Likelihood-Based Diagnostics for Influential Individuals in Non-Linear Mixed Effects Model Selection

Purpose. Data from single individuals, or a small group of subjects may influence non-linear mixed effects model selection. Diagnostics routinely applied in model building may identify such individuals, but these methods are not specifically designed for that purpose and are, therefore, not optimal. We describe two likelihood-based diagnostics for identifying individuals that can influence the choice between two competing models. Methods. One method is based on a jackknife of the raw data on the individual level and refitting the model to each new data set. The second method is a calculation which utilises the contribution each individual make to the objective function values under each of the two models. The two methods were applied to model selection during analysis of a real data set. Results. The agreement between the methods was high. Individuals for whom there was a discrepancy between the methods tended to be those for which neither of the contending models described the data appropriately. Both methods identified individuals that influenced the model selection. Conclusions. Two objective, specific and quantitative methods for identifying influential individuals in nonlinear mixed effects model selection have been presented. One of the methods doesn't require additional model fitting and is therefore particularly attractive.     

核苷类抗病毒药群体药动学研究及应用

群体药动学运用经典药动学统计学相结合的方法来定量考察目标群体中药物浓度的影响因素,并应用于优化临床药物治疗方案。核苷类抗病毒药在临床抗病毒治疗中发挥重要的作用,此类药物的疗效、不良反应与其体内药物浓度息息相关,阿昔洛韦、更昔洛韦、泛昔洛韦、齐多夫定、恩曲他滨、拉米夫定和阿巴卡韦等核苷类抗病毒药的群体药动学研究促进该类药物在临床的合理应用。     

Profile Likelihood-Based Confidence Intervals Using Monte Carlo Integration for Population Pharmacokinetic Parameters

Population pharmacokinetic (PPK) analysis usually employs nonlinear mixed effects models using first-order linearization methods. It is well known that linearization methods do not always perform well in actual situations. To avoid linearization, the Monte Carlo integration method has been proposed. Moreover, we generally utilize asymptotic confidence intervals for PPK parameters based on Fisher information. It is known that likelihood-based confidence intervals are more accurate than those from the usual asymptotic confidence intervals. We propose profile likelihood-based confidence intervals using Monte Carlo integration. We have evaluated the performance of the proposed method through a simulation study, and analyzed the erythropoietin concentration data set by the method.     

非线性混合效应模型法计算1型糖尿病大鼠环孢素药代动力学参数

目的 研究糖尿病对环孢素(Ciclosporin, CsA)体内药物代谢动力学的影响。方法 大鼠腹腔注射65 mg·kg^-1链脲菌素(STZ)建立1型糖尿病大鼠模型。造模5周后通过荧光偏振免疫分析(FPIA)法检测大鼠灌胃环孢素(10 mg·kg^-1)后全血中的环孢素浓度,采用非线性混合效应法(Nonlinear mixed effect model, NONMEM)建立药物代谢动力学模型,贝叶斯(Bayes)反馈法获取个体参数并比较。结果 STZ注射1周后,大鼠空腹血糖超过11.1 mmol·L^-1,确认1型糖尿病大鼠造模成功。造模5周后,糖尿病大鼠的血糖显著增高。给药后,环孢素在大鼠体内呈现一房室模型,群体典型值及个体间差异(Between Subject Variability, BSV)分别为：CL/F=0.525 L·h^-1, BSV=32.1%;V/F=5.18 L, BSV=35.6%; Ka=1.82,BSV= 71.1%。正常组与糖尿病组大鼠CL/F无显著性差异(P>0.05);V/F无显著性差异(P>0.05);Ka有显著性差异(P<0.05) 。结论 1型糖尿病大鼠灌胃环孢素的吸收速率常数显著改变,且存在较大的个体间差异,提示糖尿病状态下会影响环孢素的吸收。     

Estimating Area Under the Curve and Relative Exposure in a Pharmacokinetic Study with Data Below Quantification Limit

Area under the drug-concentration-over-time curve (AUC) is an important endpoint for many phase I/II clinical trials and laboratory assays. Drug concentrations are measured using laboratory assays with a lower limit of quantification (LLOQ). How to calculate AUC when some drug concentration data are below the LLOQ remains as a challenge. In this article, we develop a maximum likelihood method to estimate AUC and relative exposure (i.e., ratio of two AUCs) when data below LLOQ exists. We also compare the proposed method to several commonly used methods, including imputation with model-predicted values or ad hoc values (i.e., LLOQ, LLOQ/2, or zero) through a simulation study. The proposed method gives unbiased inference. Commonly used methods can provide biased estimation, especially when a large proportion of data is below LLOQ. Application to a case study is also presented.     

Methodological approaches to the population analysis of toxicity data

Toxicokinetics is the assessment of systemic exposure in toxicity studies, in which pharmacokinetic data are generated, either as an integral component in the conduct of the nonclinical toxicity studies or in specially designed supportive studies, in order to assess systemic exposure. The data may be used in the interpretation of toxicity findings and contribute to the assessment of the relevance of these findings to clinical safety. Data may be obtained from all animals in a toxicity study, in representative subgroups, in satellite groups or in separate studies. Applying a mixed effects modelling approach in toxicokinetics offers many advantages over the current approach of having satellite groups. Sparse samples for measuring drug/metabolite concentration are collected in all main animals in the majority of studies where toxicological findings are obtained. Such sampling is unlikely to distress the animals, disturb the conduct of a toxicological study or affect the outcome of the study. Many of the outcome measures in toxicological studies are categorical in nature. For example, lesions may be scored on a one to four scale, from none to severe. The analysis of such data is usually carried out using a general mixed modelling approach. We have implemented such models in a nonlinear mixed effects modelling framework which allows us to relate pharmacokinetic response to outcome. A case study is used to illustrate the principles of general mixed effects modelling in toxicokinetics.     

A Genetic Algorithm-Based, Hybrid Machine Learning Approach to Model Selection

We describe a general and robust method for identification of an optimal non-linear mixed effects model. This includes structural, inter-individual random effects, covariate effects and residual error models using machine learning. This method is based on combinatorial optimization using genetic algorithm. GRANT SUPPORT: NIBIB P41 EB001975, NIMH PO1 HL40962, MH064823.     

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.     

Power, Selection Bias and Predictive Performance of the Population Pharmacokinetic Covariate Model

Identification and quantification of covariate relations is often an important part of population pharmacokinetic/pharmacodynamic (PK/PD) modelling. The covariate model is regularly built in a stepwise manner. With such methods, selection bias may be a problem if only statistically significant covariates are accepted into the model. Competition between multiple covariates may further increase selection bias, especially when there is a moderate to high correlation between the covariates. This can also result in a loss of power to find the true covariates. The aim of this simulation study was to investigate the effect on power, selection bias and predictive performance of the covariate model, when altering study design and system-related quantities. Data sets with 20-1000 subjects were investigated. Five covariates were created by sampling from a multivariate standard normal distribution. The true covariate was set up to have no, low, moderate and high correlation to the other four covariates, respectively. Data sets, in which each individual had two or three PK observations, were simulated using a one-compartment i.v. bolus model. The true covariate influenced clearance according to one of several magnitudes. Different magnitudes of residual error and inter-individual variability in the structural model parameters were also introduced to the simulation model. A total of 7400 replicate data sets were simulated independently for each combination of the above conditions. Models with one of the five simulated covariates influencing clearance and the model without any covariate were fitted to the data. The probability of selecting (according to a pre-specified P-value) the different covariates, along with the estimated covariate coefficient, was recorded. The results show that selection bias is very high for small data sets (< or = 50 subjects) simulated with a weak covariate effect. If selected under these circumstances, the covariate coefficient is on average estimated to be more than twice its true value, making the covariate model useless for predictive purposes. Surprisingly, even though competition from false covariates caused substantial loss in the power of selecting the true covariate, the already high selection bias increased only marginally. This means that the bias due to competition is negligible if statistical significance is also required for covariate selection. Bias and predictive performance are direct functions of power, only indirectly affected by study design and system-related quantities. Mainly because of selection bias, low-powered covariates can be expected to harm the predictive performance when selected. For the same reason these low-powered covariates may falsely appear to be clinically relevant when selected. If the aim of an analysis is predictive modelling, we do not recommend stepwise selection or significance testing of covariates to be performed on small or moderately sized data sets (<50-100 subjects).     

Application of NONMEM to routine bioavailability data

Although NONMEM has been proposed as a modeling tool for sparse data sets, little work has described its application to pharmacokinetic data which is also amenable to typical evaluations. An analysis was performed with NONMEM using plasma concentration data obtained during the development of liquid and capsule extended-release (ER) pseudoephedrine products. A total of four studies (single dose and steady-state studies for both the liquid and capsule formulations) were evaluated, each with an immediate-release (IR) control, and consisting of 18 to 20 subjects. NONMEM analyses provided additional information which could not be obtained through traditional means. Specifically, NONMEM provided not only estimates of residual error from single dose and steady-state studies but also a stochastic measure of bioinequivalence and dose-dumping. It permitted hypothesis testing in the same process as pharmacokinetic parameter estimation, such as contrasting absorption rates from capsule and suspension ER products. A less biased estimate of absorption rate was obtainable for E R formulations by utilizing IR runs. Finally, these NONMEM runs confirmed that, even when data are plentiful and amenable to two-stage analyses, NONMEM provides estimates that may in fact be more meaningful and less susceptible to assay or residual variability. Fundamental differences between population and two-stage approaches are discussed.Glossary NONMEM NONlinearMixed Effects Models Program - ER Extended release (formulation) - IR Immediate release (formulation) - Study SUSP-SD Single dose suspension bioavailability study - Study SUSP-SS Steady-state suspension bioavailability study - Study CAP-SD Single dose capsule bioavailability study - Study CAP-SS Steady-state capsule bioavailability study - D Dose,g - V Population average apparent volume of distribution, L/kg - Ke Population average terminal elimination rate constant, hr^–1 - Ka Population average absorption rate constant, hr^–1 - V _j,ke _j, andKa _j The jth individual's estimates ofV, Ke, andKa - _jV, _j ke, and _j Ka Randomly distributed interindividual (between-subject) errors with a mean of zero and variances estimated by NONMEM - CONC Predicted concentration, ng/ml - CONC _mij The ith predicted concentrations from pharmacokinetic(V, Ke, Ka) and statistical ( _j V, _j Ke, _j ^Ka ) model - CONC _ij The ith observed concentration from the jth individual - _ij Residual intrasubject (within-subject) error corresponding toCONC _ij, - CF _Ka ,CF _BIO Contrast fractions for capsule vs. suspension parameters corresponding toCONC _ij - KaREL Relative absorption rate expressed as a ratio ofKa for Formulation ER divided byKa for Formulation IR - Population (typical) parameter estimate from NONMEM - ₂ Interindividual () variance estimate from NONMEM (reported as %CV in Tables) - ₂ Intraindividual () variance estimate from NONMEM (reported as% CV in Tables) - SEE Standard error of the estimate - 95% CI 95% Confidence interval for, ², or ² - %CV Coefficient of variation, expressed as percent - t _i The ith sample time, associated withCONC _mij , andCONC _ij - Ka _IR Ka from formulation IR - Ka _ER Ka from one of the ER formulations - BIO Bioavailability of an ER formulation relative to Formulation IR - _jBIO, _j KaREL Ratio error terms whose variances can describe frequency distribution for bioinequivalence and dosedumping of ER formulations     

基于Excel函数求解血管外给药二室模型的药动学及隔室模型参数

目的:建立以Excel函数求解血管外给药二室模型的药动学及隔室模型参数的方法。方法:采用残数法,利用Excel函数,逐步求解药动学和隔室模型参数。结果:基于Excel函数可直观演示血管外给药二室模型的药动学及隔室模型参数计算过程,结果与教材一致。结论:本方法操作简便、界面直观、结果可靠、易于推广,可用于临床教学或实验中药动学参数的计算。     

丙戊酸群体药动学模型的建立与临床应用

目的建立门诊癫痫患者应用丙戊酸的群体药代动力学模型,并进行血药浓度预测。方法162例门诊癫痫患者连续服用丙戊酸钠达稳态,测定其谷浓度附近血样标本共196个。用非线性混合效应模型（NONMEM）考察固定效应对丙戊酸相对清除率的影响。结果体重、丙戊酸钠日剂量、合并用药等因素与清除率CL（L/h）之间的拟合模型为CL=0.00482×WT＋0.110×TAMT＋0.394×CBZS＋0.108×PHT＋0.0822×PB＋0.0583。将11例患者血药浓度预测值与实测值作线性回归,其方程为DV=1.0632×PRED—3.2665（μg/ml）,r=0.     

Application of Resampling Techniques to Estimate Exact Significance Levels for Covariate Selection During Nonlinear Mixed Effects Model Building: Some Inferences

Purpose. One of the main objectives of the nonlinear mixed effects modeling is to provide rational individualized dosing strategies by explaining the interindividual variability using intrinsic and/or extrinsic factors (covariates). The aim of the current study was to evaluate, using computer simulations and real data, methods for estimating the exact significance level for including or excluding a covariate during model building. Methods. Original data were simulated using a simple one-compartment pharmacokinetic model with (full model) or without (null model) covariates (one or two). The covariate values in the original data were resampled (using either permutations or parametric bootstrap methods) to generate data under the null hypothesis that there is no covariate effect. The original and permuted data were fitted to null and full models, using first-order and first-order condition estimation (with or without interaction) methods in NONMEM, to compare the asymptotic and conditional p-value. Target log-likelihood ratio cutoffs for assessing covariate effects were derived. Results. The simulations showed that for sparse as well as dense data, the first-order condition estimation methods yielded the best results while the first-order method performs somewhat better for sparse data. Depending on the modeling objective, the appropriate asymptotic p-value can be substituted for the conditional significance level. Target log-likelihood ratio cutoffs should be determined separately for each covariate when exact p-values are important. Conclusions. Resampling methods can be employed to estimate the exact significance level for including a covariate during nonlinear mixed effects model building. Some reasonable inferences can be drawn for potential application to design future population analyses.     

Influence of pharmacogenetics on indinavir disposition and short-term response in HIV patients initiating HAART

Aims  To assess the relationship between genetic polymorphisms and indinavir pharmacokinetic variability and to study the link between concentrations and short-term response or metabolic safety. Methods  Forty protease inhibitor-naive patients initiating highly active antiretroviral therapy (HAART) including indinavir/ritonavir and enrolled in the COPHAR 2–ANRS 111 trial were studied. At week 2, four blood samples were taken before and up to 6 h following drug intake. A population pharmacokinetic analysis was performed using the stochastic approximation expectation maximization (SAEM) algorithm implemented in MONOLIX software. The area under the concentration–time curve (AUC) and maximum (C_max) and trough concentrations (C_trough) of indinavir were derived from the population model and tested for their correlation with short-term viral response and safety measurements, while for ritonavir, these same three parameters were tested for their correlation with short-term biochemical safety Results  A one-compartment model with first-order absorption and elimination best described both indinavir and ritonavir concentrations. For indinavir, the estimated clearance and volume of distribution were 22.2 L/h and 97.3 L, respectively. The eight patients with the *1B/*1B genotype for the CYP3A4 gene showed a 70% decrease in absorption compared to those with the *1A/*1B or *1A/*1A genotypes (0.5 vs. 2.1, P = 0.04, likelihood ratio test by permutation). The indinavir AUC and C_trough were positively correlated with the decrease in human immunodeficiency virus RNA between week 0 and week 2 (r = 0.4, P = 0.03 and r = -0.4, P = 0.03, respectively). Patients with the *1B/*1B genotype also had a significantly lower indinavir C_max (median 3.6, range 2.1–5.2 ng/mL) than those with the *1A/*1B or *1A/*1A genotypes (median 4.4, range 2.2–8.3 ng/mL) (P = 0.04) and a lower increase in triglycerides during the first 4 weeks of treatment (median 0.1, range −0.7 to 1.4 vs. median 0.6, range −0.5 to 1.7 mmol/L, respectively; P = 0.02). For ritonavir, the estimated clearance and volume of distribution were 8.3 L/h and 60.7 L, respectively, and concentrations were not found to be correlated to biochemical safety. Indinavir and ritonavir absorption rate constants were found to be correlated, as well as their apparent volumes of distribution and clearances, indicating correlated bioavailability of the two drugs. Conclusion  The CYP3A4*1B polymorphism was found to influence the pharmacokinetics of indinavir and, to some extent, the biochemical safety of indinavir.     

三七总皂苷和灯盏花素单用与联用时主要成分的药动学比较

目的考察三七总皂苷(主要成分为三七皂苷R1、人参皂苷Rg1、人参皂苷Re、人参皂苷Rb1、人参皂苷Rd)和灯盏花素(主要成分为野黄芩苷)复方粉针制剂在健康比格犬体内的药动学,并与单独使用三七总皂苷粉针或灯盏花素粉针时的药动学参数进行比较。方法建立检测给药后不同时间点的比格犬血样中三七总皂苷各组分及野黄芩苷浓度的液相色谱-串联质谱联用(LC-MS/MS)方法,计算各成分的药动学参数。结果单次给予复方粉针后,三七皂苷R1、人参皂苷Rg1、人参皂苷Re、人参皂苷Rb1、人参皂苷Rd及野黄芩苷的血浆消除半衰期(t1/2)分别为(1.08±0.30),(0.95±0.16),(1.40±0.39),(51.08±10.42),(64.84±17.70)及(2.00±0.88)h;峰浓度(Cmax)分别为(4641.00±758.84),(11325.00±1418.62),(1822.00±253.37),(39380.00±5644.03),(12964.00±2738.41)及(2669.00±841.79)ng·mL-1;血药浓度-时间曲线下面积(AUC0-∞)分别为(2832.31±308.38),(3454.00±473.08),(1210.80±161.06),(1360410.90±277244.88),(320529.65±101345.47),(450.68±90.50)ng·mL-1·h。与三七总皂苷粉针或灯盏花素粉针单次给药相比,复方粉针单次给药后,血药浓度-时间曲线相似;三七皂苷R1、人参皂苷Rg1、人参皂苷Re、人参皂苷Rd的Cmax显著升高(P<0.05);人参皂苷Rb1和野黄芩苷Cmax差异无统计学意义(P>0.05);t1/2、AUC0-∞差异无统计学意义(P>0.05)。结论三七总皂苷粉针和灯盏花素粉针联合用药可提高三七总皂苷部分组分的Cmax,对野黄芩苷的药动学没有明显影响。     

Pharmacokinetics and renal excretion of desmopressin after intravenous administration to healthy subjects and renally impaired patients

OBJECTIVE: To evaluate the influence of renal impairment on the pharmacokinetics of desmopressin. METHODS: Twenty-four subjects were enrolled in the study, 18 with varying degrees of renal impairment and six healthy volunteers. Each subject received a single intravenous dose of 2 microg desmopressin. Blood and urine samples were collected for 24 h and assayed for desmopressin by radioimmunoassay. Plasma concentrations and the amounts of desmopressin excreted in the urine were analysed simultaneously by use of mixed effects modelling. RESULTS: Only mild adverse events were observed. Both the renal and the nonrenal clearance of desmopressin were found to vary with the creatinine clearance (CrCL). A decrease of 1.67% in the CrCL (corresponding to 1 ml min(-1) from 60 ml min(-1)) was found to cause a 1.74% decrease in the renal clearance and a 0.93% decrease in the nonrenal clearance. The fall in renal clearance caused the amount of desmopressin excreted in urine to decrease from 47% in healthy subjects to 21% in the patients with severe renal impairment. The mean systemic clearance of desmopressin was 10 litres h(-1) in healthy subjects and 2.9 litres h(-1) in patients with severe renal impairment (difference -7.5 litres h(-1), 95% CI [-11; -4.3] litres h(-1)). Correspondingly, the mean terminal half-life, was 3.7 h in healthy subjects and 10 h in patients with severe renal impairment (difference 6.7 h, 95% CI [4.0; 9.4] h). CONCLUSION: Although desmopressin appears to be safe and well-tolerated by patients with impaired renal function, great caution should be exercised when titrating towards an efficient dosage regimen if patients with moderately or severely impaired renal function are to be treated with desmopressin at all.     

Analysis of Toxicokinetic Data Using NONMEM: Impact of Quantification Limit and Replacement Strategies for Censored Data

The purpose of this study was to examine how best to incorporate plasma samples which fall below an assay's lower limit of quantification into the process of toxicokinetic data modeling. Secondly to establish what proportion of data can be below the quantification limit without compromising NONMEM's parameter estimates. Using pharmacokinetic parameters determined in a rat toxicokinetic study we simulated datasets that might emerge from similar experiments in which only one sample was obtained per individual. A number of quantification limits were used which resulted in increasing proportions of data values being treated as if they were below the limit of quantification (BQL). For each quantification level we incorporated BQL data into our analyses in number of ways. We compared these analysis methods with respect to how well the underlying parameter values were retrieved. Omitting BQL data values or entering them as zero led to inaccurate and biased study results. We found that incorporating BQL values using more complex substitution methods via a mixed effects model produced more reliable and less biased parameter estimates. The four substitution methods that we investigated performed similarly. Parameter estimates became less reliable and more biased as the quantification level was increased depending on the method of BQL value incorporation. Naive methods of BQL data handling can produce unreliable and biased parameter estimates. An alternative is to incorporate BQL values into a population-type model, our results showed this method to be preferable. We found it advisable that the proportion of BQL data should not exceed one third and, if possible should be less than one quarter.     

Integration of Pharmacometric and Statistical Analyses Using Clinical Trial Simulations to Enhance Quantitative Decision Making in Clinical Drug Development

This article outlines a general framework in which clinical trial simulations (CTS) are employed integrating both pharmacometric and statistical analyses to support trial design and quantitative decision making in drug development. Specifically, predictive pharmacometric models are used as data-generation models to simulate data, while data-analytic models as specified in the statistical analysis plan are used to analyze the simulated data and to apply a quantitative data-analytic decision rule. Various probability metrics including probability of achieving the target value, probability of success, and probability of a correct decision are proposed to support study design recommendations and quantitative decision-making. A case study is presented to illustrate the CTS methods and procedures described in this article.