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.     

Implementation and Evaluation of the SAEM Algorithm for Longitudinal Ordered Categorical Data with an Illustration in Pharmacokinetics–Pharmacodynamics

Analysis of longitudinal ordered categorical efficacy or safety data in clinical trials using mixed models is increasingly performed. However, algorithms available for maximum likelihood estimation using an approximation of the likelihood integral, including LAPLACE approach, may give rise to biased parameter estimates. The SAEM algorithm is an efficient and powerful tool in the analysis of continuous/count mixed models. The aim of this study was to implement and investigate the performance of the SAEM algorithm for longitudinal categorical data. The SAEM algorithm is extended for parameter estimation in ordered categorical mixed models together with an estimation of the Fisher information matrix and the likelihood. We used Monte Carlo simulations using previously published scenarios evaluated with NONMEM. Accuracy and precision in parameter estimation and standard error estimates were assessed in terms of relative bias and root mean square error. This algorithm was illustrated on the simultaneous analysis of pharmacokinetic and discretized efficacy data obtained after a single dose of warfarin in healthy volunteers. The new SAEM algorithm is implemented in MONOLIX 3.1 for discrete mixed models. The analyses show that for parameter estimation, the relative bias is low for both fixed effects and variance components in all models studied. Estimated and empirical standard errors are similar. The warfarin example illustrates how simple and rapid it is to analyze simultaneously continuous and discrete data with MONOLIX 3.1. The SAEM algorithm is extended for analysis of longitudinal categorical data. It provides accurate estimates parameters and standard errors. The estimation is fast and stable.     

Evaluation of Estimation Methods and Power of Tests of Discrete Covariates in Repeated Time-to-Event Parametric Models: Application to Gaucher Patients Treated by Imiglucerase

Analysis of repeated time-to-event data is increasingly performed in pharmacometrics using parametric frailty models. The aims of this simulation study were (1) to assess estimation performance of Stochastic Approximation Expectation Maximization (SAEM) algorithm in MONOLIX, Adaptive Gaussian Quadrature (AGQ), and Laplace algorithm in PROC NLMIXED of SAS and (2) to evaluate properties of test of a dichotomous covariate on occurrence of events. The simulation setting is inspired from an analysis of occurrence of bone events after the initiation of treatment by imiglucerase in patients with Gaucher Disease (GD). We simulated repeated events with an exponential model and various dropout rates: no, low, or high. Several values of baseline hazard model, variability, number of subject, and effect of covariate were studied. For each scenario, 100 datasets were simulated for estimation performance and 500 for test performance. We evaluated estimation performance through relative bias and relative root mean square error (RRMSE). We studied properties of Wald and likelihood ratio test (LRT). We used these methods to analyze occurrence of bone events in patients with GD after starting an enzyme replacement therapy. SAEM with three chains and AGQ algorithms provided good estimates of parameters much better than SAEM with one chain and Laplace which often provided poor estimates. Despite a small number of repeated events, SAEM with three chains and AGQ gave small biases and RRMSE. Type I errors were closed to 5%, and power varied as expected for SAEM with three chains and AGQ. Probability of having at least one event under treatment was 19.1%.     

The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects

Using simulated viral load data for a given maraviroc monotherapy study design, the feasibility of different algorithms to perform parameter estimation for a pharmacokinetic-pharmacodynamic-viral dynamics (PKPD-VD) model was assessed. The assessed algorithms are the first-order conditional estimation method with interaction (FOCEI) implemented in NONMEM VI and the SAEM algorithm implemented in MONOLIX version 2.4. Simulated data were also used to test if an effect compartment and/or a lag time could be distinguished to describe an observed delay in onset of viral inhibition using SAEM. The preferred model was then used to describe the observed maraviroc monotherapy plasma concentration and viral load data using SAEM. In this last step, three modelling approaches were compared; (i) sequential PKPD-VD with fixed individual Empirical Bayesian Estimates (EBE) for PK, (ii) sequential PKPD-VD with fixed population PK parameters and including concentrations, and (iii) simultaneous PKPD-VD. Using FOCEI, many convergence problems (56%) were experienced with fitting the sequential PKPD-VD model to the simulated data. For the sequential modelling approach, SAEM (with default settings) took less time to generate population and individual estimates including diagnostics than with FOCEI without diagnostics. For the given maraviroc monotherapy sampling design, it was difficult to separate the viral dynamics system delay from a pharmacokinetic distributional delay or delay due to receptor binding and subsequent cellular signalling. The preferred model included a viral load lag time without inter-individual variability. Parameter estimates from the SAEM analysis of observed data were comparable among the three modelling approaches. For the sequential methods, computation time is approximately 25% less when fixing individual EBE of PK parameters with omission of the concentration data compared with fixed population PK parameters and retention of concentration data in the PD-VD estimation step. Computation times were similar for the sequential method with fixed population PK parameters and the simultaneous PKPD-VD modelling approach. The current analysis demonstrated that the SAEM algorithm in MONOLIX is useful for fitting complex mechanistic models requiring multiple differential equations. The SAEM algorithm allowed simultaneous estimation of PKPD and viral dynamics parameters, as well as investigation of different model sub-components during the model building process. This was not possible with the FOCEI method (NONMEM version VI or below). SAEM provides a more feasible alternative to FOCEI when facing lengthy computation times and convergence problems with complex models.     

Drug–drug interaction predictions with PBPK models and optimal multiresponse sampling time designs: application to midazolam and a phase I compound. Part 2: clinical trial results

Purpose To compare results of population PK analyses obtained with a full empirical design (FD) and an optimal sparse design (MD) in a Drug–Drug Interaction (DDI) study aiming to evaluate the potential CYP3A4 inhibitory effect of a drug in development, SX, on a reference substrate, midazolam (MDZ). Secondary aim was to evaluate the interaction of SX on MDZ in the in vivo study. Methods To compare designs, real data were analysed by population PK modelling technique using either FD or MD with NONMEM FOCEI for SX and with NONMEM FOCEI and MONOLIX SAEM for MDZ. When applicable a Wald test was performed to compare model parameter estimates, such as apparent clearance (CL/F), across designs. To conclude on the potential interaction of SX on MDZ PK, a Student paired test was applied to compare the individual PK parameters (i.e. log(AUC) and log(C_max)) obtained either by a non-compartmental approach (NCA) using FD or from empirical Bayes estimates (EBE) obtained after fitting the model separately on each treatment group using either FD or MD. Results For SX, whatever the design, CL/F was well estimated and no statistical differences were found between CL/F estimated values obtained with FD (CL/F = 8.2 l/h) and MD (CL/F = 8.2 l/h). For MDZ, only MONOLIX was able to estimate CL/F and to provide its standard error of estimation with MD. With MONOLIX, whatever the design and the administration setting, MDZ CL/F was well estimated and there were no statistical differences between CL/F estimated values obtained with FD (72 l/h and 40 l/h for MDZ alone and for MDZ with SX, respectively) and MD (77 l/h and 45 l/h for MDZ alone and for MDZ with SX, respectively). Whatever the approach, NCA or population PK modelling, and for the latter approach, whatever the design, MD or FD, comparison tests showed that there was a statistical difference (P < 0.0001) between individual MDZ log(AUC) obtained after MDZ administration alone and co-administered with SX. Regarding C_max, there was a statistical difference (P < 0.05) between individual MDZ log(C_max) obtained under the 2 administration settings in all cases, except with the sparse design with MONOLIX. However, the effect on C_max was small. Finally, SX was shown to be a moderate CYP3A4 inhibitor, which at therapeutic doses increased MDZ exposure by a factor of 2 in average and almost did not affect the C_max. Conclusion The optimal sparse design enabled the estimation of CL/F of a CYP3A4 substrate and inhibitor when co-administered together and to show the interaction leading to the same conclusion as the full empirical design.     

Comparing the performance of FOCE and different expectation-maximization methods in handling complex population physiologically-based pharmacokinetic models

For the purpose of population pharmacometric modeling, a variety of mathematic algorithms are implemented in major modeling software packages to facilitate the maximum likelihood modeling, such as FO, FOCE, Laplace, ITS and EM. These methods are all designed to estimate the set of parameters that maximize the joint likelihood of observations in a given problem. While FOCE is still currently the most widely used method in population modeling, EM methods are getting more popular as the current-generation methods of choice because of their robustness with more complex models and sparse data structures. There are several versions of EM method implementation that are available in public modeling software packages. Although there have been several studies and reviews comparing the performance of different methods in handling relatively simple models, there has not been a dedicated study to compare different versions of EM algorithms in solving complex PBPK models. This study took everolimus as a model drug and simulated PK data based on published results. Three most popular EM methods (SAEM, IMP and QRPEM) and FOCE (as a benchmark reference) were evaluated for their estimation accuracy and converging speed when solving models of increased complexity. Both sparse and rich sampling data structure were tested. We concluded that FOCE was superior to EM methods for simple structured models. For more complex models and/ or sparse data, EM methods are much more robust. While the estimation accuracy was very close across EM methods, the general ranking of speed (fastest to slowest) was: QRPEM, IMP and SAEM. IMP gave the most realistic estimation of parameter standard errors, while under- and over- estimation of standard errors were observed in SAEM and QRPEM methods.     

Evaluation of Uncertainty Parameters Estimated by Different Population PK Software and Methods

The uncertainty associated with parameter estimations is essential for population model building, evaluation, and simulation. Summarized by the standard error (SE), its estimation is sometimes questionable. Herein, we evaluate SEs provided by different non linear mixed-effect estimation methods associated with their estimation performances. Methods based on maximum likelihood (FO and FOCE in NONMEM^TM, nlme in Splus^TM, and SAEM in MONOLIX) and Bayesian theory (WinBUGS) were evaluated on datasets obtained by simulations of a one-compartment PK model using 9 different designs. Bootstrap techniques were applied to FO, FOCE, and nlme. We compared SE estimations, parameter estimations, convergence, and computation time. Regarding SE estimations, methods provided concordant results for fixed effects. On random effects, SAEM and WinBUGS, tended respectively to under or over-estimate them. With sparse data, FO provided biased estimations of SE and discordant results between bootstrapped and original datasets. Regarding parameter estimations, FO showed a systematic bias on fixed and random effects. WinBUGS provided biased estimations, but only with sparse data. SAEM and WinBUGS converged systematically while FOCE failed in half of the cases. Applying bootstrap with FOCE yielded CPU times too large for routine application and bootstrap with nlme resulted in frequent crashes. In conclusion, FO provided bias on parameter estimations and on SE estimations of random effects. Methods like FOCE provided unbiased results but convergence was the biggest issue. Bootstrap did not improve SEs for FOCE methods, except when confidence interval of random effects is needed. WinBUGS gave consistent results but required long computation times. SAEM was in-between, showing few under-estimated SE but unbiased parameter estimations.     

Prediction of Apparent Oral Clearance of Small-Molecule Inhibitors in Pediatric Patients

The purpose of this study was to build regression models for the prediction of apparent oral clearance (CL/F) for small-molecule inhibitors in the pediatric population using data obtained from adults. Two approaches were taken; a simple allometric regression model which considers no interdrug or interindividual variability and an allometric regression model with mixed-effects modeling where some variability parameters are included in the model. Average CL/F values were obtained for 15 drugs at various dosages from 31 literatures (a total of 139 data sets) conducted in adults and for 15 drugs from 26 literatures (62 data sets) conducted in children. Data were randomly separated into the “modeling” or “validation” data set, and the 2 allometric regression models were applied to the modeling data set. The predictive ability of the models was examined by comparing the observed and model-predicted CL/F in children using the validation data set. The percentage root mean square error was 17.2% and 26.3% in the simple allometric regression model and the allometric regression model with mixed-effects modeling, respectively. The predictive ability of the 2 models seems acceptable, suggesting that they could be useful for predicting the CL/F of new small-molecule inhibitors and for determining adequate doses in clinical pharmacotherapy for children.     

用模型和模拟方法设计氨氯地平的群体药动学研究方案

合理的采样设计是建立可靠群体药动学模型的重要基础。应用非线性混合效应模型的群体药动学研究,是一种有效利用稀疏血样数据估算群体药动学参数的方法。本研究根据D最优化设计和贝叶斯法设计采样方案。以已报道的氨氯地平群体药动学模型为基础,根据临床研究的目的、给药方案和随访时间等设计几套采样方案,采用WinPOPT软件计算优化采样方案,用蒙特卡罗法(Monte Carlo)对各优化的采样方案分别建立一套含400个患者的NONMEM数据文件,用NONMEM7.2软件模拟氨氯地平的浓度数据,然后估算其重要药动学参数(CL/F,V/F和Ka),并计算其平均预测误差(MPE)和平均绝对预测误差(MAPE)。在6个采样方案中,以方案6和3对CL/F估算的准确度和精密度较优,MPE分别为0.1%和0.6%,MAPE均为0.7%。对V的估算,各采样方案间无明显差异。因此,选用氨氯地平拟合药动学参数的准确度和精密度较优,且采样点个数较少的方案3为最佳临床研究方案。本研究旨在为开展氨氯地平在肾功能损害合并高血压患者的群体药动学研究提供科学、有效的采样方法,为群体PK/PD研究提供一种优化设计临床研究方案的科学方法。     

基于随机微分方程的群体药物代谢动力学参数的极大似然估计

目的:阐述基于随机微分方程的混合模型在群体药物代谢动力学中参数估计的应用。方法:在随机微分方程的框架下,写出精确的似然函数,通过极大似然估计求解参数值。结果:利用计算机随机模拟证明方法的可行性,并对模拟的结果进行统计分析,得到各参数的点估计值和置信域,符合模拟的预设值。结论:在群体药物代谢动力学研究中,对基于随机微分方程的混合效应模型采用极大似然估计可以得到较好的估计值。     

A Fast Method for Testing Covariates in Population PK/PD Models

The development of covariate models within the population modeling program like NONMEM is generally a time-consuming and non-trivial task. In this study, a fast procedure to approximate the change in objective function values of covariate-parameter models is presented and evaluated. The proposed method is a first-order conditional estimation (FOCE)-based linear approximation of the influence of covariates on the model predictions. Simulated and real datasets were used to compare this method with the conventional nonlinear mixed effect model using both first-order (FO) and FOCE approximations. The methods were mainly assessed in terms of difference in objective function values (ΔOFV) between base and covariate models. The FOCE linearization was superior to the FO linearization and showed a high degree of concordance with corresponding nonlinear models in ΔOFV. The linear and nonlinear FOCE models provided similar coefficient estimates and identified the same covariate-parameter relations as statistically significant or non-significant for the real and simulated datasets. The time required to fit tesaglitazar and docetaxel datasets with 4 and 15 parameter-covariate relations using the linearization method was 5.1 and 0.5 min compared with 152 and 34 h, respectively, with the nonlinear models. The FOCE linearization method allows for a fast estimation of covariate-parameter relations models with good concordance with the nonlinear models. This allows a more efficient model building and may allow the utilization of model building techniques that would otherwise be too time-consuming.     

Population pharmacokinetics of tacrolimus in whole blood and plasma in asian liver transplant patients

OBJECTIVES: The objectives of this study were to develop population pharmacokinetic models of tacrolimus in an Asian population with whole blood and plasma drug concentration data, to compare the variability of the pharmacokinetic parameters in these two matrices and to search for the main patient characteristics that explain the variability in pharmacokinetic parameters. STUDY DESIGN: Prospective pharmacokinetic assessment followed by model fitting. PATIENTS: Whole blood samples from 31 liver transplant patients in a local hospital receiving oral tacrolimus as part of their immunosuppressive therapy were assessed. Plasma samples from 29 of the 31 patients were also evaluated. Concentrations of tacrolimus in whole blood and plasma were determined by an electrospray high-performance liquid chromatography with tandem mass spectrometry. Two hundred and thirteen whole blood and 157 plasma tacrolimus concentrations were used for building two nonlinear mixed-effects population models to describe the disposition of tacrolimus in whole blood and plasma, respectively. Covariates that were investigated included demographic characteristics, biological markers of liver and renal functions, corticosteroid dose and haematological parameter. RESULTS: A one-compartment model was used to describe the whole blood and plasma concentration-time data of tacrolimus after oral administration. For the whole blood population model, the population estimates of the first-order absorption rate constant (k(a)), apparent clearance based on whole blood concentration after oral administration (CL(B)/F) and apparent volume of distribution based on whole blood concentrations after oral administration (V(d,B)/F) were 2.08h(-1), 14.1 L/h and 217L, respectively. The coefficient of variations (CVs) of interpatient variabilities in CL(B)/F and V(d,B)/F were 65.7% and 63.8%, respectively. Bodyweight, liver and renal function influenced CL(B)/F, while height and haematocrit influenced V(d,B)/F. The residual (unexplained) variability was 34.8%. For the plasma population model, the population estimates of the k(a), apparent clearance based on plasma concentrations after oral administration (CL(P)/F) and apparent volume of distribution based on plasma concentrations after oral administration (V(d,P)/F) were 5.21h(-1), 537 L/h and 563L, respectively. The CVs of interpatient variabilities in CL(P)/F and V(d,P)/F were 96.0% and 105.4%, respectively. Bodyweight was found to influence CL(P)/F, while the erythrocyte-to-plasma concentration ratio influenced V(d,P)/F. The residual (unexplained) variability was 49.8% at the mean plasma concentration of 1.1 ng/mL. CONCLUSIONS: Whole blood and plasma population pharmacokinetic models of tacrolimus in Asian adult and paediatric liver transplant patients were developed using prospective data in a clinical setting. This has identified and quantified sources of interindividual variability in CL(B)/F, V(d,B)/F, CL(P)/F and V(d,P)/F of tacrolimus in Asian liver transplant patients. Information derived from the whole blood population model may subsequently be used by clinicians for dosage individualisation through Bayesian forecasting.     

Evaluation of bootstrap methods for estimating uncertainty of parameters in nonlinear mixed-effects models: a simulation study in population pharmacokinetics

Bootstrap methods are used in many disciplines to estimate the uncertainty of parameters, including multi-level or linear mixed-effects models. Residual-based bootstrap methods which resample both random effects and residuals are an alternative approach to case bootstrap, which resamples the individuals. Most PKPD applications use the case bootstrap, for which software is available. In this study, we evaluated the performance of three bootstrap methods (case bootstrap, nonparametric residual bootstrap and parametric bootstrap) by a simulation study and compared them to that of an asymptotic method (Asym) in estimating uncertainty of parameters in nonlinear mixed-effects models (NLMEM) with heteroscedastic error. This simulation was conducted using as an example of the PK model for aflibercept, an anti-angiogenic drug. As expected, we found that the bootstrap methods provided better estimates of uncertainty for parameters in NLMEM with high nonlinearity and having balanced designs compared to the Asym, as implemented in MONOLIX. Overall, the parametric bootstrap performed better than the case bootstrap as the true model and variance distribution were used. However, the case bootstrap is faster and simpler as it makes no assumptions on the model and preserves both between subject and residual variability in one resampling step. The performance of the nonparametric residual bootstrap was found to be limited when applying to NLMEM due to its failure to reflate the variance before resampling in unbalanced designs where the Asym and the parametric bootstrap performed well and better than case bootstrap even with stratification.     

Prediction Discrepancies for the Evaluation of Nonlinear Mixed-Effects Models

Reliable estimation methods for non-linear mixed-effects models are now available and, although these models are increasingly used, only a limited number of statistical developments for their evaluation have been reported. We develop a criterion and a test to evaluate nonlinear mixed-effects models based on the whole predictive distribution. For each observation, we define the prediction discrepancy (pd) as the percentile of the observation in the whole marginal predictive distribution under H₀. We propose to compute prediction discrepancies using Monte Carlo integration which does not require model approximation. If the model is valid, these pd should be uniformly distributed over [0, 1] which can be tested by a Kolmogorov–Smirnov test. In a simulation study based on a standard population pharmacokinetic model, we compare and show the interest of this criterion with respect to the one most frequently used to evaluate nonlinear mixed-effects models: standardized prediction errors (spe) which are evaluated using a first order approximation of the model. Trends in pd can also be evaluated via several plots to check for specific departures from the model     

Retrospective population pharmacokinetic analysis of cetirizine in children aged 6 months to 12 years

AIMS: To evaluate retrospectively the population pharmacokinetics of cetirizine, a second-generation antihistamine, in children. METHODS: Data were pooled from six clinical trials, in which cetirizine was administered orally in various formulations and in single and multiple dosage regimens. The population consisted of 112 children (33 female and 79 male) aged 6 months to 12 years. A one-compartment open model with first-order absorption and elimination was fitted to the plasma concentration-time profiles using nonlinear mixed effects modelling with first-order estimation. RESULTS: A linear association was found between apparent clearance (CL/F) and age with the former increasing by 0.12 l h(-1) per year. The intercept of the relationship was slightly lower for female children (0.59 vs. 0.77 l h(-1) in male). The population estimate of CL/F for an average age of 7 years was 1.61 and 1.43 l h(-1) for male and female children, respectively. A linear association was found between apparent volume of distribution (V/F) and age with the former increasing by 1.4 l year(-1), with an intercept of 4.0 l. The population estimate of V/F for an average age of 7 years was 13.9 l. The magnitudes of interpatient variability were 35.6% for CL/F and 19.7% for V/F. The magnitude of residual variability in cetirizine concentrations was 26.9%. CONCLUSIONS: Population analysis predicts a linear increase in cetirizine CL/F and V/F with age, with CL/F being slightly lower in female children, relative to males of the same age. However, this gender difference probably has no clinical consequences. Since V/F increased more rapidly with age than CL/F, a nonlinear increase in half-life was seen, from < 4 h in infants to near the adult value at 12 years of age. The current recommended dosing regimens that younger children should receive lower but more frequent doses, are confirmed by the present analysis.     

Impact of MDR1 and CYP3A5 on the oral clearance of tacrolimus and tacrolimus-related renal dysfunction in adult living-donor liver transplant patients

OBJECTIVE: The potential influence of the multidrug resistance 1 (MDR1) gene and the cytochrome P450 (CYP) genes, CYP3A4 and CYP3A5, on the oral clearance (CL/F) of tacrolimus in adult living-donor liver transplant patients was examined. Furthermore, the development of renal dysfunction was analyzed in relation to the CYP3A5 genotype. METHODS: Sixty de novo adult liver transplant patients receiving tacrolimus were enrolled in this study. The effects of various covariates (including intestinal and hepatic mRNA levels of MDR1 and CYP3A4, measured in each tissue taken at the time of transplantation, and the CYP3A5*3 polymorphism) on CL/F during the first 50 days after surgery were investigated with the nonlinear mixed-effects modeling program. RESULTS: CL/F increased linearly until postoperative day 14, and thereafter reached a steady state. The initial CL/F immediately after liver transplantation was significantly affected by the intestinal MDR1 mRNA level (P<0.005). Furthermore, patients carrying the CYP3A5*1 allele in the native intestine, but not in the graft liver, showed a 1.47 times higher (95% confidence interval, 1.17-1.77 times, P<0.005) recovery of CL/F with time than patients having the intestinal CYP3A5*3/*3 genotype. The cumulative incidence of renal dysfunction within 1 year after transplantation, evaluated by the Kaplan-Meier method, was significantly associated with the recipient's but not donor's CYP3A5 genotype (*1/*1 and *1/*3 vs. *3/*3: recipient, 17 vs. 46%, P<0.05; donor, 35 vs. 38%, P=0.81). CONCLUSION: These findings suggest that the CYP3A5*1 genotype as well as the MDR1 mRNA level in enterocytes contributes to interindividual variation in the CL/F of tacrolimus in adult recipients early after living-donor liver transplantation. Furthermore, CYP3A5 in the kidney may play a protective role in the development of tacrolimus-related nephrotoxicity.     

Responder cell frequency estimation and binomial three-level nonlinear mixed effects model in limiting dilution assays

Responder cell frequencies (RCF), which describe vaccine-boosted immune responses in herpes zoster (HZ) prevention studies, have been estimated by using limiting dilution assays (LDA). The theoretical linearity assumption between the logarithm of the proportion of nonresponding wells (s) and the cell concentration (N) (or dilution level) in LDA, based on the single-hit Poisson model, is often violated with observed data resulting in biased estimates of RCF. In this article, the Poisson assumption is modified by applying a mixture of Poisson and gamma distributions, resulting in a negative binomial assumption, which presents a better fit between s and N. In LDA for HZ prevention studies, binary responses (responder or non-responder wells) are measured repeatedly at different cell concentrations and over time. To account for the correlation between responses to varying dilution levels from individuals, and the correlation between repeated assays of individuals over time simultaneously, a binomial three-level nonlinear mixed-effects model is proposed. For parameter estimation, a maximum likelihood method is applied via adaptive Gaussian quadrature. There is a lack of non-Gaussian multilevel nonlinear mixed-effects software, which can execute such a complicated fit. In this article, an algorithm for the three-level nonlinear mixed-effects model, which can be inserted into the code in the SAS procedure NLMIXED, is suggested.     

Comparison of different methods to evaluate population dose-response and relative potency: importance of interoccasion variability.

Different mixed-effects models were compared to evaluate the population dose-response and relative potency of two albuterol inhalers. Bronchodilator response was measured after ascending doses of each inhaler in 37 asthmatic patients. A linear mixed-effects model was developed based on the approach proposed by Finney for the evaluation of bioassay data. A nonlinear mixed-effects (Emax) model with interindividual and interoccasion variability (IOV) in the different pharmacodynamic parameters was also fit to the data. Both methods produced a similar estimate of relative potency. However, the estimate of relative potency was 22% lower with the nonlinear mixed-effects model if IOV was not taken into account. Monte Carlo simulations based on a similar study design demonstrated that more biased and variable estimates of ED50 and relative potency were obtained when the nonlinear mixed-effects model ignored the presence of IOV in the data. Furthermore, the linear mixed-effects model that did not account for IOV produced confidence intervals for relative potency that were too narrow and thus could lead to erroneous conclusions. These problems were avoided when the estimation model could account for IOV. Results of the simulations were consistent with those of the experimental data. Although the linear or the nonlinear mixed-effects model may be used to evaluate population dose-response and relative potency, there are important differences in the assumptions made by each method.     

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.