For external model evaluation, prediction distribution errors are recommended when the aim is to use the model to simulate data. Metrics through hyperparameters should be preferred when the aim is to compare two populations and metrics based on the objective function are useful during the model building process.
Model evaluation is an important issue in population analyses. We aimed to perform a systematic review of all population pharmacokinetic and/or pharmacodynamic analyses published between 2002 and 2004 to survey the current methods used to evaluate models and to assess whether those models were adequately evaluated. We selected 324 articles in MEDLINE using defined key words and built a data abstraction form composed of a checklist of items to extract the relevant information from these articles with respect to model evaluation. In the data abstraction form, evaluation methods were divided into three subsections: basic internal methods (goodness-of-fit [GOF] plots, uncertainty in parameter estimates and model sensitivity), advanced internal methods (data splitting, resampling techniques and Monte Carlo simulations) and external model evaluation. Basic internal evaluation was the most frequently described method in the reports: 65% of the models involved GOF evaluation. Standard errors or confidence intervals were reported for 50% of fixed effects but only for 22% of random effects. Advanced internal methods were used in approximately 25% of models: data splitting was more often used than bootstrap and cross-validation; simulations were used in 6% of models to evaluate models by a visual predictive check or by a posterior predictive check. External evaluation was performed in only 7% of models. Using the subjective synthesis of model evaluation for each article, we judged the models to be adequately evaluated in 28% of pharmacokinetic models and 26% of pharmacodynamic models. Basic internal evaluation was preferred to more advanced methods, probably because the former is performed easily with most software. We also noticed that when the aim of modelling was predictive, advanced internal methods or more stringent methods were more often used.
This study shows that ivabradine exerts a dose-dependent bradycardic effect and that its N-dealkylated metabolite contributes to this bradycardic effect.
What is already known about this subject • The reviews already published on population pharmacokinetic/pharmacodynamic (PK/PD) analyses have focused on theory and have presented some clinical applications, evaluated validation practices in limited circumstances, defined the interest and sometimes the complexity of this approach in drug development or proposed a list of relevant articles.• None of them has exhaustively evaluated published analyses and more precisely the model-building steps.• In view of the statistical complexity of population PK/PD methodology, more attention is required to how models are built and how they are reported in the literature. What this study adds• With a strict methodology and by establishing a standardized tool, this survey provides an exhaustive, objective and up-to-date review of model-building practices.• It reveals deficiencies in information reporting in most articles and the genuine need for guidance in publishing.• An initial, minimal list of items is suggested, which can be used by authors and reviewers in pharmacology journals.• The value of published peer-reviewed papers could be greatly improved if authors were to address the suggested list of items systematically. MethodsWe selected 324 articles in Pubmed using defined keywords. A data abstraction form (DAF) was then built comprising two parts: general characteristics including article identification, context of the analysis, description of clinical studies from which the data arose, and model building, including description of the processes of modelling. The papers were examined by two readers, who extracted the relevant information and transmitted it directly to a MySQL database, from which descriptive statistical analysis was performed. ResultsMost published papers concerned patients with severe pathology and therapeutic classes suffering from narrow therapeutic index and/or high PK/PD variability. Most of the time, modelling was performed for descriptive purposes, with rich rather than sparse data and using NONMEM software. PK and PD models were rarely complex (one or two compartments for PK; Emax for PD models). Covariate testing was frequently performed and essentially based on the likelihood ratio test. Based on a minimal list of items that should systematically be found in a population PK-PD analysis, it was found that only 39% and 8.5% of the PK and PD analyses, respectively, published from 2002 to 2004 provided sufficient detail to support the model-building methodology. ConclusionsThis survey allowed an efficient description of recent published population analyses, but also revealed deficiencies in reporting information on model building.
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