Change search
ReferencesLink to record
Permanent link

Direct link
Pharmacometric Methods and Novel Models for Discrete Data
Uppsala University, Disciplinary Domain of Medicine and Pharmacy, Faculty of Pharmacy, Department of Pharmaceutical Biosciences.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Pharmacodynamic processes and disease progression are increasingly characterized with pharmacometric models. However, modelling options for discrete-type responses remain limited, although these response variables are commonly encountered clinical endpoints. Types of data defined as discrete data are generally ordinal, e.g. symptom severity, count, i.e. event frequency, and time-to-event, i.e. event occurrence. Underlying assumptions accompanying discrete data models need investigation and possibly adaptations in order to expand their use. Moreover, because these models are highly non-linear, estimation with linearization-based maximum likelihood methods may be biased.

The aim of this thesis was to explore pharmacometric methods and novel models for discrete data through (i) the investigation of benefits of treating discrete data with different modelling approaches, (ii) evaluations of the performance of several estimation methods for discrete models, and (iii) the development of novel models for the handling of complex discrete data recorded during (pre-)clinical studies.

A simulation study indicated that approaches such as a truncated Poisson model and a logit-transformed continuous model were adequate for treating ordinal data ranked on a 0-10 scale. Features that handled serial correlation and underdispersion were developed for the models to subsequently fit real pain scores. The performance of nine estimation methods was studied for dose-response continuous models. Other types of serially correlated count models were studied for the analysis of overdispersed data represented by the number of epilepsy seizures per day. For these types of models, the commonly used Laplace estimation method presented a bias, whereas the adaptive Gaussian quadrature method did not. Count models were also compared to repeated time-to-event models when the exact time of gastroesophageal symptom occurrence was known. Two new model structures handling repeated time-to-categorical events, i.e. events with an ordinal severity aspect, were introduced. Laplace and two expectation-maximisation estimation methods were found to be performing well for frequent repeated time-to-event models.

In conclusion, this thesis presents approaches, estimation methods, and diagnostics adapted for treating discrete data. Novel models and diagnostics were developed when lacking and applied to biological observations.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis , 2011. , 80 p.
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Pharmacy, ISSN 1651-6192 ; 145
Keyword [en]
Pharmacometrics, pharmacodynamics, disease progression, modelling, discrete data, count, ordered categorical, repeated time-to-event, RTTCE, RCEpT, NONMEM, FOCE, LAPLACE, SAEM, AGQ, pain scores, epilepsy seizures, gastroesophageal symptoms, statistical power, simulations, diagnostics
National Category
Pharmaceutical Sciences
Research subject
Pharmacokinetics and Drug Therapy
Identifiers
URN: urn:nbn:se:uu:diva-150929ISBN: 978-91-554-8064-6OAI: oai:DiVA.org:uu-150929DiVA: diva2:409333
Public defence
2011-05-20, B41, BMC, Husargatan 3, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2011-04-28 Created: 2011-04-07 Last updated: 2011-05-05Bibliographically approved
List of papers
1. Approaches to Likert-type Ordered Categorical Data Analysis
Open this publication in new window or tab >>Approaches to Likert-type Ordered Categorical Data Analysis
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Purpose: Ordinal variables are common pharmacodynamic responses, but when the number of categories reaches 11, current approaches to fit this type of data may not be suitable. This article aims at exploring modeling approach candidates for 11-point ordered categorical data.

Methods: The study consisted of two sets of 100 stochastic simulations and estimations in NONMEM VI. A first set was generated with a baseline response ordered categorical model, whose parameter values were derived from a real case study with 100 observations on average per individual. A second set included a linear drug effect observed in a 4 parallel dose arm treatment trial. Simulated data were analyzed with an ordered categorical (OC), a truncated generalized Poisson (PO), and a logit-transformed continuous (CO) models.

Results: The dose-response OC model needed 13 parameters, compared to 7 and 6 with the other models. Score distributions were closely mimicked by OC resimulations at all dose levels. The agreement with PO resimulated scores was best at low doses, in contrast to CO showing less discrepancy at high doses.

Conclusions: Truncated count (PO) or logit-transformed continuous (CO) models may be alternatives to ordered categorical models for Likert scores in case of sparse data or in presence of serial correlations.

 

Keyword
Ordered categorical, count, Poisson, continuous, Likert, scale, score, NONMEM, power
National Category
Pharmaceutical Sciences
Identifiers
urn:nbn:se:uu:diva-150922 (URN)
Available from: 2011-04-07 Created: 2011-04-07 Last updated: 2013-08-20
2. 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, 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.

Keyword
Nonlinear Mixed Effects Models, Maximum Likelihood Estimation, FOCE, Laplace, adaptive gaussian quadrature, SAEM
National Category
Medical and Health Sciences
Identifiers
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: 2013-12-09Bibliographically approved
3. Likert Pain Scores Modeling: A Markov Integer Model and an Autoregressive Continuous Model
Open this publication in new window or tab >>Likert Pain Scores Modeling: A Markov Integer Model and an Autoregressive Continuous Model
Show others...
2012 (English)In: Clinical Pharmacology and Therapeutics, ISSN 0009-9236, E-ISSN 1532-6519, Vol. 91, no 5, 820-828 p.Article in journal (Refereed) Published
Abstract [en]

Pain intensity is principally assessed using rating scales such as the 11-point Likert scale. In general, frequent pain assessments are serially correlated and underdispersed. The aim of this investigation was to develop population models adapted to fit the 11-point pain scale. Daily Likert scores were recorded over 18 weeks by 231 patients with neuropathic pain from a clinical trial placebo group. An integer model consisting of a truncated generalized Poisson (GP) distribution with Markovian transition probability inflation was implemented in NONMEM 7.1.0. It was compared to a logit-transformed autoregressive continuous model with correlated residual errors. In both models, the score baseline was estimated to be 6.2 and the placebo effect to be 19%. Developed models similarly retrieved consistent underlying features of the data and therefore correspond to platform models for drug effect detection. The integer model was complex but flexible, whereas the continuous model can more easily be developed, although requires longer runtimes.

 

Keyword
Pain, Likert, Score, Poisson, Markov, Underdispersion, Correlation, Placebo, NONMEM
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:uu:diva-150926 (URN)10.1038/clpt.2011.301 (DOI)000303047400015 ()
Available from: 2011-04-07 Created: 2011-04-07 Last updated: 2012-05-28Bibliographically approved
4. Modelling overdispersion and Markovian features in count data.
Open this publication in new window or tab >>Modelling overdispersion and Markovian features in count data.
2009 (English)In: Journal of Pharmacokinetics and Pharmacodynamics, ISSN 1567-567X, E-ISSN 1573-8744, Vol. 36, no 5, 461-477 p.Article in journal (Refereed) Published
Abstract [en]

The number of counts (events) per unit of time is a discrete response variable that is generally analyzed with the Poisson distribution (PS) model. The PS model makes two assumptions: the mean number of counts (lambda) is assumed equal to the variance, and counts occurring in non-overlapping intervals are assumed independent. However, many counting outcomes show greater variability than predicted by the PS model, a phenomenon called overdispersion. The purpose of this study was to implement and explore, in the population context, different distribution models accounting for overdispersion and Markov patterns in the analysis of count data. Daily seizures count data obtained from 551 subjects during the 12-week screening phase of a double-blind, placebo-controlled, parallel-group multicenter study performed in epileptic patients with medically refractory partial seizures, were used in the current investigation. The following distribution models were fitted to the data: PS, Zero-Inflated PS (ZIP), Negative Binomial (NB), and Zero-Inflated Negative Binomial (ZINB) models. Markovian features were introduced estimating different lambdas and overdispersion parameters depending on whether the previous day was a seizure or a non-seizure day. All analyses were performed with NONMEM VI. All models were successfully implemented and all overdispersed models improved the fit with respect to the PS model. The NB model resulted in the best description of the data. The inclusion of Markovian features in lambda and in the overdispersion parameter improved the fit significantly (P < 0.001). The plot of the variance versus mean daily seizure count profiles, and the number of transitions, are suggested as model performance tools reflecting the capability to handle overdispersion and Markovian features, respectively.

Keyword
Count data, population pharmacodynamic modelling, NONMEM, epilepsy, Gabapentin
National Category
Pharmaceutical Sciences
Identifiers
urn:nbn:se:uu:diva-122144 (URN)10.1007/s10928-009-9131-y (DOI)000271673000005 ()19798550 (PubMedID)
Available from: 2010-04-06 Created: 2010-04-06 Last updated: 2013-08-20Bibliographically approved
5. 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.

Keyword
NONMEM, LAPLACE, Laplacian approximation, SAS, Gaussian quadrature, Maximum likelihood approximation, Count data, Poisson model
National Category
Pharmaceutical Sciences
Identifiers
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
6. Modeling longitudinal daily seizure frequency data from pregabalin add-on treatment
Open this publication in new window or tab >>Modeling longitudinal daily seizure frequency data from pregabalin add-on treatment
2012 (English)In: Journal of clinical pharmacology, ISSN 0091-2700, E-ISSN 1552-4604, Vol. 52, no 6, 880-892 p.Article in journal (Refereed) Published
Abstract [en]

The purpose of this study was to describe longitudinal daily seizure count data with respect to the effects of time and pregabalin add-on therapy. Models were developed in step-wise manner: base model, time effect model, and time and drug effect (final) model, using a negative binomial distribution with Markovian features. Mean daily seizure count (λ) was estimated to be 0.385 (RSE 3.09%) and was further increased depending on the seizure count on the previous day. An overdispersion parameter (OVDP), representing extra-Poisson variation, was estimated to be 0.330 (RSE 11.7%). Inter-individual variances on λ and OVDP were 84.7% and 210%, respectively. Over time, λ tended to increase exponentially with a rate constant of 0.272 year-1 (RSE 26.8%). A mixture model was applied to classify responders/non-responders to pregabalin treatment. Within the responders, λ decreased exponentially with respect to dose with a constant of 0.00108 mg-1 (RSE 11.9%). The estimated responder rate was 66% (RSE 27.6%). Simulation-based diagnostics showed the model reasonably reproduced the characteristics of observed data. Highly variable daily seizure frequency was successfully characterized incorporating baseline characteristics, time effect, and the effect of pregabalin with classification of responders/non-responders, all of which are necessary to adequately assess the efficacy of antiepileptic drugs.

 

Keyword
Count data, negative binomial distribution, pregabalin, epilepsy, NONMEM 7
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:uu:diva-150927 (URN)10.1177/0091270011407193 (DOI)000304228900010 ()21646441 (PubMedID)
Available from: 2011-04-07 Created: 2011-04-07 Last updated: 2012-06-18Bibliographically approved
7. Transient Lower Esophageal Sphincter Relaxations PKPD Modeling: Count Model and Repeated Time-To-Event Model
Open this publication in new window or tab >>Transient Lower Esophageal Sphincter Relaxations PKPD Modeling: Count Model and Repeated Time-To-Event Model
Show others...
2011 (English)In: Journal of Pharmacology and Experimental Therapeutics, ISSN 0022-3565, E-ISSN 1521-0103Article in journal (Refereed) Published
Abstract [en]

Transient lower esophageal sphincter relaxation (TLESR) is the major mechanism for gastro-esophageal reflux. Characterization of candidate compounds for reduction of TLESRs are traditionally done through summary exposure and response measures and would benefit from model-based analyses of exposure-TLESR events relationships. PKPD modeling approaches treating TLESR either as count data or as repeated time-to-event (RTTE) data were developed and compared in terms of ability to characterize system and drug characteristics. Vehicle data comprising 294 TLESR events were collected from 9 dogs. Compound (WIN55251-2) data containing 66 TLESR events, as well as plasma concentrations, were obtained from 4 dogs. Each experiment lasted for 45min and was initiated with a meal. Counts in equispaced 5-min intervals and 1-min intervals were modeled based on a Poisson probability distribution model. TLESR events were analyzed with the RTTE model. PK was connected to PD models with a 1-compartment model. Vehicle data were described by a baseline and a surge function; the surge peak was determined around 9.69min by all approaches and its width of 5min (1-min count and RTTE) or 10min (5-min count). TLESRs inhibition by WIN55251-2 was described by an Imax model, with an IC50 of on average 2.39nmol.L-1. Modeling approaches utilizing count or RTTE data linked to a dynamic PKPD representation of exposure is superior to using summary PK and PD measures. Differences in terms of predictions and power to detect a significant drug effect are illustrated with a simulation-based investigation, and a range of diagnostics for such modeling approaches is presented.

 

Keyword
PKPD, pharmacokinetic-pharmacodynamic, TLESR, Transient lower esophageal sphincter relaxation, RTTE, repeated time-to-event
National Category
Medical and Health Sciences
Identifiers
urn:nbn:se:uu:diva-150928 (URN)10.1124/jpet.111.181636 (DOI)000297267800016 ()21890509 (PubMedID)
Note
E.L.P. and G.M. are two equally-contributing first authorsAvailable from: 2011-04-07 Created: 2011-04-07 Last updated: 2011-12-21Bibliographically approved
8. Performance of three estimation methods in repeated time-to-event modeling
Open this publication in new window or tab >>Performance of three estimation methods in repeated time-to-event modeling
2011 (English)In: AAPS Journal, ISSN 1550-7416, Vol. 13, no 1, 83-91 p.Article in journal (Refereed) Published
Abstract [en]

It is not uncommon that the outcome measurements, symptoms or side effects, of a clinical trial belong to the family of event type data, e.g., bleeding episodes or emesis events. Event data is often low in information content and the mixed-effects modeling software NONMEM has previously been shown to perform poorly with low information ordered categorical data. The aim of this investigation was to assess the performance of the Laplace method, the stochastic approximation expectation-maximization (SAEM) method, and the importance sampling method when modeling repeated time-to-event data. The Laplace method already existed, whereas the two latter methods have recently become available in NONMEM 7. A stochastic simulation and estimation study was performed to assess the performance of the three estimation methods when applied to a repeated time-to-event model with a constant hazard associated with an exponential interindividual variability. Various conditions were investigated, ranging from rare to frequent events and from low to high interindividual variability. The method performance was assessed by parameter bias and precision. Due to the lack of information content under conditions where very few events were observed, all three methods exhibit parameter bias and imprecision, however most pronounced by the Laplace method. The performance of the SAEM and importance sampling were generally higher than Laplace when the frequency of individuals with events was less than 43%, while at frequencies above that all methods were equal in performance.

Keyword
importance sampling, Laplace, mixed-effects modeling, NONMEM, repeated time-toevent, SAEM
National Category
Pharmaceutical Sciences
Identifiers
urn:nbn:se:uu:diva-132775 (URN)10.1208/s12248-010-9248-3 (DOI)000290204800009 ()21229340 (PubMedID)
Available from: 2010-11-01 Created: 2010-10-26 Last updated: 2011-05-26Bibliographically approved
9. Approaches to simultaneous analysis of frequency and severity of symptoms
Open this publication in new window or tab >>Approaches to simultaneous analysis of frequency and severity of symptoms
2010 (English)In: Clinical Pharmacology and Therapeutics, ISSN 0009-9236, E-ISSN 1532-6519, Vol. 88, no 2, 255-259 p.Article in journal (Refereed) Published
Abstract [en]

Mechanistic models that synthesize pharmacological and (patho) physiological process information provide a rich basis for the characterization of drug action. However, the underlying clinical data are often simplified in a manner that does not allow models to fully elucidate the structure of the drug effect. In this article, we describe data-simplification strategies that are in routine use to describe disease symptoms and compare them with a model developed for handling the true complexities of the data.

National Category
Pharmaceutical Sciences
Identifiers
urn:nbn:se:uu:diva-132773 (URN)10.1038/clpt.2010.118 (DOI)000280147500025 ()20613722 (PubMedID)
Available from: 2010-10-26 Created: 2010-10-26 Last updated: 2013-12-09Bibliographically approved

Open Access in DiVA

inside(4666 kB)496 downloads
File information
File name INSIDE01.pdfFile size 4666 kBChecksum SHA-512
0ac2bb9aed51ea5750176112be75fad3fb657a2e4bf15a4153bf47fafa1459960b046bba10654cceb18d9f7af71cad5fb5a63959e7958754e5d5c9565185443e
Type insideMimetype application/pdf
cover(64 kB)45 downloads
File information
File name COVER01.pdfFile size 64 kBChecksum SHA-512
607a6fa4f251a6e3d571d8decb91dc43d83a9a42d96211ce3d1259880c3c10ef95ad658f5e55b2e243aa6de3f455035e2209a464ff134dee62bd19489e704ab3
Type coverMimetype application/pdf
fulltext(3812 kB)1864 downloads
File information
File name FULLTEXT01.pdfFile size 3812 kBChecksum SHA-512
23f108963fd8239726228ff0b3638089376149b76457912add9cf179908d8673d615457ec97ea2ae4b017fc98b77cc3bfec668139f32c6362744fa63ff4e03bb
Type fulltextMimetype application/pdf
Buy this publication >>

By organisation
Department of Pharmaceutical Biosciences
Pharmaceutical Sciences

Search outside of DiVA

GoogleGoogle Scholar
Total: 1864 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

Total: 824 hits
ReferencesLink to record
Permanent link

Direct link