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France Mentré - One of the best experts on this subject based on the ideXlab platform.
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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 Medical Research Methodology, 2013Co-Authors: Cédric Laouénan, Jeremie Guedj, France MentréAbstract: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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Some alternatives to asymptotic Tests for the analysis of pharmacogenetic data using nonlinear mixed effects models.
Biometrics, 2012Co-Authors: Julie Bertrand, Emmanuelle Comets, Marylore Chenel, France MentréAbstract:Nonlinear mixed effects models allow investigating individual differences in drug concentration profiles (pharmacokinetics) and responses. Pharmacogenetics focuses on the genetic component of this variability. Two Tests often used to detect a gene effect on a pharmacokinetic parameter are (1) the Wald Test, assessing whether estimates for the gene effect are significantly different from 0 and (2) the likelihood ratio Test comparing models with and without the genetic effect. Because those asymptotic Tests show inflated type I error on small sample size and/or with unevenly distributed genotypes, we develop two alternatives and evaluate them by means of a simulation study. First, we assess the performance of the permutation Test using the Wald and the likelihood ratio statistics. Second, for the Wald Test we propose the use of the F-distribution with four different values for the denominator degrees of freedom. We also explore the influence of the estimation algorithm using both the first-order conditional estimation with interaction linearization-based algorithm and the stochastic approximation expectation maximization algorithm. We apply these methods to the analysis of the pharmacogenetics of indinavir in HIV patients recruited in the COPHAR2-ANRS 111 trial. Results of the simulation study show that the permutation Test seems appropriate but at the cost of an additional computational burden. One of the four F-distribution-based approaches provides a correct type I error estimate for the Wald Test and should be further investigated.
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Model-based analyses of bioequivalence crossover trials using the stochastic approximation expectation maximisation algorithm.
Statistics in Medicine, 2011Co-Authors: Anne Dubois, Marc Lavielle, Sandro Gsteiger, Etienne Pigeolet, France MentréAbstract:In this work, we develop a bioequivalence analysis using nonlinear mixed effects models (NLMEM) that mimics the standard noncompartmental analysis (NCA). We estimate NLMEM parameters, including between-subject and within-subject variability and treatment, period and sequence effects. We explain how to perform a Wald Test on a secondary parameter, and we propose an extension of the likelihood ratio Test for bioequivalence. We compare these NLMEM-based bioequivalence Tests with standard NCA-based Tests. We evaluate by simulation the NCA and NLMEM estimates and the type I error of the bioequivalence Tests. For NLMEM, we use the stochastic approximation expectation maximisation (SAEM) algorithm implemented in monolix. We simulate crossover trials under H(0) using different numbers of subjects and of samples per subject. We simulate with different settings for between-subject and within-subject variability and for the residual error variance. The simulation study illustrates the accuracy of NLMEM-based geometric means estimated with the SAEM algorithm, whereas the NCA estimates are biased for sparse design. NCA-based bioequivalence Tests show good type I error except for high variability. For a rich design, type I errors of NLMEM-based bioequivalence Tests (Wald Test and likelihood ratio Test) do not differ from the nominal level of 5%. Type I errors are inflated for sparse design. We apply the bioequivalence Wald Test based on NCA and NLMEM estimates to a three-way crossover trial, showing that Omnitrope®; (Sandoz GmbH, Kundl, Austria) powder and solution are bioequivalent to Genotropin®; (Pfizer Pharma GmbH, Karlsruhe, Germany). NLMEM-based bioequivalence Tests are an alternative to standard NCA-based Tests. However, caution is needed for small sample size and highly variable drug.
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The SAEM algorithm for group comparison Tests in longitudinal data analysis based on non-linear mixed-effects model.
Statistics in Medicine, 2007Co-Authors: Adeline Samson, Marc Lavielle, France MentréAbstract:Non-linear mixed-effects models (NLMEMs) are used to improve information gathering from longitudinal studies and are applied to treatment evaluation in disease-evolution studies, such as human immunodeficiency virus (HIV) infection. The estimation of parameters and the statistical Tests are critical issues in NLMEMs since the likelihood and the Fisher information matrix have no closed form. An alternative method to numerical integrations, in which convergence is slow, and to methods based on linearization, in which asymptotic convergence has not been proved, is the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. For the Wald Test and the likelihood ratio Test, we propose estimating the Fisher information matrix by stochastic approximation and the likelihood by importance sampling. We evaluate these SAEM-based Tests in a simulation study in the context of HIV viral load decrease after initiation of an antiretroviral treatment. The results from this simulation illustrate the theoretical convergence properties of SAEM. We also propose a method based on the SAEM algorithm to compute the minimum sample size required to perform a Wald Test of a given power for a covariate effect in NLMEMs. Lastly, we illustrate these Tests on the evaluation of the effect of ritonavir on the indinavir pharmacokinetics in HIV patients and compare the results with those obtained using the adaptative Gaussian quadrature method implemented in the SAS procedure NLMIXED. Copyright (c) 2007 John Wiley & Sons, Ltd.
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Design in nonlinear mixed effects models: Optimization using the Fedorov-Wynn algorithm and power of the Wald Test for binary covariates.
Statistics in Medicine, 2007Co-Authors: Sylvie Retout, Emmanuelle Comets, Adeline Samson, France MentréAbstract:We extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi-exponential model. We first show the relevance of the predicted standard errors (SEs) given by the computation of the population Fisher information matrix using the R function PFIM, in comparison to those computed with the stochastic approximation expectation-maximization algorithm, implemented in the Monolix software. We then highlight the usefulness of the Fedorov-Wynn (FW) algorithm for designs optimization compared to the Simplex algorithm. From the predicted SE of PFIM, we compute the predicted power of the Wald Test to detect a treatment effect as well as the number of subjects needed to achieve a given power. Using the FW algorithm, we investigate the influence of the design on the power and show that, for optimized designs with the same total number of samples, the power increases when the number of subjects increases and the number of samples per subject decreases. A simulation study is also performed with the nlme function of R to confirm this result and show the relevance of the predicted powers compared to those observed by simulation. Copyright (c) 2007 John Wiley & Sons, Ltd.
Raoul P. P. P. Grasman - One of the best experts on this subject based on the ideXlab platform.
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the Wald Test and crame spl acute r rao bound for misspecified models in electromagnetic source analysis
IEEE Transactions on Signal Processing, 2005Co-Authors: Lourens J. Waldorp, Hilde M. Huizenga, Raoul P. P. P. GrasmanAbstract:By using signal processing techniques, an estimate of activity in the brain from the electro- or magneto-encephalogram (EEG or MEG) can be obtained. For a proper analysis, a Test is required to indicate whether the model for brain activity fits. A problem in using such Tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a Test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald Test for these cases. One of the advantages of the Wald Test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald Tests in electromagnetic source analysis (EMSA) are examined: a Test on source amplitudes and a Test on the closeness of source pairs. The Wald Test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald Test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Crame/spl acute/r-Rao bound (CRB) is required for the use of the Wald Test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald Test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald Test are still good, with a moderate number of trials. Additionally, the CRB and Wald Test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude.
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The Wald Test and Crame/spl acute/r-Rao bound for misspecified models in electromagnetic source analysis
IEEE Transactions on Signal Processing, 2005Co-Authors: Lourens J. Waldorp, Hilde M. Huizenga, Raoul P. P. P. GrasmanAbstract:By using signal processing techniques, an estimate of activity in the brain from the electro- or magneto-encephalogram (EEG or MEG) can be obtained. For a proper analysis, a Test is required to indicate whether the model for brain activity fits. A problem in using such Tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a Test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald Test for these cases. One of the advantages of the Wald Test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald Tests in electromagnetic source analysis (EMSA) are examined: a Test on source amplitudes and a Test on the closeness of source pairs. The Wald Test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald Test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Crame/spl acute/r-Rao bound (CRB) is required for the use of the Wald Test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald Test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald Test are still good, with a moderate number of trials. Additionally, the CRB and Wald Test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude.
Adeline Samson - One of the best experts on this subject based on the ideXlab platform.
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design in nonlinear mixed effects models optimization using the fedorov wynn algorithm and power of the Wald Test for binary covariates
Statistics in Medicine, 2007Co-Authors: Sylvie Retout, Emmanuelle Comets, Adeline SamsonAbstract:We extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi-exponential model. We first show the relevance of the predicted standard errors (SEs) given by the computation of the population Fisher information matrix using the R function PFIM, in comparison to those computed with the stochastic approximation expectation-maximization algorithm, implemented in the Monolix software. We then highlight the usefulness of the Fedorov-Wynn (FW) algorithm for designs optimization compared to the Simplex algorithm. From the predicted SE of PFIM, we compute the predicted power of the Wald Test to detect a treatment effect as well as the number of subjects needed to achieve a given power. Using the FW algorithm, we investigate the influence of the design on the power and show that, for optimized designs with the same total number of samples, the power increases when the number of subjects increases and the number of samples per subject decreases. A simulation study is also performed with the nlme function of R to confirm this result and show the relevance of the predicted powers compared to those observed by simulation.
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The SAEM algorithm for group comparison Tests in longitudinal data analysis based on non-linear mixed-effects model.
Statistics in Medicine, 2007Co-Authors: Adeline Samson, Marc Lavielle, France MentréAbstract:Non-linear mixed-effects models (NLMEMs) are used to improve information gathering from longitudinal studies and are applied to treatment evaluation in disease-evolution studies, such as human immunodeficiency virus (HIV) infection. The estimation of parameters and the statistical Tests are critical issues in NLMEMs since the likelihood and the Fisher information matrix have no closed form. An alternative method to numerical integrations, in which convergence is slow, and to methods based on linearization, in which asymptotic convergence has not been proved, is the Stochastic Approximation Expectation-Maximization (SAEM) algorithm. For the Wald Test and the likelihood ratio Test, we propose estimating the Fisher information matrix by stochastic approximation and the likelihood by importance sampling. We evaluate these SAEM-based Tests in a simulation study in the context of HIV viral load decrease after initiation of an antiretroviral treatment. The results from this simulation illustrate the theoretical convergence properties of SAEM. We also propose a method based on the SAEM algorithm to compute the minimum sample size required to perform a Wald Test of a given power for a covariate effect in NLMEMs. Lastly, we illustrate these Tests on the evaluation of the effect of ritonavir on the indinavir pharmacokinetics in HIV patients and compare the results with those obtained using the adaptative Gaussian quadrature method implemented in the SAS procedure NLMIXED. Copyright (c) 2007 John Wiley & Sons, Ltd.
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Design in nonlinear mixed effects models: Optimization using the Fedorov-Wynn algorithm and power of the Wald Test for binary covariates.
Statistics in Medicine, 2007Co-Authors: Sylvie Retout, Emmanuelle Comets, Adeline Samson, France MentréAbstract:We extend the methodology for designs evaluation and optimization in nonlinear mixed effects models with an illustration of the decrease of human immunodeficiency virus viral load after antiretroviral treatment initiation described by a bi-exponential model. We first show the relevance of the predicted standard errors (SEs) given by the computation of the population Fisher information matrix using the R function PFIM, in comparison to those computed with the stochastic approximation expectation-maximization algorithm, implemented in the Monolix software. We then highlight the usefulness of the Fedorov-Wynn (FW) algorithm for designs optimization compared to the Simplex algorithm. From the predicted SE of PFIM, we compute the predicted power of the Wald Test to detect a treatment effect as well as the number of subjects needed to achieve a given power. Using the FW algorithm, we investigate the influence of the design on the power and show that, for optimized designs with the same total number of samples, the power increases when the number of subjects increases and the number of samples per subject decreases. A simulation study is also performed with the nlme function of R to confirm this result and show the relevance of the predicted powers compared to those observed by simulation. Copyright (c) 2007 John Wiley & Sons, Ltd.
Lourens J. Waldorp - One of the best experts on this subject based on the ideXlab platform.
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the Wald Test and crame spl acute r rao bound for misspecified models in electromagnetic source analysis
IEEE Transactions on Signal Processing, 2005Co-Authors: Lourens J. Waldorp, Hilde M. Huizenga, Raoul P. P. P. GrasmanAbstract:By using signal processing techniques, an estimate of activity in the brain from the electro- or magneto-encephalogram (EEG or MEG) can be obtained. For a proper analysis, a Test is required to indicate whether the model for brain activity fits. A problem in using such Tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a Test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald Test for these cases. One of the advantages of the Wald Test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald Tests in electromagnetic source analysis (EMSA) are examined: a Test on source amplitudes and a Test on the closeness of source pairs. The Wald Test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald Test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Crame/spl acute/r-Rao bound (CRB) is required for the use of the Wald Test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald Test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald Test are still good, with a moderate number of trials. Additionally, the CRB and Wald Test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude.
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The Wald Test and Crame/spl acute/r-Rao bound for misspecified models in electromagnetic source analysis
IEEE Transactions on Signal Processing, 2005Co-Authors: Lourens J. Waldorp, Hilde M. Huizenga, Raoul P. P. P. GrasmanAbstract:By using signal processing techniques, an estimate of activity in the brain from the electro- or magneto-encephalogram (EEG or MEG) can be obtained. For a proper analysis, a Test is required to indicate whether the model for brain activity fits. A problem in using such Tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a Test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald Test for these cases. One of the advantages of the Wald Test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald Tests in electromagnetic source analysis (EMSA) are examined: a Test on source amplitudes and a Test on the closeness of source pairs. The Wald Test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald Test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Crame/spl acute/r-Rao bound (CRB) is required for the use of the Wald Test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald Test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald Test are still good, with a moderate number of trials. Additionally, the CRB and Wald Test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude.
Hilde M. Huizenga - One of the best experts on this subject based on the ideXlab platform.
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the Wald Test and crame spl acute r rao bound for misspecified models in electromagnetic source analysis
IEEE Transactions on Signal Processing, 2005Co-Authors: Lourens J. Waldorp, Hilde M. Huizenga, Raoul P. P. P. GrasmanAbstract:By using signal processing techniques, an estimate of activity in the brain from the electro- or magneto-encephalogram (EEG or MEG) can be obtained. For a proper analysis, a Test is required to indicate whether the model for brain activity fits. A problem in using such Tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a Test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald Test for these cases. One of the advantages of the Wald Test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald Tests in electromagnetic source analysis (EMSA) are examined: a Test on source amplitudes and a Test on the closeness of source pairs. The Wald Test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald Test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Crame/spl acute/r-Rao bound (CRB) is required for the use of the Wald Test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald Test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald Test are still good, with a moderate number of trials. Additionally, the CRB and Wald Test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude.
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The Wald Test and Crame/spl acute/r-Rao bound for misspecified models in electromagnetic source analysis
IEEE Transactions on Signal Processing, 2005Co-Authors: Lourens J. Waldorp, Hilde M. Huizenga, Raoul P. P. P. GrasmanAbstract:By using signal processing techniques, an estimate of activity in the brain from the electro- or magneto-encephalogram (EEG or MEG) can be obtained. For a proper analysis, a Test is required to indicate whether the model for brain activity fits. A problem in using such Tests is that often, not all assumptions are satisfied, like the assumption of the number of shells in an EEG. In such a case, a Test on the number of sources (model order) might still be of interest. A detailed analysis is presented of the Wald Test for these cases. One of the advantages of the Wald Test is that it can be used when not all assumptions are satisfied. Two different, previously suggested, Wald Tests in electromagnetic source analysis (EMSA) are examined: a Test on source amplitudes and a Test on the closeness of source pairs. The Wald Test is analytically studied in terms of alternative hypotheses that are close to the null hypothesis (local alternatives). It is shown that the Wald Test is asymptotically unbiased, that it has the correct level and power, which makes it appropriate to use in EMSA. An accurate estimate of the Crame/spl acute/r-Rao bound (CRB) is required for the use of the Wald Test when not all assumptions are satisfied. The sandwich CRB is used for this purpose. It is defined for nonseparable least squares with constraints required for the Wald Test on amplitudes. Simulations with EEG show that when the sensor positions are incorrect, or the number of shells is incorrect, or the conductivity parameter is incorrect, then the CRB and Wald Test are still good, with a moderate number of trials. Additionally, the CRB and Wald Test appear robust against an incorrect assumption on the noise covariance. A combination of incorrect sensor positions and noise covariance affects the possibility of detecting a source with small amplitude.
