Non-linear mixed effects modeling - from methodology and software development to driving implementation in drug development science

Advancing pharmacometrics in Africa-Transition from capacity development toward job creation

Trained pharmacometricians remain scarce in Africa due to limited training opportunities, lack of a pharmaceutical product development ecosystem, and emigration to high-income countries. The Applied Pharmacometrics Training (APT) fellowship program was established to address these gaps and specifically foster job creation for talent retention. We review the APT program's progress over 3 years and encourage collaboration to enhance local clinical data analysis in Africa. Initiated in 2021 by Pharmacometrics Africa, a non-profit educational entity, with support from partners including the Bill & Melinda Gates Foundation and Certara, the APT program targets African doctoral-level scientists and clinicians. This 6-month program is jointly managed by partners, with Pharmacometrics Africa handling logistics and sponsor liaison. Job creation initiatives include inviting fellows to join consulting teams or local research centers. Over the 3 year reporting period, 177 applications were received, with 27 individuals (41% female, median age 35 years) from nine African countries selected into and completing the full program. The fellows worked on 13 data analysis projects, with six so far being presented at international conferences and/or submitted for publication in peer-reviewed journals. Nine fellows have joined consulting teams or research centers working from offices in Africa. Currently, in the 3rd year, the APT program has demonstrated success in skills development, job creation, and fostering a critical mass of African pharmacometricians. Collaboration is essential for the sustainable advancement of model-informed drug development in Africa.

Pharmacokinetics and pharmacodynamics of finerenone in patients with chronic kidney disease and type 2 diabetes: Insights based on FIGARO-DKD and FIDELIO-DKD

AIMS

To perform dose-exposure-response analyses to determine the effects of finerenone doses.

MATERIALS AND METHODS

Two randomized, double-blind, placebo-controlled phase 3 trials enrolling 13 026 randomized participants with type 2 diabetes (T2D) from global sites, each with an estimated glomerular filtration rate (eGFR) of 25 to 90 mL/min/1.73 m2 , a urine albumin-creatinine ratio (UACR) of 30 to 5000 mg/g, and serum potassium ≤ 4.8 mmol/L were included. Interventions were titrated doses of finerenone 10 or 20 mg versus placebo on top of standard of care. The outcomes were trajectories of plasma finerenone and serum potassium concentrations, UACR, eGFR and kidney composite outcomes, assessed using nonlinear mixed-effects population pharmacokinetic (PK)/pharmacodynamic (PD) and parametric time-to-event models.

RESULTS

For potassium, lower serum levels and lower rates of hyperkalaemia were associated with higher doses of finerenone 20 mg compared to 10 mg (p < 0.001). The PK/PD model analysis linked this observed inverse association to potassium-guided dose titration. Simulations of a hypothetical trial with constant finerenone doses revealed a shallow but increasing exposure-potassium response relationship. Similarly, increasing finerenone exposures led to less than dose-proportional increasing reductions in modelled UACR. Modelled UACR explained 95% of finerenone's treatment effect in slowing chronic eGFR decline. No UACR-independent finerenone effects were identified. Neither sodium-glucose cotransporter-2 (SGLT2) inhibitor nor glucagon-like peptide-1 receptor agonist (GLP-1RA) treatment significantly modified the effects of finerenone in reducing UACR and eGFR decline. Modelled eGFR explained 87% of finerenone's treatment effect on kidney outcomes. No eGFR-independent effects were identified.

CONCLUSIONS

The analyses provide strong evidence for the effectiveness of finerenone dose titration in controlling serum potassium elevations. UACR and eGFR are predictive of kidney outcomes during finerenone treatment. Finerenone's kidney efficacy is independent of concomitant use of SGLT2 inhibitors and GLP-1RAs.

A tutorial for model-based evaluation and translation of cardiovascular safety in preclinical trials

Assessment of drug-induced effects on the cardiovascular (CV) system remains a critical component of the drug discovery process enabling refinement of the therapeutic index. Predicting potential drug-related unintended CV effects in the preclinical stage is necessary for first-in-human dose selection and preclusion of adverse CV effects in the clinical stage. According to the current guidelines for small molecules, nonclinical CV safety assessment conducted via telemetry analyses should be included in the safety pharmacology core battery studies. However, the manual for quantitative evaluation of the CV safety signals in animals is available only for electrocardiogram parameters (i.e., QT interval assessment), not for hemodynamic parameters (i.e., heart rate, blood pressure, etc.). Various model-based approaches, including empirical pharmacokinetic-toxicodynamic analyses and systems pharmacology modeling could be used in the framework of telemetry data evaluation. In this tutorial, we provide a comprehensive workflow for the analysis of nonclinical CV safety on hemodynamic parameters with a sequential approach, highlight the challenges associated with the data, and propose respective solutions, complemented with a reproducible example. The work is aimed at helping researchers conduct model-based analyses of the CV safety in animals with subsequent translation of the effect to humans seamlessly and efficiently.

A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics

Clinical trials investigate treatment endpoints that usually include measurements of pharmacodynamic and efficacy biomarkers in early-phase studies and patient-reported outcomes as well as event risks or rates in late-phase studies. In recent years, a systematic trend in clinical trial data analytics and modeling has been observed, where retrospective data are integrated into a quantitative framework to prospectively support analyses of interim data and design of ongoing and future studies of novel therapeutics. Joint modeling is an advanced statistical methodology that allows for the investigation of clinical trial outcomes by quantifying the association between baseline and/or longitudinal biomarkers and event risk. Using an exemplar data set from non-small cell lung cancer studies, we propose and test a workflow for joint modeling. It allows a modeling scientist to comprehensively explore the data, build survival models, investigate goodness-of-fit, and subsequently perform outcome predictions using interim biomarker data from an ongoing study. The workflow illustrates a full process, from data exploration to predictive simulations, for selected multivariate linear and nonlinear mixed-effects models and software tools in an integrative and exhaustive manner.

Practical identifiability in the frame of nonlinear mixed effects models: the example of the in vitro erythropoiesis

Background

Nonlinear mixed effects models provide a way to mathematically describe experimental data involving a lot of inter-individual heterogeneity. In order to assess their practical identifiability and estimate confidence intervals for their parameters, most mixed effects modelling programs use the Fisher Information Matrix. However, in complex nonlinear models, this approach can mask practical unidentifiabilities.

Results

Herein we rather propose a multistart approach, and use it to simplify our model by reducing the number of its parameters, in order to make it identifiable. Our model describes several cell populations involved in the in vitro differentiation of chicken erythroid progenitors grown in the same environment. Inter-individual variability observed in cell population counts is explained by variations of the differentiation and proliferation rates between replicates of the experiment. Alternatively, we test a model with varying initial condition.

Conclusions

We conclude by relating experimental variability to precise and identifiable variations between the replicates of the experiment of some model parameters.

Concept and utility of population pharmacokinetic and pharmacokinetic/pharmacodynamic models in drug development and clinical practice

Due to frequent clinical trial failures and consequently fewer new drug approvals, the need for improvement in drug development has, to a certain extent, been met using model-based drug development. Pharmacometrics is a part of pharmacology that quantifies drug behaviour, treatment response and disease progression based on different models (pharmacokinetic - PK, pharmacodynamic - PD, PK/PD models, etc.) and simulations. Regulatory bodies (European Medicines Agency, Food and Drug Administration) encourage the use of modelling and simulations to facilitate decision-making throughout all drug development phases. Moreover, the identification of factors that contribute to variability provides a basis for dose individualisation in routine clinical practice. This review summarises current knowledge regarding the application of pharmacometrics in drug development and clinical practice with emphasis on the population modelling approach.

Clinical pharmacology applications in clinical drug development and clinical care: A focus on Saudi Arabia

Drug development, from preclinical to clinical studies, is a lengthy and complex process. There is an increased interest in the Kingdom of Saudi Arabia (KSA) to promote innovation, research and local content including clinical trials (Phase I-IV). Currently, there are over 650 registered clinical trials in Saudi Arabia, and this number is expected to increase. An important part of drug development and clinical trials is to assure the safe and effective use of drugs. Clinical pharmacology plays a vital role in informed decision making during the drug development stage as it focuses on the effects of drugs in humans. Disciplines such as pharmacokinetics, pharmacodynamics and pharmacogenomics are components of clinical pharmacology. It is a growing discipline with a range of applications in all phases of drug development, including selecting optimal doses for Phase I, II and III studies, evaluating bioequivalence and biosimilar studies and designing clinical studies. Incorporating clinical pharmacology in research as well as in the requirements of regulatory agencies will improve the drug development process and accelerate the pipeline. Clinical pharmacology is also applied in direct patient care with the goal of personalizing treatment. Tools such as therapeutic drug monitoring, pharmacogenomics and model informed precision dosing are used to optimize dosing for patients at an individual level. In KSA, the science of clinical pharmacology is underutilized and we believe it is important to raise awareness and educate the scientific community and healthcare professionals in terms of its applications and potential. In this review paper, we provide an overview on the use and applications of clinical pharmacology in both drug development and clinical care.

Opioids and alpha-2-agonists for analgesia and sedation in newborn infants: protocol of a systematic review

BACKGROUND

Hospitalized newborn infants may require analgesia and sedation either for the management of procedural pain, during or after surgery, and other painful conditions. The benefits and harms of opioids administered at different doses and routes of administration have been reported in numerous trials and systematic reviews. The use of alpha-2-agonists such as clonidine and dexmedetomidine in newborn infants is more recent, and they might be prescribed to reduce the total amount of opioids which are thought to have more side effects. Moreover, alpha-2-agonists might play an important role in the management of agitation and discomfort.

METHODS

We will conduct a systematic review and meta-analysis on the use of opioids, alpha-2-agonists, or the combination of both drugs. We will include randomized controlled trials to assess benefits and harms and observational studies to assess adverse events and pharmacokinetics; preterm and term infants; studies on any opioids or alpha-2-agonists administered for any indication and by any route except spinal, intraosseous, or administration for nerve blocks and wound infusions. The use of opioids or alpha-2-agonists will be compared to no intervention; placebo with normal saline or other non-sedative, non-analgesic drug; control with oral sugar solution or non-pharmacological intervention; same drug of different dose or route; or a different drug (not limiting to opioids and alpha-2-agonists) or combinations of such drugs. The primary outcomes for this review will be all-cause mortality during initial hospitalization and hypotension requiring medical therapy. We will conduct a search in the following databases: The Cochrane Central Register of Controlled Trials (CENTRAL, The Cochrane Library), MEDLINE, Embase, and CINAHL. Two review authors will independently screen records for inclusion, undertake data abstraction using a data extraction form and assess the risk of bias of all included trials using the Cochrane "Risk of bias" tool.

DISCUSSION

This systematic review will summarize and update our knowledge about neonatal analgesia and sedation including pharmacokinetics/pharmacodynamics, and provide a platform for developing evidence-based guidelines that we can immediately apply to our clinical practice.

SYSTEMATIC REVIEW REGISTRATION

PROSPERO 2020 CRD42020170852.

Pharmacokinetic Modeling of Ceftiofur Sodium Using Non-linear Mixed-Effects in Healthy Beagle Dogs

Ceftiofur (CEF) sodium is a third-generation broad-spectrum cephalosporin commonly used in an extra-label manner in dogs for the treatment of respiratory and urinary system infections. To contribute to the literature supporting CEF use in companion animals, we have developed a compartmental, non-linear mixed-effects (NLME) model of CEF pharmacokinetics in dogs (PK). We then used the mathematical model to predict (via Monte Carlo simulation) the duration of time for which plasma concentrations of CEF and its pharmacologically active metabolites remained above minimum inhibitory concentrations (respiratory tract Escherichia coli spp.). Twelve healthy beagle dogs were administered either 2.2 mg/kg ceftiofur-sodium (CEF-Na) intravenously (I.V) or 2.2 mg/kg CEF-Na subcutaneously (S.C). Plasma samples were collected over a period of 72 h post-administration. To produce a measurement of total CEF, both CEF and CEF metabolites were derivatized into desfuroylceftiofur acetamide (DCA) before analysis by UPLC-MS/MS. No adverse effects were reported after I.V or S.C dosing. The NLME PK models were parameterized using the stochastic approximation expectation maximization algorithm as implemented in Monolix 2018R2. A two-compartment mamillary model with first-order elimination and first-order S.C absorption best described the available kinetic data. Final parameter estimates indicate that CEF has a low systemic clearance (0.25 L/h/kg) associated with a low global extraction ratio E = 0.02) and a moderate volume of distribution (2.97 L/kg) in dogs. The absolute bioavailability after S.C administration was high (93.7%). Gender was determined to be a significant covariate in explaining the variability of S.C absorption. Our simulations predicted that a dose of 2.2 mg/kg CEF-Na S.C would produce median plasma concentrations of CEF of at least 0.5 μg/mL (MIC₅₀) for ~30 h.

Individualized Empiric Vancomycin Dosing in Neonates Using a Model-Based Approach

BACKGROUND

Vancomycin dosing in neonates is challenging because of the large variation in pharmacokinetics. Existing empiric dosing recommendations use table-based formats, within which a neonate is categorized on the basis of underlying characteristics. The ability to individualize dosing is limited because of the small number of "dose categories," and achieving narrow exposure targets is difficult. Our objective was to evaluate a model-based dosing approach (which we designated Neo-Vanco) designed to individualize empiric vancomycin dosing in neonates.

METHODS

Neo-Vanco was developed on the basis of a published, externally validated population pharmacokinetic model. Using a simulation-based methodology, individualized empiric doses that maximize the probability of attaining a 24-hour area under the curve/minimum inhibitory concentration ratio (AUC24/MIC) of >400 while minimizing troughs >20 mg/L are calculated. To evaluate the Neo-Vanco strategy, retrospective data from neonates treated with vancomycin at 2 healthcare systems were used, and empiric dose recommendations from the following 4 sources were examined: Neo-Vanco, Neofax, Red Book, and Lexicomp. Predicted AUC24 and troughs were calculated and compared.

RESULTS

Overall, 492 neonates were evaluated (median postmenstrual age, 36 weeks [5th-95th percentiles (90% range), 25-47 weeks]; median weight, 2.4 kg [90% range, 0.6-4.8 kg]). The percentage of neonates predicted to achieve an AUC24/MIC of >400 was 94% with Neo-Vanco, 18% with Neofax, 23% with Red Book, and 55% with Lexicomp (all P < .0001 vs Neo-Vanco). Predicted troughs of >20 mg/L were infrequent and similar across the dosing approaches (Neo-Vanco, 2.8%; Neofax, 1.0% [P = .03]; Red Book, 2.6% [P = .99]; and Lexicomp, 4.1% [P = .27].

CONCLUSION

A model-based dosing approach that individualizes empiric vancomycin dosing was predicted to improve achievement of target exposure levels in neonates. Prospective clinical evaluation is warranted.

Fuzzy Evaluation of Pharmacokinetic Models

Population pharmacokinetic (PopPK) models allow researchers to predict and analyze drug behavior in a population of individuals and to quantify the different sources of variability among these individuals. In the development of PopPK models, the most frequently used method is the nonlinear mixed effect model (NLME). However, once the PopPK model has been developed, it is necessary to determine if the selected model is the best one of the developed models during the population pharmacokinetic study, and this sometimes becomes a multiple criteria decision making (MCDM) problem, and frequently, researchers use statistical evaluation criteria to choose the final PopPK model. The used evaluation criteria mentioned above entail big problems since the selection of the best model becomes susceptible to the human error mainly by misinterpretation of the results. To solve the previous problems, we introduce the development of a software robot that can automate the task of selecting the best PopPK model considering the knowledge of human expertise. The software robot is a fuzzy expert system that provides a method to systematically perform evaluations on a set of candidate PopPK models of commonly used statistical criteria. The presented results strengthen our hypothesis that the software robot can be successfully used to evaluate PopPK models ensuring the selection of the best PopPK model.

PFIM 4.0, an extended R program for design evaluation and optimization in nonlinear mixed-effect models

BACKGROUND AND OBJECTIVE

Nonlinear mixed-effect models (NLMEMs) are increasingly used for the analysis of longitudinal studies during drug development. When designing these studies, the expected Fisher information matrix (FIM) can be used instead of performing time-consuming clinical trial simulations. The function PFIM is the first tool for design evaluation and optimization that has been developed in R. In this article, we present an extended version, PFIM 4.0, which includes several new features.

METHODS

Compared with version 3.0, PFIM 4.0 includes a more complete pharmacokinetic/pharmacodynamic library of models and accommodates models including additional random effects for inter-occasion variability as well as discrete covariates. A new input method has been added to specify user-defined models through an R function. Optimization can be performed assuming some fixed parameters or some fixed sampling times. New outputs have been added regarding the FIM such as eigenvalues, conditional numbers, and the option of saving the matrix obtained after evaluation or optimization. Previously obtained results, which are summarized in a FIM, can be taken into account in evaluation or optimization of one-group protocols. This feature enables the use of PFIM for adaptive designs. The Bayesian individual FIM has been implemented, taking into account a priori distribution of random effects. Designs for maximum a posteriori Bayesian estimation of individual parameters can now be evaluated or optimized and the predicted shrinkage is also reported. It is also possible to visualize the graphs of the model and the sensitivity functions without performing evaluation or optimization.

RESULTS

The usefulness of these approaches and the simplicity of use of PFIM 4.0 are illustrated by two examples: (i) an example of designing a population pharmacokinetic study accounting for previous results, which highlights the advantage of adaptive designs; (ii) an example of Bayesian individual design optimization for a pharmacodynamic study, showing that the Bayesian individual FIM can be a useful tool in therapeutic drug monitoring, allowing efficient prediction of estimation precision and shrinkage for individual parameters.

CONCLUSION

PFIM 4.0 is a useful tool for design evaluation and optimization of longitudinal studies in pharmacometrics and is freely available at http://www.pfim.biostat.fr.

Estimating individual benefits of medical or behavioral treatments in severely ill patients

There is a need for statistical methods appropriate for the analysis of clinical trials from a personalized-medicine viewpoint as opposed to the common statistical practice that simply examines average treatment effects. This article proposes an approach to quantifying, reporting and analyzing individual benefits of medical or behavioral treatments to severely ill patients with chronic conditions, using data from clinical trials. The approach is a new development of a published framework for measuring the severity of a chronic disease and the benefits treatments provide to individuals, which utilizes regression models with random coefficients. Here, a patient is considered to be severely ill if the patient’s basal severity is close to one. This allows the derivation of a very flexible family of probability distributions of individual benefits that depend on treatment duration and the covariates included in the regression model. Our approach may enrich the statistical analysis of clinical trials of severely ill patients because it allows investigating the probability distribution of individual benefits in the patient population and the variables that influence it, and we can also measure the benefits achieved in specific patients including new patients. We illustrate our approach using data from a clinical trial of the anti-depressant imipramine.

Model-Based Approach to Predict Adherence to Protocol During Antiobesity Trials

Development of antiobesity drugs is continuously challenged by high dropout rates during clinical trials. The objective was to develop a population pharmacodynamic model that describes the temporal changes in body weight, considering disease progression, lifestyle intervention, and drug effects. Markov modeling (MM) was applied for quantification and characterization of responder and nonresponder as key drivers of dropout rates, to ultimately support the clinical trial simulations and the outcome in terms of trial adherence. Subjects (n = 4591) from 6 Contrave^® trials were included in this analysis. An indirect‐response model developed by van Wart et al was used as a starting point. Inclusion of drug effect was dose driven using a population dose‐ and time‐dependent pharmacodynamic (DTPD) model. Additionally, a population‐pharmacokinetic parameter‐ and data (PPPD)‐driven model was developed using the final DTPD model structure and final parameter estimates from a previously developed population pharmacokinetic model based on available Contrave^® pharmacokinetic concentrations. Last, MM was developed to predict transition rate probabilities among responder, nonresponder, and dropout states driven by the pharmacodynamic effect resulting from the DTPD or PPPD model. Covariates included in the models and parameters were diabetes mellitus and race. The linked DTPD‐MM and PPPD‐MM was able to predict transition rates among responder, nonresponder, and dropout states well. The analysis concluded that body‐weight change is an important factor influencing dropout rates, and the MM depicted that overall a DTPD model‐driven approach provides a reasonable prediction of clinical trial outcome probabilities similar to a pharmacokinetic‐driven approach.

A Longitudinal HbA1c Model Elucidates Genes Linked to Disease Progression on Metformin

One-third of type-2 diabetic patients respond poorly to metformin. Despite extensive research, the impact of genetic and nongenetic factors on long-term outcome is unknown. In this study we combine nonlinear mixed effect modeling with computational genetic methodologies to identify predictors of long-term response. In all, 1,056 patients contributed their genetic, demographic, and long-term HbA1c data. The top nine variants (of 12,000 variants in 267 candidate genes) accounted for approximately one-third of the variability in the disease progression parameter. Average serum creatinine level, age, and weight were determinants of symptomatic response; however, explaining negligible variability. Two single nucleotide polymorphisms (SNPs) in CSMD1 gene (rs2617102, rs2954625) and one SNP in a pharmacologically relevant SLC22A2 gene (rs316009) influenced disease progression, with minor alleles leading to less and more favorable outcomes, respectively. Overall, our study highlights the influence of genetic factors on long-term HbA1c response and provides a computational model, which when validated, may be used to individualize treatment.

Estimating the variability in fraction absorbed as a paradigm for informing formulation development in early clinical drug development

PURPOSE

Inter-subject variability in oral drug absorption is usually reported using bioavailability, which has the components: fraction absorbed (fa), fraction passing the gut wall (fg) and fraction escaping hepatic metabolism (fh). In this study, we sought to separate the absorption (fa∗fg) and elimination (fh) components of bioavailability to study variability of absorption and to investigate the effect of formulations, gastric pH and food on absorption variability.

METHODS

Four compounds from the AstraZeneca database with a range of reported bioavailabilities (high, intermediate 1&2 and low) were selected. First, a disposition model using intravenous data was developed; Second, intrinsic clearance and hence hepatic extraction ratio was estimated based on the "well stirred" model; lastly, the oral data were included to enable estimation of fa∗fg as a separate component to hepatic extraction. Population pharmacokinetic model fitting was undertaken with NONMEM v.7.2.

RESULTS

The limiting step in absorption for intermediate 1 was dissolution rate and fa∗fg variability increased under elevated gastric pH (15% vs. 38%, respectively). Absorption of solution formulation intermediate 2 increased by 17% in the presence of food but the prolonged release formulation's absorption didn't differ under fasted or fed state. Variability wasn't affected by food for both formulations (~30%). For the low bioavailable compound, variability decreased when formulated as a prolonged-release formulation (39% vs. 15%).

CONCLUSIONS

The method described here enables an exploration of drug absorption inter-subject variability using population pharmacokinetics. Implementation of such an approach may aid the formulation design process through a better understanding of the factors affecting oral drug absorption variability.

Measuring the individual benefit of a medical or behavioral treatment using generalized linear mixed-effects models

We propose statistical definitions of the individual benefit of a medical or behavioral treatment and of the severity of a chronic illness. These definitions are used to develop a graphical method that can be used by statisticians and clinicians in the data analysis of clinical trials from the perspective of personalized medicine. The method focuses on assessing and comparing individual effects of treatments rather than average effects and can be used with continuous and discrete responses, including dichotomous and count responses. The method is based on new developments in generalized linear mixed-effects models, which are introduced in this article. To illustrate, analyses of data from the Sequenced Treatment Alternatives to Relieve Depression clinical trial of sequences of treatments for depression and data from a clinical trial of respiratory treatments are presented. The estimation of individual benefits is also explained. Copyright © 2016 John Wiley & Sons, Ltd.

Mathematical modeling and simulation in animal health. Part I: Moving beyond pharmacokinetics

The application of mathematical modeling to problems in animal health has a rich history in the form of pharmacokinetic modeling applied to problems in veterinary medicine. Advances in modeling and simulation beyond pharmacokinetics have the potential to streamline and speed-up drug research and development programs. To foster these goals, a series of manuscripts will be published with the following goals: (i) expand the application of modeling and simulation to issues in veterinary pharmacology; (ii) bridge the gap between the level of modeling and simulation practiced in human and veterinary pharmacology; (iii) explore how modeling and simulation concepts can be used to improve our understanding of common issues not readily addressed in human pharmacology (e.g. breed differences, tissue residue depletion, vast weight ranges among adults within a single species, interspecies differences, small animal species research where data collection is limited to sparse sampling, availability of different sampling matrices); and (iv) describe how quantitative pharmacology approaches could help understanding key pharmacokinetic and pharmacodynamic characteristics of a drug candidate, with the goal of providing explicit, reproducible, and predictive evidence for optimizing drug development plans, enabling critical decision making, and eventually bringing safe and effective medicines to patients. This study introduces these concepts and introduces new approaches to modeling and simulation as well as clearly articulate basic assumptions and good practices. The driving force behind these activities is to create predictive models that are based on solid physiological and pharmacological principles as well as adhering to the limitations that are fundamental to applying mathematical and statistical models to biological systems.

Improved Estimation of Human Lipoprotein Kinetics with Mixed Effects Models

Context

Mathematical models may help the analysis of biological systems by providing estimates of otherwise un-measurable quantities such as concentrations and fluxes. The variability in such systems makes it difficult to translate individual characteristics to group behavior. Mixed effects models offer a tool to simultaneously assess individual and population behavior from experimental data. Lipoproteins and plasma lipids are key mediators for cardiovascular disease in metabolic disorders such as diabetes mellitus type 2. By the use of mathematical models and tracer experiments fluxes and production rates of lipoproteins may be estimated.

Results

We developed a mixed effects model to study lipoprotein kinetics in a data set of 15 healthy individuals and 15 patients with type 2 diabetes. We compare the traditional and the mixed effects approach in terms of group estimates at various sample and data set sizes.

Conclusion

We conclude that the mixed effects approach provided better estimates using the full data set as well as with both sparse and truncated data sets. Sample size estimates showed that to compare lipoprotein secretion the mixed effects approach needed almost half the sample size as the traditional method.

Logic-Based and Cellular Pharmacodynamic Modeling of Bortezomib Responses in U266 Human Myeloma Cells

Systems models of biological networks show promise for informing drug target selection/qualification, identifying lead compounds and factors regulating disease progression, rationalizing combinatorial regimens, and explaining sources of intersubject variability and adverse drug reactions. However, most models of biological systems are qualitative and are not easily coupled with dynamical models of drug exposure-response relationships. In this proof-of-concept study, logic-based modeling of signal transduction pathways in U266 multiple myeloma (MM) cells is used to guide the development of a simple dynamical model linking bortezomib exposure to cellular outcomes. Bortezomib is a commonly used first-line agent in MM treatment; however, knowledge of the signal transduction pathways regulating bortezomib-mediated cell cytotoxicity is incomplete. A Boolean network model of 66 nodes was constructed that includes major survival and apoptotic pathways and was updated using responses to several chemical probes. Simulated responses to bortezomib were in good agreement with experimental data, and a reduction algorithm was used to identify key signaling proteins. Bortezomib-mediated apoptosis was not associated with suppression of nuclear factor κB (NFκB) protein inhibition in this cell line, which contradicts a major hypothesis of bortezomib pharmacodynamics. A pharmacodynamic model was developed that included three critical proteins (phospho-NFκB, BclxL, and cleaved poly (ADP ribose) polymerase). Model-fitted protein dynamics and cell proliferation profiles agreed with experimental data, and the model-predicted IC50 (3.5 nM) is comparable to the experimental value (1.5 nM). The cell-based pharmacodynamic model successfully links bortezomib exposure to MM cellular proliferation via protein dynamics, and this model may show utility in exploring bortezomib-based combination regimens.

Lewis Sheiner ISoP/UCSF Lecturer Award: From Drug Use to Statistical Models and Vice Versa

I was very honored to receive the University of California, San Francisco, and the International Society of Pharmacometrics Lewis Sheiner lecturer award in May 2013. In the present perspective, I outline the main points of my lecture at the American Conference of Pharmacometrics (slides in Supplementary Material 1). I first emphasize the scientific contributions of Lewis Sheiner as a quantitative pharmacologist toward the better use of drugs. I then focus on three statistical topics in pharmacometrics, describing Lewis Sheiner's impact and my own contributions and interactions with him.

The inverse problem in mathematical biology

Biological systems present particular challengers to model for the purposes of formulating predictions of generating biological insight. These systems are typically multi-scale, complex, and empirical observations are often sparse and subject to variability and uncertainty. This manuscript will review some of these specific challenges and introduce current methods used by modelers to construct meaningful solutions, in the context of preserving biological relevance. Opportunities to expand these methods are also discussed.

Powers of the likelihood ratio test and the correlation test using empirical bayes estimates for various shrinkages in population pharmacokinetics

We compared the powers of the likelihood ratio test (LRT) and the Pearson correlation test (CT) from empirical Bayes estimates (EBEs) for various designs and shrinkages in the context of nonlinear mixed-effect modeling. Clinical trial simulation was performed with a simple pharmacokinetic model with various weight (WT) effects on volume (V). Data sets were analyzed with NONMEM 7.2 using first-order conditional estimation with interaction and stochastic approximation expectation maximization algorithms. The powers of LRT and CT in detecting the link between individual WT and V or clearance were computed to explore hidden or induced correlations, respectively. Although the different designs and variabilities could be related to the large shrinkage of the EBEs, type 1 errors and powers were similar in LRT and CT in all cases. Power was mostly influenced by covariate effect size and, to a lesser extent, by the informativeness of the design. Further studies with more models are needed.

Largazole pharmacokinetics in rats by LC-MS/MS

A highly sensitive and specific LC-MS/MS method for the quantitation of largazole thiol, the active species of the marine-derived preclinical histone deacetylase inhibitor, largazole (prodrug), was developed and validated. Largazole thiol was extracted with ethyl acetate from human or rat plasma along with the internal standard, harmine. Samples were separated on an Onyx Monolithic C18 column by a stepwise gradient elution with 0.1% formic acid in methanol and 0.1% aqueous formic acid employing multiple reaction monitoring (MRM) detection. Linear calibration curves were obtained in the range of 12.5-400 ng/mL with 200 µL of human plasma. The overall intra-day precision was from 3.87% to 12.6%, and the inter-day precision was from 7.12% to 9.8%. The accuracy at low, medium and high concentrations ranged from 101.55% to 105.84%. Plasma protein bindings of largazole thiol in human and rat plasma as determined by an ultrafiltration method were 90.13% and 77.14%, respectively. Plasma drug concentrations were measured by this LC-MS/MS method. The pharmacokinetics of largazole thiol in rats was studied following i.v. administration at 10 mg/kg and found to follow a two-compartment model. Largazole thiol was rapidly eliminated from systemic circulation within 2 h. The established LC-MS/MS method is suitable for the analysis of largazole thiol in human plasma, as well.

Population pharmacometrics in support of analgesics studies

Population pharmacometric modeling is used to explain both population trends as well as the sources and magnitude of variability in pharmacokinetic and pharmacodynamics data; the later, in part, by taking into account patient characteristics such as weight, age, renal function and genetics. The approach is best known for its ability to analyze sparse data, i.e. when only a few measurements have been collected from each subject, but other benefits include its flexibility and the potential to construct more detailed models than those used in the traditional individual curve fitting approach. This review presents the basic concepts of population pharmacokinetic and pharmacodynamic modeling and includes several analgesic drug examples. In addition, the use of these models to design and optimize future studies is discussed. In this context, finding the best design factors, such as the sampling times or the dose, for future studies within pre-defined criteria using a previously constructed population pharmacokinetic model can help researchers acquire clinically meaningful data without wasting resources and unnecessarily exposing vulnerable patient groups to study drugs and additional blood sampling.

Predicting drug-drug interactions: application of physiologically based pharmacokinetic models under a systems biology approach

The development of in vitro-in vivo extrapolation (IVIVE), a 'bottom-up' approach, to predict pharmacokinetic parameters and drug-drug interactions (DDIs) has accelerated mainly due to an increase in the understanding of the multiple mechanisms involved in these interactions and the availability of appropriate in vitro systems that act as surrogates for delineating various elements of the interactions relevant to absorption, distribution, metabolism and elimination. Recent advances in the knowledge of the population variables required for IVIVE (demographic, anatomical, genetic and physiological parameters) have also contributed to the appreciation of the sources of variability and wider use of this approach for different scenarios within the pharmaceutical industry. Initially, the authors present an overview of the integration of IVIVE into 'static' and 'dynamic' models for the quantitative prediction of DDIs. The main purpose of this review is to discuss the application of IVIVE in conjunction with physiologically based pharmacokinetic modeling under a systems biology approach to characterize the potential DDIs in individual patients, including those who cannot be investigated in formal clinical trials for ethical reasons. In addition, we address the issues related to the prediction of complex DDIs involving the inhibition of cytochrome P- and transporter-mediated activities through multiple drugs.

Non linear mixed effects analysis in PET PK-receptor occupancy studies

The characterisation of a pharmacokinetic-receptor occupancy (PK-RO) relationship derived from a PET study is typically modelled in a conventional non-linear least squares (NLLS) framework. In the present work, we explore the application of a non-linear mixed effects approach (NLME) and compare this with NLLS estimation (using both naive pooled data and two-stage approaches) in the context of a direct PK-RO relationship described by an Emax model, using simulated data sets. Target and reference tissue time-activity curves were simulated using a two-tissue compartmental model and an arterial plasma input function for a typical PET study (12 subjects in 3 dose groups with 3 scans each). A range of different PET scenarios was considered to evaluate the impact of between-subject variability and reference region availability. The PET outcome measures derived from the simulations were then used to estimate the parameters of the PK-RO model. The performance of the two approaches was compared in terms of parameters estimates (square mean error SME, root mean square error RMSE) and prediction of the exposure-occupancy relationship. In general, both NLME and NLLS estimation methods provided unbiassed and precise population estimates for the Emax model parameters, although a slight bias was observed for the individual-NLLS method due to a few outliers. The increased value of NLME over NLLS was most notable in the estimation of the between-subject variability (BSV), especially in the case of a more complex PK-RO model when no reference region was available (maximum SME and RMSE values related to BSV of EC₅₀ of 27.6% and 86.5% from NLME versus 264.6% and 689.5% from NLLS). Overall, the NLME approach provided a more robust estimation and produced less-biassed estimates of the population means and variances than either the NLLS approach for the simulations considered.

Prediction of shrinkage of individual parameters using the bayesian information matrix in non-linear mixed effect models with evaluation in pharmacokinetics

PURPOSE

When information is sparse, individual parameters derived from a non-linear mixed effects model analysis can shrink to the mean. The objective of this work was to predict individual parameter shrinkage from the Bayesian information matrix (M BF ). We 1) Propose and evaluate an approximation of M BF by First-Order linearization (FO), 2) Explore by simulations the relationship between shrinkage and precision of estimates and 3) Evaluate prediction of shrinkage and individual parameter precision.

METHODS

We approximated M BF using FO. From the shrinkage formula in linear mixed effects models, we derived the predicted shrinkage from M BF . Shrinkage values were generated for parameters of two pharmacokinetic models by varying the structure and the magnitude of the random effect and residual error models as well as the design. We then evaluated the approximation of M BF FO and compared it to Monte-Carlo (MC) simulations. We finally compared expected and observed shrinkage as well as the predicted and estimated Standard Errors (SE) of individual parameters.

RESULTS

M BF FO was similar to M BF MC. Predicted and observed shrinkages were close . Predicted and estimated SE were similar.

CONCLUSIONS

M BF FO enables prediction of shrinkage and SE of individual parameters. It can be used for design optimization.

Bayesian inference

This chapter provides an overview of the Bayesian approach to data analysis, modeling, and statistical decision making. The topics covered go from basic concepts and definitions (random variables, Bayes' rule, prior distributions) to various models of general use in biology (hierarchical models, in particular) and ways to calibrate and use them (MCMC methods, model checking, inference, and decision). The second half of this Bayesian primer develops an example of model setup, calibration, and inference for a physiologically based analysis of 1,3-butadiene toxicokinetics in humans.

Fundamentals of Population Pharmacokinetic Modelling : Modelling and Software

Population pharmacokinetic modelling is widely used within the field of clinical pharmacology as it helps to define the sources and correlates of pharmacokinetic variability in target patient populations and their impact upon drug disposition. This review focuses on the fundamentals of population pharmacokinetic modelling and provides an overview of the commonly available software programs that perform these functions.This review attempts to define the common, fundamental aspects of population pharmacokinetic modelling through a discussion of the literature describing the techniques and placing them in the appropriate context. An overview of the most commonly available software programs is also provided.Population pharmacokinetic modelling is a powerful approach where sources and correlates of pharmacokinetic variability can be identified in a target patient population receiving a pharmacological agent. There is a need to further standardize and establish the best approaches in modelling so that any model created can be systematically evaluated and the results relied upon. Various nonlinear mixed-effects modelling methods, packaged in a variety of software programs, are available today. When selecting population pharmacokinetic software programs, the consumer needs to consider several factors, including usability (e.g. user interface, native platform, price, input and output specificity, as well as intuitiveness), content (e.g. algorithms and data output) and support (e.g. technical and clinical).

Drug dosage individualization based on a random-effects linear model

This article investigates drug dosage individualization when the patient population can be described with a random-effects linear model of a continuous pharmacokinetic or pharmacodynamic response. Specifically, we show through both decision-theoretic arguments and simulations that a published clinical algorithm may produce better individualized dosages than some traditional methods of therapeutic drug monitoring. Since empirical evidence suggests that the linear model may adequately describe drugs and patient populations, and linear models are easier to handle than the nonlinear models traditionally used in population pharmacokinetics, our results highlight the potential applicability of linear mixed models to dosage computations and personalized medicine.

Pharmacokinetic modeling of P-glycoprotein function at the rat and human blood-brain barriers studied with (R)-[11C]verapamil positron emission tomography

Background

This study investigated the influence of P-glycoprotein (P-gp) inhibitor tariquidar on the pharmacokinetics of P-gp substrate radiotracer (R)-[¹¹C]verapamil in plasma and brain of rats and humans by means of positron emission tomography (PET).

Methods

Data obtained from a preclinical and clinical study, in which paired (R)-[¹¹C]verapamil PET scans were performed before, during, and after tariquidar administration, were analyzed using nonlinear mixed effects (NLME) modeling. Administration of tariquidar was included as a covariate on the influx and efflux parameters (Q_in and Q_out) in order to investigate if tariquidar increased influx or decreased outflux of radiotracer across the blood–brain barrier (BBB). Additionally, the influence of pilocarpine-induced status epilepticus (SE) was tested on all model parameters, and the brain-to-plasma partition coefficient (V_T-NLME) was calculated.

Results

Our model indicated that tariquidar enhances brain uptake of (R)-[¹¹C]verapamil by decreasing Q_out. The reduction in Q_out in rats during and immediately after tariquidar administration (sevenfold) was more pronounced than in the second PET scan acquired 2 h after tariquidar administration (fivefold). The effect of tariquidar on Q_out in humans was apparent during and immediately after tariquidar administration (twofold reduction in Q_out) but was negligible in the second PET scan. SE was found to influence the pharmacological volume of distribution of the central brain compartment V_br1. Tariquidar treatment lead to an increase in V_T-NLME, and pilocarpine-induced SE lead to increased (R)-[¹¹C]verapamil distribution to the peripheral brain compartment.

Conclusions

Using NLME modeling, we were able to provide mechanistic insight into the effects of tariquidar and SE on (R)-[¹¹C]verapamil transport across the BBB in control and 48 h post SE rats as well as in humans.

Basic concepts in population modeling, simulation, and model-based drug development

Modeling is an important tool in drug development; population modeling is a complex process requiring robust underlying procedures for ensuring clean data, appropriate computing platforms, adequate resources, and effective communication. Although requiring an investment in resources, it can save time and money by providing a platform for integrating all information gathered on new therapeutic agents. This article provides a brief overview of aspects of modeling and simulation as applied to many areas in drug development.

Performance comparison of various maximum likelihood nonlinear mixed-effects estimation methods for dose-response models

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.

Role of Statistical Random-Effects Linear Models in Personalized Medicine

Some empirical studies and recent developments in pharmacokinetic theory suggest that statistical random-effects linear models are valuable tools that allow describing simultaneously patient populations as a whole and patients as individuals. This remarkable characteristic indicates that these models may be useful in the development of personalized medicine, which aims at finding treatment regimes that are appropriate for particular patients, not just appropriate for the average patient. In fact, published developments show that random-effects linear models may provide a solid theoretical framework for drug dosage individualization in chronic diseases. In particular, individualized dosages computed with these models by means of an empirical Bayesian approach may produce better results than dosages computed with some methods routinely used in therapeutic drug monitoring. This is further supported by published empirical and theoretical findings that show that random effects linear models may provide accurate representations of phase III and IV steady-state pharmacokinetic data, and may be useful for dosage computations. These models have applications in the design of clinical algorithms for drug dosage individualization in chronic diseases; in the computation of dose correction factors; computation of the minimum number of blood samples from a patient that are necessary for calculating an optimal individualized drug dosage in therapeutic drug monitoring; measure of the clinical importance of clinical, demographic, environmental or genetic covariates; study of drug-drug interactions in clinical settings; the implementation of computational tools for web-site-based evidence farming; design of pharmacogenomic studies; and in the development of a pharmacological theory of dosage individualization.

Population pharmacokinetics of recombinant factor VIII: the relationships of pharmacokinetics to age and body weight

Comparison of the pharmacokinetics (PK) of a coagulation factor between groups of patients can be biased by differences in study protocols, in particular between blood sampling schedules. This could affect clinical dose tailoring, especially in children. The aim of this study was to describe the relationships of the PK of factor VIII (FVIII) with age and body weight by a population PK model. The potential to reduce blood sampling was also explored. A model was built for FVIII PK from 236 infusions of recombinant FVIII in 152 patients (1-65 years of age) with severe hemophilia A. The PK of FVIII over the entire age range was well described by a 2-compartment model and a previously reported problem, resulting from differences in blood sampling, to compare findings from children and adults was practically abolished. The decline in FVIII clearance and increase in half-life with age could be described as continuous functions. Retrospective reduction of blood sampling from 11 to 5 samples made no important difference to the estimates of PK parameters. The obtained findings can be used as a basis for PK-based dose tailoring of FVIII in clinical practice, in all age groups, with minimal blood sampling.

Pharmacokinetic similarity of biologics: analysis using nonlinear mixed-effects modeling

Our objective was to show, using two examples, that a pharmacokinetic (PK) similarity analysis can be performed using nonlinear mixed-effects models (NLMEM). We used two studies that compared different biosimilars: a three-way crossover trial with somatropin and a parallel-group trial with epoetin-α. For both data sets, the results of NLMEM-based analysis were compared with those of noncompartmental analysis (NCA). For the latter analysis, we performed an NLMEM-based equivalence Wald test on secondary parameters of the model: the area under the curve and the maximal concentration. Somatropin PK was described by a one-compartment model and epoetin-α PK by a two-compartment model with linear and Michaelis-Menten elimination. For both studies, similarity of PK was demonstrated by means of both NCA and NLMEM, and both methods led to similar results. Therefore, for establishing similarity, PK data can be analyzed by either of the methods. NCA is an easier approach because it does not require data modeling; however, NLMEM leads to a better understanding of the underlying biological system.

Interpreting population pharmacokinetic-pharmacodynamic analyses - a clinical viewpoint

The population analysis approach is an important tool for clinical pharmacology in aiding the dose individualization of medicines. However, due to their statistical complexity the clinical utility of population analyses is often overlooked. One of the key reasons to conduct a population analysis is to investigate the potential benefits of individualization of drug dosing based on patient characteristics (termed covariate identification). The purpose of this review is to provide a tool to interpret and extract information from publications that describe population analysis. The target audience is those readers who are aware of population analyses but have not conducted the technical aspects of an analysis themselves. Initially we introduce the general framework of population analysis and work through a simple example with visual plots. We then follow-up with specific details on how to interpret population analyses for the purpose of identifying covariates and how to interpret their likely importance for dose individualization.

A survey of the way pharmacokinetics are reported in published phase I clinical trials, with an emphasis on oncology

BACKGROUND AND OBJECTIVE

During the drug development process, phase I trials are the first occasion to study the pharmacokinetics of a drug. They are performed in healthy subjects, or in patients in oncology, and are designed to determine a safe and acceptable dose for the later phases of clinical trials. We performed a bibliographic survey to investigate the way pharmacokinetics are described and reported in phase I clinical trials.

METHODS

We performed a MEDLINE search to retrieve the list of papers published between 2005 and 2006 and reporting phase I clinical trials with a pharmacokinetic study. We used a spreadsheet to record general information concerning the study and specific information regarding the pharmacokinetics, such as the sampling times, number of subjects and method of analysis.

RESULTS

The search yielded 349 papers, of which 37 were excluded for various reasons. Nearly all of the papers in our review concerned cancer studies, although this was not a requirement in the search. Consistent with the selection process, 84% papers explicitly stated pharmacokinetics as an objective of the study. The methods section usually included a description of the pharmacokinetics (88%), but 10% of the papers provided no information concerning the methods used for the pharmacokinetics and in 2% the description was only partial. The analytical method was usually basic, with non-compartmental or purely descriptive methods. Observed concentrations and areas under the concentration-time curves were the pharmacokinetic variables most often reported. The results of the pharmacokinetic study were frequently reported in a separate paragraph of the results section, and only 22% of the studies related the pharmacokinetic findings to other results from the study, such as toxicity or efficacy. In addition, important information such as the number of subjects included in the pharmacokinetic study or the pharmacokinetic sampling scheme was sometimes not reported explicitly.

CONCLUSION

Concerns about the decreasing cost-effectiveness of the drug development process prompted the regulatory authorities to recently recommend better integration of all available information - including, in particular, pharmacokinetics - in this process. In our review, we found that this information was often either missing or incomplete, which hinders that objective. We suggest several improvements in the design and the reporting of the methods and results of these studies, to ensure that all relevant information has been included. Pharmacokinetic findings should also be integrated into the broader perspective of drug development, through the study of their relationship with toxicity and/or efficacy, even in the early phase I stages.

Design evaluation and optimisation in multiple response nonlinear mixed effect models: PFIM 3.0

Nonlinear mixed effect models (NLMEM) with multiple responses are increasingly used in pharmacometrics, one of the main examples being the joint analysis of the pharmacokinetics (PK) and pharmacodynamics (PD) of a drug. Efficient tools for design evaluation and optimisation in NLMEM are necessary. The R functions PFIM 1.2 and PFIMOPT 1.0 were proposed for these purposes, but accommodate only single response models. The methodology used is based on the Fisher information matrix, developed using a linearisation of the model. In this paper, we present an extended version, PFIM 3.0, dedicated to both design evaluation and optimisation for multiple response models, using a similar method as for single response models. In addition to handling multiple response models, several features have been integrated into PFIM 3.0 for model specification and optimisation. The extension includes a library of classical analytical pharmacokinetics models and allows the user to describe more complex models using differential equations. Regarding the optimisation algorithm, an alternative to the Simplex algorithm has been implemented, the Fedorov-Wynn algorithm to optimise more practical D-optimal design. Indeed, this algorithm optimises design among a set of sampling times specified by the user. This R function is freely available at http://www.pfim.biostat.fr. The efficiency of this approach and the simplicity of use of PFIM 3.0 are illustrated with a real example of the joint PKPD analysis of warfarin, an oral anticoagulant, with a model defined by ordinary differential equations.

Fisher information matrix for nonlinear mixed effects multiple response models: evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

We focus on the Fisher information matrix used for design evaluation and optimization in nonlinear mixed effects multiple response models. We evaluate the appropriateness of its expression computed by linearization as proposed for a single response model. Using a pharmacokinetic-pharmacodynamic (PKPD) example, we first compare the computation of the Fisher information matrix with approximation to one derived from the observed matrix on a large simulation using the stochastic approximation expectation-maximization algorithm (SAEM). The expression of the Fisher information matrix for multiple responses is also evaluated by comparison with the empirical information obtained through a replicated simulation study using the first-order linearization estimation methods implemented in the NONMEM software (first-order (FO), first-order conditional estimate (FOCE)) and the SAEM algorithm in the MONOLIX software. The predicted errors given by the approximated information matrix are close to those given by the information matrix obtained without linearization using SAEM and to the empirical ones obtained with FOCE and SAEM. The simulation study also illustrates the accuracy of both FOCE and SAEM estimation algorithms when jointly modelling multiple responses and the major limitations of the FO method. This study highlights the appropriateness of the approximated Fisher information matrix for multiple responses, which is implemented in PFIM 3.0, an extension of the R function PFIM dedicated to design evaluation and optimization. It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite.

Pharmacogenetics and population pharmacokinetics: impact of the design on three tests using the SAEM algorithm

Pharmacogenetics is now widely investigated and health institutions acknowledge its place in clinical pharmacokinetics. Our objective is to assess through a simulation study, the impact of design on the statistical performances of three different tests used for analysis of pharmacogenetic information with nonlinear mixed effects models: (i) an ANOVA to test the relationship between the empirical Bayes estimates of the model parameter of interest and the genetic covariate, (ii) a global Wald test to assess whether estimates for the gene effect are significant, and (iii) a likelihood ratio test (LRT) between the model with and without the genetic covariate. We use the stochastic EM algorithm (SAEM) implemented in MONOLIX 2.1 software. The simulation setting is inspired from a real pharmacokinetic study. We investigate four designs with N the number of subjects and n the number of samples per subject: (i) N = 40/n = 4, similar to the original study, (ii) N = 80/n = 2 sorted in 4 groups, a design optimized using the PFIM software, (iii) a combined design, N = 20/n = 4 plus N = 80 with only a trough concentration and (iv) N = 200/n = 4, to approach asymptotic conditions. We find that the ANOVA has a correct type I error estimate regardless of design, however the sparser design was optimized. The type I error of the Wald test and LRT are moderatly inflated in the designs far from the asymptotic (<10%). For each design, the corrected power is analogous for the three tests. Among the three designs with a total of 160 observations, the design N = 80/n = 2 optimized with PFIM provides both the lowest standard error on the effect coefficients and the best power for the Wald test and the LRT while a high shrinkage decreases the power of the ANOVA. In conclusion, a correction method should be used for model-based tests in pharmacogenetic studies with reduced sample size and/or sparse sampling and, for the same amount of samples, some designs have better power than others.