clinical areas. The Poisson distribution provides an intuitive platform for modelling such data, especially when combined with random effects which allow subjects to differ in their response rates. This work investigated three Poisson dose-response models of increasing complexity. A simple Emax model was used to describe the drug effect, and D optimal designs under a range of different parameter values (scenarios) were found. The relative performances between scenarios were assessed using: the precision of all parameters, the precision of the drug effect parameters, and the percent coefficient of variation (%CV) of the ED50 parameter. The results showed that the D optimal designs were similar across models and scenarios, with the D optimal designs consisting of placebo, the maximum dose, and a dose just below the ED50. However the relative performance of the optimal designs was very different. For example, with 1000 subjects, the %CV of the ED50 parameter ranged from 1.4% to 91%. Performance typically improved with higher baseline counts, smaller random effects, and larger Emax. This work introduces a framework for determining and evaluating the performance of D optimal designs for phase II dose ranging studies with count data as the primary endpoint.

Place, publisher, year, edition, pages
Springer: , 2013
Poisson, Count, Optimal, Emax model, Phase II, Dose-response
National Category
Pharmaceutical Sciences
urn:nbn:se:uu:diva-182276 (URN)10.1007/s10928-013-9300-x (DOI)000317974200006 ()
Available from: 2012-10-08 Created: 2012-10-08 Last updated: 2017-12-07

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