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Chen X, Nyberg HB, Donnelly M, Zhao L, Fang L, Karlsson MO, Hooker AC. Development and comparison of model-integrated evidence approaches for bioequivalence studies with pharmacokinetic end points. CPT Pharmacometrics Syst Pharmacol 2024. [PMID: 39177211 DOI: 10.1002/psp4.13216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2023] [Revised: 06/26/2024] [Accepted: 07/19/2024] [Indexed: 08/24/2024] Open
Abstract
By applying nonlinear mixed-effect (NLME) models, model-integrated evidence (MIE) approaches are able to analyze bioequivalence (BE) data with pharmacokinetic end points that have sparse sampling, which is problematic for non-compartmental analysis (NCA). However, MIE approaches may suffer from inflation of type I error due to underestimation of parameter uncertainty and to the assumption of asymptotic normality. In this study, we developed a MIE BE analysis method that is based on a pre-defined model and consists of several steps including model fitting, uncertainty assessment, simulation, and BE determination. The presented MIE approach has several improvements compared with the previously reported model-integrated methods: (1) treatment, sequence, and period effects are only added to absorption parameters (such as relative bioavailability and rate of absorption) instead of all PK parameters; (2) a simulation step is performed to generate confidence intervals of the pharmacokinetic metrics for BE assessment; and (3) in an effort to maintain type I error, two more advanced parameter uncertainty evaluation approaches are explored, a nonparametric (case resampling) bootstrap, and sampling importance resampling (SIR). To evaluate the developed method and compare the uncertainty assessment methods, simulation experiments were performed for BE studies using a two-way crossover design with different amounts of information (sparse to rich designs) and levels of variability. Based on the simulation results, the method using SIR for parameter uncertainty quantification controls type I error at the nominal level of 0.05 (i.e., the significance level set for BE evaluation) even for studies with small sample size and/or sparse sampling. As expected, our MIE approach for BE assessment exhibited higher power than the NCA-based method, especially as the data becomes sparser and/or more variable.
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Affiliation(s)
- Xiaomei Chen
- Department of Pharmacy, Uppsala University, Uppsala, Sweden
| | | | - Mark Donnelly
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, USA
| | - Liang Zhao
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, USA
| | - Lanyan Fang
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, USA
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2
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Philipp M, Tessier A, Donnelly M, Fang L, Feng K, Zhao L, Grosser S, Sun G, Sun W, Mentré F, Bertrand J. Model-based bioequivalence approach for sparse pharmacokinetic bioequivalence studies: Model selection or model averaging? Stat Med 2024; 43:3403-3416. [PMID: 38847215 DOI: 10.1002/sim.10088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2023] [Revised: 03/16/2024] [Accepted: 04/14/2024] [Indexed: 07/17/2024]
Abstract
Conventional pharmacokinetic (PK) bioequivalence (BE) studies aim to compare the rate and extent of drug absorption from a test (T) and reference (R) product using non-compartmental analysis (NCA) and the two one-sided test (TOST). Recently published regulatory guidance recommends alternative model-based (MB) approaches for BE assessment when NCA is challenging, as for long-acting injectables and products which require sparse PK sampling. However, our previous research on MB-TOST approaches showed that model misspecification can lead to inflated type I error. The objective of this research was to compare the performance of model selection (MS) on R product arm data and model averaging (MA) from a pool of candidate structural PK models in MBBE studies with sparse sampling. Our simulation study was inspired by a real case BE study using a two-way crossover design. PK data were simulated using three structural models under the null hypothesis and one model under the alternative hypothesis. MB-TOST was applied either using each of the five candidate models or following MS and MA with or without the simulated model in the pool. Assuming T and R have the same PK model, our simulation shows that following MS and MA, MB-TOST controls type I error rates at or below 0.05 and attains similar or even higher power than when using the simulated model. Thus, we propose to use MS prior to MB-TOST for BE studies with sparse PK sampling and to consider MA when candidate models have similar Akaike information criterion.
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Affiliation(s)
| | - Adrien Tessier
- Clinical Pharmacometrics, Quantitative Pharmacology, Servier, Suresnes, France
| | - Mark Donnelly
- Division of Quantitative Methods and Modeling, Office of Research and Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, Maryland, USA
| | - Lanyan Fang
- Division of Quantitative Methods and Modeling, Office of Research and Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, Maryland, USA
| | - Kairui Feng
- Division of Quantitative Methods and Modeling, Office of Research and Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, Maryland, USA
| | - Liang Zhao
- Division of Quantitative Methods and Modeling, Office of Research and Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, Maryland, USA
| | - Stella Grosser
- Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, Maryland, USA
| | - Guoying Sun
- Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, Maryland, USA
| | - Wanjie Sun
- Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, U.S. Food and Drug Administration, Silver Spring, Maryland, USA
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Guhl M, Bertrand J, Fayette L, Mercier F, Comets E. Uncertainty Computation at Finite Distance in Nonlinear Mixed Effects Models-a New Method Based on Metropolis-Hastings Algorithm. AAPS J 2024; 26:53. [PMID: 38722435 DOI: 10.1208/s12248-024-00905-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Accepted: 02/29/2024] [Indexed: 06/07/2024] Open
Abstract
The standard errors (SE) of the maximum likelihood estimates (MLE) of the population parameter vector in nonlinear mixed effect models (NLMEM) are usually estimated using the inverse of the Fisher information matrix (FIM). However, at a finite distance, i.e. far from the asymptotic, the FIM can underestimate the SE of NLMEM parameters. Alternatively, the standard deviation of the posterior distribution, obtained in Stan via the Hamiltonian Monte Carlo algorithm, has been shown to be a proxy for the SE, since, under some regularity conditions on the prior, the limiting distributions of the MLE and of the maximum a posterior estimator in a Bayesian framework are equivalent. In this work, we develop a similar method using the Metropolis-Hastings (MH) algorithm in parallel to the stochastic approximation expectation maximisation (SAEM) algorithm, implemented in the saemix R package. We assess this method on different simulation scenarios and data from a real case study, comparing it to other SE computation methods. The simulation study shows that our method improves the results obtained with frequentist methods at finite distance. However, it performed poorly in a scenario with the high variability and correlations observed in the real case study, stressing the need for calibration.
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Affiliation(s)
- Mélanie Guhl
- Université Paris Cité, Inserm, IAME, F-75018, Paris, France.
| | - Julie Bertrand
- Université Paris Cité, Inserm, IAME, F-75018, Paris, France
| | - Lucie Fayette
- Université Paris Cité, Inserm, IAME, F-75018, Paris, France
| | - François Mercier
- Department of Biostatistics, Roche Innovation Center Basel, Basel, Switzerland
| | - Emmanuelle Comets
- Université Paris Cité, Inserm, IAME, F-75018, Paris, France
- Univ Rennes, Inserm, EHESP, Irset - UMR_S 1085, F-35000, Rennes, France
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4
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Tardivon C, Loingeville F, Donnelly M, Feng K, Sun W, Sun G, Grosser S, Zhao L, Fang L, Mentré F, Bertrand J. Evaluation of model-based bioequivalence approach for single sample pharmacokinetic studies. CPT Pharmacometrics Syst Pharmacol 2023; 12:904-915. [PMID: 37114321 PMCID: PMC10349197 DOI: 10.1002/psp4.12960] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2022] [Revised: 03/02/2023] [Accepted: 03/03/2023] [Indexed: 04/29/2023] Open
Abstract
In a traditional pharmacokinetic (PK) bioequivalence (BE) study, a two-way crossover study is conducted, PK parameters (namely the area under the time-concentration curve [AUC] and the maximal concentration [C max ]) are obtained by noncompartmental analysis (NCA), and the BE analysis is performed using the two one-sided test (TOST) method. For ophthalmic drugs, however, only one sample of aqueous humor, in one eye, per eye can be obtained in each patient, which precludes the traditional BE analysis. To circumvent this issue, the U.S. Food and Drug Administration (FDA) has proposed an approach coupling NCA with either parametric or nonparametric bootstrap (NCA bootstrap). The model-based TOST (MB-TOST) has previously been proposed and evaluated successfully for various settings of sparse PK BE studies. In this paper, we evaluate, via simulations, MB-TOST in the specific setting of single sample PK BE study and compare its performance to NCA bootstrap. We performed BE study simulations using a published PK model and parameter values and evaluated multiple scenarios, including study design (parallel or crossover), sampling times (5 or 10 spread across the dosing interval), and geometric mean ratio (of 0.8, 0.9, 1, and 1.25). Using the simulated structural PK model, MB-TOST performed similarly to NCA bootstrap for AUC. ForC max , the latter tended to be conservative and less powerful. Our research suggests that MB-TOST may be considered as an alternative BE approach for single sample PK studies, provided that the PK model is correctly specified and the test drug has the same structural model as the reference drug.
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Affiliation(s)
- Coralie Tardivon
- INSERM, IAMEUniversité de ParisParisFrance
- Département Epidémiologie Biostatistiques et Recherche CliniqueAP‐HP, Hôpital BichatParisFrance
| | - Florence Loingeville
- INSERM, IAMEUniversité de ParisParisFrance
- METRICS: Evaluation of Health Technologies and Medical PracticesUniversity of Lille, CHU Lille, ULR 2694LilleFrance
| | - Mark Donnelly
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic DrugsCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringMaryland20993USA
| | - Kairui Feng
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic DrugsCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringMaryland20993USA
| | - Wanjie Sun
- Office of Biostatistics, Office of Translational SciencesCenter for Drug Evaluation and Research, U.S. Food and Drug AdministrationSilver SpringMaryland20993USA
| | - Guoying Sun
- Office of Biostatistics, Office of Translational SciencesCenter for Drug Evaluation and Research, U.S. Food and Drug AdministrationSilver SpringMaryland20993USA
| | - Stella Grosser
- Office of Biostatistics, Office of Translational SciencesCenter for Drug Evaluation and Research, U.S. Food and Drug AdministrationSilver SpringMaryland20993USA
| | - Liang Zhao
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic DrugsCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringMaryland20993USA
| | - Lanyan Fang
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic DrugsCenter for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringMaryland20993USA
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Cruz Gutierrez NA, Melo OO, Martinez CA. Semiparametric generalized estimating equations for repeated measurements in cross-over designs. Stat Methods Med Res 2023:9622802231158736. [PMID: 36919447 DOI: 10.1177/09622802231158736] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/16/2023]
Abstract
A model for cross-over designs with repeated measures within each period was developed. It was obtained using an extension of generalized estimating equations that includes a parametric component to model treatment effects and a non-parametric component to model time and carry-over effects; the estimation approach for the non-parametric component is based on splines. A simulation study was carried out to explore the model properties. Thus, when there is a carry-over effect or a functional temporal effect, the proposed model presents better results than the standard models. Among the theoretical properties, the solution is found to be analogous to weighted least squares. Therefore, model diagnostics can be made by adapting the results from a multiple regression. The proposed methodology was implemented in the data sets of the cross-over experiments that motivated the approach of this work: systolic blood pressure and insulin in rabbits.
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Affiliation(s)
| | - Oscar Orlando Melo
- Departamento de Estadística, Facultad de Ciencias, 28021Universidad Nacional de Colombia, Mosquera, Colombia
| | - Carlos Alberto Martinez
- Corporaciòn Colombiana de Investigaciòn Agropecuaria - AGROSAVIA, Sede Central, Mosquera,Colombia
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Zou Y, de Jager V, Hesseling AC, Diacon AH, Wiesner L, Mostert J, Svensson EM, Garcia-Prats A. Relative bioavailability of delamanid 50 mg tablets dispersed in water in healthy adult volunteers. Br J Clin Pharmacol 2023:10.1111/bcp.15672. [PMID: 36692865 PMCID: PMC10363574 DOI: 10.1111/bcp.15672] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/05/2022] [Revised: 01/13/2023] [Accepted: 01/16/2023] [Indexed: 01/25/2023] Open
Abstract
AIM Delamanid is a novel drug for the treatment of drug-resistant tuberculosis, manufactured as 50-mg solid and 25-mg dispersible tablets. We evaluated the effects of dispersing the 50-mg tablet, focusing on the relative bioavailability. METHODS Delamanid, 50-mg tablets administered dispersed vs swallowed whole, was investigated in a phase I, four-period, crossover study. Two of three dose strengths of delamanid (25, 50 or 100 mg) were given to healthy adult participants, in both whole and dispersed forms, with a 7-day washout period. Blood samples were collected over 168 h after each dose. Delamanid and its metabolite DM-6705 were analysed with a validated liquid chromatography tandem mass spectrometry assay. The pharmacokinetics of both analytes were analysed using nonlinear mixed-effect modelling. Palatability and acceptability were determined using a standardized questionnaire. RESULTS Twenty-four participants completed the study. The bioavailability of dispersed tablets was estimated to be 107% of whole tablets, with a 90% confidence interval of 99.7-114%, fulfilling bioequivalence criteria. The two formulations were not significantly different regarding either bioavailability or its variability. Bioavailability increased at lower doses, by 34% (26-42%) at 50 mg and by 74% (64-86%) at 25 mg, relative to 100 mg. The majority of participants (93%) found the dispersed formulation acceptable in palatability across all delamanid doses. CONCLUSIONS Dispersed 50-mg delamanid tablets have similar bioavailability to tablets swallowed whole in adult volunteers. This can be an option for children and other patients who cannot swallow whole tablets, improving access to treatment.
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Affiliation(s)
- Yuanxi Zou
- Department of Pharmacy, Uppsala University, Uppsala, Sweden
| | - Veronique de Jager
- TASK Applied Science, TASK Clinical Research Centre, Cape Town, South Africa
| | - Anneke C. Hesseling
- Desmond Tutu TB Centre, Department of Paediatrics and Child Health, Stellenbosch University, Tygerberg, South Africa
| | - Andreas H. Diacon
- TASK Applied Science, TASK Clinical Research Centre, Cape Town, South Africa
| | - Lubbe Wiesner
- UCT Pharmacology Research Laboratory, Division of Clinical Pharmacology, Department of Medicine, University of Cape Town, Cape Town, South Africa
| | - Joni Mostert
- TASK Applied Science, TASK Clinical Research Centre, Cape Town, South Africa
| | - Elin M. Svensson
- Department of Pharmacy, Uppsala University, Uppsala, Sweden
- Department of Pharmacy, Radboud University Medical Center, Nijmegen, The Netherlands
| | - Anthony Garcia-Prats
- Desmond Tutu TB Centre, Department of Paediatrics and Child Health, Stellenbosch University, Tygerberg, South Africa
- Department of Pediatrics, University of Wisconsin-Madison, Madison, WI, USA
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7
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Cruz NA, Melo OO, Martinez CA. A correlation structure for the analysis of Gaussian and non-Gaussian responses in crossover experimental designs with repeated measures. Stat Pap (Berl) 2023. [DOI: 10.1007/s00362-022-01391-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
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8
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Guhl M, Mercier F, Hofmann C, Sharan S, Donnelly M, Feng K, Sun W, Sun G, Grosser S, Zhao L, Fang L, Mentré F, Comets E, Bertrand J. Impact of model misspecification on model-based tests in PK studies with parallel design: real case and simulation studies. J Pharmacokinet Pharmacodyn 2022; 49:557-577. [PMID: 36112338 PMCID: PMC9483500 DOI: 10.1007/s10928-022-09821-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2022] [Accepted: 08/11/2022] [Indexed: 11/26/2022]
Abstract
This article evaluates the performance of pharmacokinetic (PK) equivalence testing between two formulations of a drug through the Two-One Sided Tests (TOST) by a model-based approach (MB-TOST), as an alternative to the classical non-compartmental approach (NCA-TOST), for a sparse design with a few time points per subject. We focused on the impact of model misspecification and the relevance of model selection for the reference data. We first analysed PK data from phase I studies of gantenerumab, a monoclonal antibody for the treatment of Alzheimer’s disease. Using the original rich sample data, we compared MB-TOST to NCA-TOST for validation. Then, the analysis was repeated on a sparse subset of the original data with MB-TOST. This analysis inspired a simulation study with rich and sparse designs. With rich designs, we compared NCA-TOST and MB-TOST in terms of type I error and study power. With both designs, we explored the impact of misspecifying the model on the performance of MB-TOST and adding a model selection step. Using the observed data, the results of both approaches were in general concordance. MB-TOST results were robust with sparse designs when the underlying PK structural model was correctly specified. Using the simulated data with a rich design, the type I error of NCA-TOST was close to the nominal level. When using the simulated model, the type I error of MB-TOST was controlled on rich and sparse designs, but using a misspecified model led to inflated type I errors. Adding a model selection step on the reference data reduced the inflation. MB-TOST appears as a robust alternative to NCA-TOST, provided that the PK model is correctly specified and the test drug has the same PK structural model as the reference drug.
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9
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Sharan S, Fang L, Lukacova V, Chen X, Hooker AC, Karlsson MO. Model-Informed Drug Development for Long-Acting Injectable Products: Summary of American College of Clinical Pharmacology Symposium. Clin Pharmacol Drug Dev 2021; 10:220-228. [PMID: 33624456 DOI: 10.1002/cpdd.928] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2020] [Accepted: 01/30/2021] [Indexed: 01/12/2023]
Affiliation(s)
- Satish Sharan
- Division of Quantitative Methods and Modeling (DQMM), Office of Research and Standards (ORS), Office of Generic Drugs (OGD), Center for Drug Evaluation and Research (CDER), U.S. Food and Drug Administration (FDA), Silver Spring, Maryland, USA
| | - Lanyan Fang
- Division of Quantitative Methods and Modeling (DQMM), Office of Research and Standards (ORS), Office of Generic Drugs (OGD), Center for Drug Evaluation and Research (CDER), U.S. Food and Drug Administration (FDA), Silver Spring, Maryland, USA
| | - Viera Lukacova
- Simulation Sciences, Simulations Plus, Inc., Lancaster, CA, USA
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10
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Debavelaere V, Allassonnière S. On the curved exponential family in the Stochastic Approximation Expectation Maximization Algorithm. ESAIM-PROBAB STAT 2021. [DOI: 10.1051/ps/2021015] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
The Expectation-Maximization Algorithm (EM) is a widely used method allowing to estimate the maximum likelihood of models involving latent variables. When the Expectation step cannot be computed easily, one can use stochastic versions of the EM such as the Stochastic Approximation EM. This algorithm, however, has the drawback to require the joint likelihood to belong to the curved exponential family. To overcome this problem, [16] introduced a rewriting of the model which “exponentializes” it by considering the parameter as an additional latent variable following a Normal distribution centered on the newly defined parameters and with fixed variance. The likelihood of this new exponentialized model now belongs to the curved exponential family. Although often used, there is no guarantee that the estimated mean is close to the maximum likelihood estimate of the initial model. In this paper, we quantify the error done in this estimation while considering the exponentialized model instead of the initial one. By verifying those results on an example, we see that a trade-off must be made between the speed of convergence and the tolerated error. Finally, we propose a new algorithm allowing a better estimation of the parameter in a reasonable computation time to reduce the bias.
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11
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Loingeville F, Bertrand J, Nguyen TT, Sharan S, Feng K, Sun W, Han J, Grosser S, Zhao L, Fang L, Möllenhoff K, Dette H, Mentré F. New Model-Based Bioequivalence Statistical Approaches for Pharmacokinetic Studies with Sparse Sampling. AAPS JOURNAL 2020; 22:141. [PMID: 33125589 DOI: 10.1208/s12248-020-00507-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Accepted: 09/01/2020] [Indexed: 11/30/2022]
Abstract
In traditional pharmacokinetic (PK) bioequivalence analysis, two one-sided tests (TOST) are conducted on the area under the concentration-time curve and the maximal concentration derived using a non-compartmental approach. When rich sampling is unfeasible, a model-based (MB) approach, using nonlinear mixed effect models (NLMEM) is possible. However, MB-TOST using asymptotic standard errors (SE) presents increased type I error when asymptotic conditions do not hold. In this work, we propose three alternative calculations of the SE based on (i) an adaptation to NLMEM of the correction proposed by Gallant, (ii) the a posteriori distribution of the treatment coefficient using the Hamiltonian Monte Carlo algorithm, and (iii) parametric random effects and residual errors bootstrap. We evaluate these approaches by simulations, for two-arms parallel and two-period, two-sequence cross-over design with rich (n = 10) and sparse (n = 3) sampling under the null and the alternative hypotheses, with MB-TOST. All new approaches correct for the inflation of MB-TOST type I error in PK studies with sparse designs. The approach based on the a posteriori distribution appears to be the best compromise between controlled type I errors and computing times. MB-TOST using non-asymptotic SE controls type I error rate better than when using asymptotic SE estimates for bioequivalence on PK studies with sparse sampling.
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Affiliation(s)
- Florence Loingeville
- University of Paris, IAME INSERM, UMR 1137, 75018, Paris, France. .,University of Lille, CHU Lille, ULR 2694 - METRICS : Evaluation of Health Technologies and Medical Practices, F-59000, Lille, France. .,Laboratoire de Biomathématiques, Faculté de Pharmacie, 3 Rue du Professeur Laguesse, 59 000, Lille, France.
| | - Julie Bertrand
- University of Paris, IAME INSERM, UMR 1137, 75018, Paris, France
| | - Thu Thuy Nguyen
- University of Paris, IAME INSERM, UMR 1137, 75018, Paris, France
| | - Satish Sharan
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, 20993, USA
| | - Kairui Feng
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, 20993, USA
| | - Wanjie Sun
- Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, 20993, USA
| | - Jing Han
- Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, 20993, USA
| | - Stella Grosser
- Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, 20993, USA
| | - Liang Zhao
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, 20993, USA
| | - Lanyan Fang
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, Maryland, 20993, USA
| | - Kathrin Möllenhoff
- Department of Mathematics, Ruhr-Universitat Bochum, Bochum, Germany.,Institute of Medical Statistics and Computational Biology, Faculty of Medicine, University of Cologne, Cologne, Germany
| | - Holger Dette
- Department of Mathematics, Ruhr-Universitat Bochum, Bochum, Germany
| | - France Mentré
- University of Paris, IAME INSERM, UMR 1137, 75018, Paris, France
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12
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Möllenhoff K, Loingeville F, Bertrand J, Nguyen TT, Sharan S, Zhao L, Fang L, Sun G, Grosser S, Mentré F, Dette H. Efficient model-based bioequivalence testing. Biostatistics 2020; 23:314-327. [DOI: 10.1093/biostatistics/kxaa026] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/29/2020] [Revised: 06/18/2020] [Accepted: 06/21/2020] [Indexed: 11/14/2022] Open
Abstract
SummaryThe classical approach to analyze pharmacokinetic (PK) data in bioequivalence studies aiming to compare two different formulations is to perform noncompartmental analysis (NCA) followed by two one-sided tests (TOST). In this regard, the PK parameters area under the curve (AUC) and $C_{\max}$ are obtained for both treatment groups and their geometric mean ratios are considered. According to current guidelines by the U.S. Food and Drug Administration and the European Medicines Agency, the formulations are declared to be sufficiently similar if the $90\%$ confidence interval for these ratios falls between $0.8$ and $1.25 $. As NCA is not a reliable approach in case of sparse designs, a model-based alternative has already been proposed for the estimation of $\rm AUC$ and $C_{\max}$ using nonlinear mixed effects models. Here we propose another, more powerful test than the TOST and demonstrate its superiority through a simulation study both for NCA and model-based approaches. For products with high variability on PK parameters, this method appears to have closer type I errors to the conventionally accepted significance level of $0.05$, suggesting its potential use in situations where conventional bioequivalence analysis is not applicable.
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Affiliation(s)
- Kathrin Möllenhoff
- Department of Mathematics, Ruhr-Universität Bochum and Institute of Medical Statistics and Computational Biology, Faculty of Medicine, University of Cologne, Cologne, Germany
| | - Florence Loingeville
- Faculty of Pharmacy, University of Lille, EA 2694: Public health: Epidemiology and Healthcare Quality, 59000 Lille, France
| | | | | | - Satish Sharan
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, MD 20993, USA
| | - Liang Zhao
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, MD 20993, USA
| | - Lanyan Fang
- Division of Quantitative Methods and Modeling, Office of Research Standards, Office of Generic Drugs, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, MD 20993, USA
| | - Guoying Sun
- Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, MD 20993, USA
| | - Stella Grosser
- Office of Biostatistics, Office of Translational Sciences, Center for Drug Evaluation and Research, Food and Drug Administration, Silver Spring, MD 20993, USA
| | - France Mentré
- IAME INSERM, Université de Paris, 75018 Paris, France
| | - Holger Dette
- Department of Mathematics, Ruhr-Universität Bochum, Germany
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Seurat J, Nguyen TT, Mentré F. Robust designs accounting for model uncertainty in longitudinal studies with binary outcomes. Stat Methods Med Res 2019; 29:934-952. [DOI: 10.1177/0962280219850588] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Abstract
To optimize designs for longitudinal studies analyzed by mixed-effect models with binary outcomes, the Fisher information matrix can be used. Optimal design approaches, however, require a priori knowledge of the model. We aim to propose, for the first time, a robust design approach accounting for model uncertainty in longitudinal trials with two treatment groups, assuming mixed-effect logistic models. To optimize designs given one model, we compute several optimality criteria based on Fisher information matrix evaluated by the new approach based on Monte-Carlo/Hamiltonian Monte-Carlo. We propose to use the DDS-optimality criterion, as it ensures a compromise between the precision of estimation of the parameters, and hence the Wald test power, and the overall precision of parameter estimation. To account for model uncertainty, we assume candidate models with their respective weights. We compute robust design across these models using compound DDS-optimality. Using the Fisher information matrix, we propose to predict the average power over these models. Evaluating this approach by clinical trial simulations, we show that the robust design is efficient across all models, allowing one to achieve good power of test. The proposed design strategy is a new and relevant approach to design longitudinal studies with binary outcomes, accounting for model uncertainty.
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Affiliation(s)
- Jérémy Seurat
- IAME, UMR 1137, INSERM, Université Paris Diderot, Paris, France
| | - Thu Thuy Nguyen
- IAME, UMR 1137, INSERM, Université Paris Diderot, Paris, France
| | - France Mentré
- IAME, UMR 1137, INSERM, Université Paris Diderot, Paris, France
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14
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Yan F, Zhu H, Liu J, Jiang L, Huang X. Design and inference for 3-stage bioequivalence testing with serial sampling data. Pharm Stat 2018; 17:458-476. [PMID: 29726096 PMCID: PMC6146059 DOI: 10.1002/pst.1865] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2017] [Revised: 03/21/2018] [Accepted: 03/29/2018] [Indexed: 11/07/2022]
Abstract
A bioequivalence test is to compare bioavailability parameters, such as the maximum observed concentration (Cmax ) or the area under the concentration-time curve, for a test drug and a reference drug. During the planning of a bioequivalence test, it requires an assumption about the variance of Cmax or area under the concentration-time curve for the estimation of sample size. Since the variance is unknown, current 2-stage designs use variance estimated from stage 1 data to determine the sample size for stage 2. However, the estimation of variance with the stage 1 data is unstable and may result in too large or too small sample size for stage 2. This problem is magnified in bioequivalence tests with a serial sampling schedule, by which only one sample is collected from each individual and thus the correct assumption of variance becomes even more difficult. To solve this problem, we propose 3-stage designs. Our designs increase sample sizes over stages gradually, so that extremely large sample sizes will not happen. With one more stage of data, the power is increased. Moreover, the variance estimated using data from both stages 1 and 2 is more stable than that using data from stage 1 only in a 2-stage design. These features of the proposed designs are demonstrated by simulations. Testing significance levels are adjusted to control the overall type I errors at the same level for all the multistage designs.
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Affiliation(s)
- Fangrong Yan
- Research Center of Biostatistics and Computational Pharmacy, China Pharmaceutical University, Nanjing 210009, P.R. China
| | - Huihong Zhu
- Research Center of Biostatistics and Computational Pharmacy, China Pharmaceutical University, Nanjing 210009, P.R. China
| | - Junlin Liu
- Research Center of Biostatistics and Computational Pharmacy, China Pharmaceutical University, Nanjing 210009, P.R. China
| | - Liyun Jiang
- Research Center of Biostatistics and Computational Pharmacy, China Pharmaceutical University, Nanjing 210009, P.R. China
| | - Xuelin Huang
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, Texas, 77030, USA
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15
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Willemsen SP, Russo CM, Lesaffre E, Leão D. Flexible multivariate nonlinear models for bioequivalence problems. STAT MODEL 2017. [DOI: 10.1177/1471082x17706018] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Modelling the concentration of a drug in the bloodstream over time is usually done using compartment models. In pharmacokinetic data, they turn into highly nonlinear mixed-effects models (NLMEMs) when we take the heterogeneity between subjects into account. Fitting of NLMEMs can be difficult and may involve complex algorithms, with convergence critically depending on the initial values and maybe requiring data transformations. In this article, we propose a flexible alternative to the usual parametric compartment models, inspired by the Multivariate SuperImposition by Translation and Rotation (MSITAR) model but adapted to be applicable in this new field. A fully parametric one-compartment NLMEM is considered for comparison. We make use of a Bayesian approach and illustrate the method on a real dataset where the interest lies in contrasting the average and individual bioequivalence of a test and reference formulation of an anti-hypertensive drug.
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Affiliation(s)
- Sten P Willemsen
- Department of Biostatistics, Erasmus Medical Center Rotterdam, The Netherlands
| | - Cibele M Russo
- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brazil
| | - Emmanuel Lesaffre
- Department of Biostatistics, Erasmus Medical Center Rotterdam, The Netherlands
- L-BioStat, KU Leuven, Leuven, Belgium
| | - Dorival Leão
- Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, SP, Brazil
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16
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A SAEM algorithm for fused lasso penalized NonLinear Mixed Effect Models: Application to group comparison in pharmacokinetics. Comput Stat Data Anal 2016. [DOI: 10.1016/j.csda.2015.10.006] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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17
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Population Pharmacokinetic Analysis of the Oral Absorption Process and Explaining Intra-Subject Variability in Plasma Exposures of Imatinib in Healthy Volunteers. Eur J Drug Metab Pharmacokinet 2015; 41:527-39. [PMID: 26189007 DOI: 10.1007/s13318-015-0292-3] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
BACKGROUND AND OBJECTIVE Imatinib mesylate is presently the first-line treatment for chronic myeloid leukemia (CML). The aim of this study was to investigate the absorption and distribution kinetics of imatinib in healthy Iranian volunteers using nonlinear mixed effects modeling (NLMEM) to assess the overall, intra- and inter-subject variabilities in pharmacokinetic parameters after oral administration. METHODS This analysis was based on data from 24 healthy subjects who participated in a bioequivalence study after administering a single dose of 200 mg of each formulation. Imatinib concentrations were quantified using a validated liquid chromatography method. To simultaneously describe the imatinib pharmacokinetic profiles obtained with both formulations, a population pharmacokinetic model was applied to data using SAEM algorithm implemented in MONOLIX, whilst simulations were used by numerical solving of ordinary differential equations to calculate secondary parameters in individuals for bioequivalence studies. RESULTS According to goodness-of-fit criteria, a two-compartment open model with sequential zero- then first-order absorption and first-order elimination was used as the structural pharmacokinetic model. Inter-individual variability (IIV) was considered for all parameters. Typical population estimates (% IIV) were fraction of the drug absorbed with a zero-order kinetic (Fr) of 0.153 (47.9 %) in period (Tk0) of 0.714 h (47.4 %), first-order absorption rate constant (k a) of 0.94 h(-1)(31.2 %), oral clearance of 19 L/h (27.9 %), central volume of distribution (V c/F) of 139 L (21.5 %), apparent peripheral volume of distribution (V p/F) of 130 L (29.7 %) and the apparent inter-compartment clearance (Q/F) of 29.6 L/h (41.8 %). Body mass index (BMI) was the only covariate found to significantly affect V p /F. The coefficient of variation for intra-individual plasma exposure (AUC0-∞) was 27.8 %. CONCLUSIONS Analyses using NLMEM for imatinib exhibited absorption complexities such as two input rates and medium to high intra-individual variability in drug exposure.
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18
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Burton JH, Volaufova J. Approximate testing in two-stage nonlinear mixed models. J STAT COMPUT SIM 2015; 85:2656-2665. [PMID: 26139949 DOI: 10.1080/00949655.2014.948442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Abstract
We investigate here small sample properties of approximate F-tests about fixed effects parameters in nonlinear mixed models. For estimation of population fixed effects parameters as well as variance components, we apply the two-stage approach. This method is useful and popular when the number of observations per sampling unit is large enough. The approximate F-test is constructed based on large sample approximation to the distribution of nonlinear least squares estimates of subject-specific parameters. We recommend a modified test statistic that takes into consideration approximation to the large sample Fisher information matrix (See [1]). Our main focus is on comparing finite sample properties of broadly used approximate tests (Wald test and likelihood ratio test) and the modified F-test under the null hypothesis, especially accuracy of p-values (See [2]). For that purpose two extensive simulation studies are conducted based on pharmacokinetic models (See [3, 4]).
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Affiliation(s)
- J H Burton
- Pennington Biomedical Research Center, LSU, Baton Rouge, LA, USA
| | - J Volaufova
- LSUHSC School of Public Health, New Orleans, LA, USA
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19
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Volaufova J. Approximate Small-Sample Tests of Fixed Effects in Nonlinear Mixed Models. COMMUN STAT-SIMUL C 2014. [DOI: 10.1080/03610918.2013.835407] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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20
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Kloprogge F, Simpson JA, Day NPJ, White NJ, Tarning J. Statistical power calculations for mixed pharmacokinetic study designs using a population approach. AAPS JOURNAL 2014; 16:1110-8. [PMID: 25011414 PMCID: PMC4147042 DOI: 10.1208/s12248-014-9641-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/12/2014] [Accepted: 06/19/2014] [Indexed: 11/30/2022]
Abstract
Simultaneous modelling of dense and sparse pharmacokinetic data is possible with a population approach. To determine the number of individuals required to detect the effect of a covariate, simulation-based power calculation methodologies can be employed. The Monte Carlo Mapped Power method (a simulation-based power calculation methodology using the likelihood ratio test) was extended in the current study to perform sample size calculations for mixed pharmacokinetic studies (i.e. both sparse and dense data collection). A workflow guiding an easy and straightforward pharmacokinetic study design, considering also the cost-effectiveness of alternative study designs, was used in this analysis. Initially, data were simulated for a hypothetical drug and then for the anti-malarial drug, dihydroartemisinin. Two datasets (sampling design A: dense; sampling design B: sparse) were simulated using a pharmacokinetic model that included a binary covariate effect and subsequently re-estimated using (1) the same model and (2) a model not including the covariate effect in NONMEM 7.2. Power calculations were performed for varying numbers of patients with sampling designs A and B. Study designs with statistical power >80% were selected and further evaluated for cost-effectiveness. The simulation studies of the hypothetical drug and the anti-malarial drug dihydroartemisinin demonstrated that the simulation-based power calculation methodology, based on the Monte Carlo Mapped Power method, can be utilised to evaluate and determine the sample size of mixed (part sparsely and part densely sampled) study designs. The developed method can contribute to the design of robust and efficient pharmacokinetic studies.
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Affiliation(s)
- Frank Kloprogge
- Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, 420/6 Rajvithi Road, Bangkok, 10400, Thailand,
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Chen YI, Huang CS. New approach to assess bioequivalence parameters using generalized gamma mixed-effect model (model-based asymptotic bioequivalence test). Stat Med 2014; 33:786-97. [PMID: 24105871 DOI: 10.1002/sim.5978] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Revised: 06/04/2013] [Accepted: 08/27/2013] [Indexed: 11/07/2022]
Abstract
In the pharmacokinetic (PK) study under a 2x2 crossover design that involves both the test and reference drugs, we propose a mixed-effects model for the drug concentration-time profiles obtained from subjects who receive different drugs at different periods. In the proposed model, the drug concentrations repeatedly measured from the same subject at different time points are distributed according to a multivariate generalized gamma distribution, and the drug concentration-time profiles are described by a compartmental PK model with between-subject and within-subject variations. We then suggest a bioequivalence test based on the estimated bioavailability parameters in the proposed mixed-effects model. The results of a Monte Carlo study further show that the proposed model-based bioequivalence test is not only better on maintaining its level but also more powerful for detecting the bioequivalence of the two drugs than the conventional bioequivalence test based on a non-compartmental analysis or the one based on a mixed-effects model with a normal error variable. The application of the proposed model and test is finally illustrated by using data sets in two PK studies.
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Affiliation(s)
- Yuh-Ing Chen
- Institute of Statistics, National Central University, Jhongli 32054, Taiwan
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22
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Mbogning C, Bleakley K, Lavielle M. Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm. J STAT COMPUT SIM 2014. [DOI: 10.1080/00949655.2013.878938] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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23
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Dodds M, Chow V, Markus R, Pérez-Ruixo JJ, Shen D, Gibbs M. The use of pharmacometrics to optimize biosimilar development. J Pharm Sci 2013; 102:3908-14. [PMID: 24027111 DOI: 10.1002/jps.23697] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/19/2012] [Revised: 06/07/2013] [Accepted: 07/24/2013] [Indexed: 12/27/2022]
Abstract
Pharmacometric approaches can assist in biosimilar development by leveraging quantitative knowledge of the originator product characteristics such as dose-exposure and exposure-response information to support a targeted approach to clinical studies. The degree to which these approaches can be applied relies on the level of information known about the originator and information that supports application of the originator model to the biosimilar. A model-based approach testing the hypothesis that the biosimilar PK and/or PK/PD profile is similar to the originator in the target patient population is aligned with the central comparability exercise required for the biosimilar approval. This Commentary details the key opportunities in study design and study analysis where pharmacometrics approaches can aid biosimilar development.
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Affiliation(s)
- Mike Dodds
- Pharmacokinetics & Drug Metabolism, Amgen Inc., Seattle, Washington, 98119
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24
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Laouénan C, Guedj J, Mentré F. Clinical trial simulation to evaluate power to compare the antiviral effectiveness of two hepatitis C protease inhibitors using nonlinear mixed effect models: a viral kinetic approach. BMC Med Res Methodol 2013; 13:60. [PMID: 23617810 PMCID: PMC3651343 DOI: 10.1186/1471-2288-13-60] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/26/2012] [Accepted: 04/12/2013] [Indexed: 12/15/2022] Open
Abstract
BACKGROUND Models of hepatitis C virus (HCV) kinetics are increasingly used to estimate and to compare in vivo drug's antiviral effectiveness of new potent anti-HCV agents. Viral kinetic parameters can be estimated using non-linear mixed effect models (NLMEM). Here we aimed to evaluate the performance of this approach to precisely estimate the parameters and to evaluate the type I errors and the power of the Wald test to compare the antiviral effectiveness between two treatment groups when data are sparse and/or a large proportion of viral load (VL) are below the limit of detection (BLD). METHODS We performed a clinical trial simulation assuming two treatment groups with different levels of antiviral effectiveness. We evaluated the precision and the accuracy of parameter estimates obtained on 500 replication of this trial using the stochastic approximation expectation-approximation algorithm which appropriately handles BLD data. Next we evaluated the type I error and the power of the Wald test to assess a difference of antiviral effectiveness between the two groups. Standard error of the parameters and Wald test property were evaluated according to the number of patients, the number of samples per patient and the expected difference in antiviral effectiveness. RESULTS NLMEM provided precise and accurate estimates for both the fixed effects and the inter-individual variance parameters even with sparse data and large proportion of BLD data. However Wald test with small number of patients and lack of information due to BLD resulted in an inflation of the type I error as compared to the results obtained when no limit of detection of VL was considered. The corrected power of the test was very high and largely outperformed what can be obtained with empirical comparison of the mean VL decline using Wilcoxon test. CONCLUSION This simulation study shows the benefit of viral kinetic models analyzed with NLMEM over empirical approaches used in most clinical studies. When designing a viral kinetic study, our results indicate that the enrollment of a large number of patients is to be preferred to small population sample with frequent assessments of VL.
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Affiliation(s)
- Cédric Laouénan
- INSERM, UMR 738, Université Paris Diderot, Sorbonne Paris Cité, Paris F-75018, France.
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Pharmacokinetic similarity of biologics: analysis using nonlinear mixed-effects modeling. Clin Pharmacol Ther 2011; 91:234-42. [PMID: 22205196 DOI: 10.1038/clpt.2011.216] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
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.
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Nguyen TT, Bazzoli C, Mentré F. Design evaluation and optimisation in crossover pharmacokinetic studies analysed by nonlinear mixed effects models. Stat Med 2011; 31:1043-58. [PMID: 21965170 DOI: 10.1002/sim.4390] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2010] [Revised: 07/13/2011] [Accepted: 08/04/2011] [Indexed: 01/15/2023]
Abstract
Bioequivalence or interaction trials are commonly studied in crossover design and can be analysed by nonlinear mixed effects models as an alternative to noncompartmental approach. We propose an extension of the population Fisher information matrix in nonlinear mixed effects models to design crossover pharmacokinetic trials, using a linearisation of the model around the random effect expectation, including within-subject variability and discrete covariates fixed or changing between periods. We use the expected standard errors of treatment effect to compute the power for the Wald test of comparison or equivalence and the number of subjects needed for a given power. We perform various simulations mimicking crossover two-period trials to show the relevance of these developments. We then apply these developments to design a crossover pharmacokinetic study of amoxicillin in piglets and implement them in the new version 3.2 of the r function PFIM.
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