Using spline-enhanced ordinary differential equations for PK/PD model development

A spline-enhanced ordinary differential equation (ODE) method is proposed for developing a proper parametric kinetic ODE model and is shown to be a useful approach to PK/PD model development. The new method differs substantially from a previously proposed model development approach using a stochastic differential equation (SDE)-based method. In the SDE-based method, a Gaussian diffusion term is introduced into an ODE to quantify the system noise. In our proposed method, we assume an ODE system with form dx/dt = A(t)x + B(t) where B(t) is a nonparametric function vector that is estimated using penalized splines. B(t) is used to construct a quantitative measure of model uncertainty useful for finding the proper model structure for a given data set. By means of two examples with simulated data, we demonstrate that the spline-enhanced ODE method can provide model diagnostics and serve as a basis for systematic model development similar to the SDE-based method. We compare and highlight the differences between the SDE-based and the spline-enhanced ODE methods of model development. We conclude that the spline-enhanced ODE method can be useful for PK/PD modeling since it is based on a relatively uncomplicated estimation algorithm which can be implemented with readily available software, provides numerically stable, robust estimation for many models, is distribution-free and allows for identification and accommodation of model deficiencies due to model misspecification.     

Population PK/PD analysis of metformin using the signal transduction model

AIMS

To develop a population pharmacokinetic (PK) and pharmacodynamic (PD) model for metformin (500 mg) using the signal transduction model in healthy humans and to predict the PK/PD profile in patients with type 2 diabetes.

METHODS

Following the oral administration of 500 mg metformin to healthy humans, plasma concentrations of metformin were measured using LC-MS/MS. A sequential modelling approach using NONMEM VI was used to facilitate data analysis. Monte Carlo simulation was performed to predict the antihyperglycaemic effect in patients with type 2 diabetes.

RESULTS

Forty-two healthy humans were included in the study. Population mean estimates (relative standard error, RSE) of apparent clearance, apparent volume of distribution and the absorption rate constant were 52.6 l h⁻¹ (4.18%), 113 l (56.6%) and 0.41 h⁻¹, respectively. Covariate analyses revealed that creatinine clearance (CL_CR) significantly influenced metformin: CL/F= 52.6 × (CL_cr/106.5)^0.782. The signal transduction model was applied to describe the antihyperglycaemic effect of metformin. The population means for efficacy, potency, transit time and the Hill coefficient were estimated to be 19.8 (3.17%), 3.68 µg ml⁻¹ (3.89%), 0.5 h (2.89%) and 0.547 (9.05%), respectively. The developed model was used to predict the antihyperglycaemic effect in patients with type 2 diabetes. The predicted plasma glucose concentration value was similar to previous values.

CONCLUSIONS

The population signal transduction model was developed and evaluated for metformin use in healthy volunteers. Model evaluation by non-parametric bootstrap analysis suggested that the proposed model was robust and parameter values were estimated with good precision.     

比伐卢定在中国健康人群的药代动力学/药效学模型研究

目的 建立静脉注射比伐卢定药代动力/药效学(PK/PD)模型.方法 选36名健康受试者,男女各半,随机分为3组,分别单次静脉推注注射用比伐卢定0.50,0.75,1.05 mg·kg-1,在不同时间点监测血药浓度及活性凝血时间(ACT),用WinNonlin软件建立模型.结果 比伐卢定静脉注射二房室线性代谢药代动力学模型AIC值最小,药效学用有基础效应的M-M equation模型,建立比伐卢定PK/PD统一模型,模型数理参数分别为Vc=0.12,k10=3.54,k12=0.75,k21=1.44,E0=126.87,Emax=340.03,EC50=4258.03.经验证,不同剂量组比伐卢定PK/PD曲线预测值落在实测值的95％置信区间内,与实测值吻合良好.结论 建立的比伐卢定PK/PD模型有较好的适用性.     

Sample Size Computations for PK/PD Population Models

We describe an accurate, yet simple and fast sample size computation method for hypothesis testing in population PK/PD studies. We use a first order approximation to the nonlinear mixed effects model and chi-square distributed Wald statistic to compute the minimum sample size to achieve given degree of power in rejecting a null hypothesis in population PK/PD studies. The method is an extension of Rochon’s sample size computation method for repeated measurement experiments. We compute sample sizes for PK and PK/PD models with different conditions, and use Monte Carlo simulation to show that the computed sample size retrieves the required power. We also show the effect of different sampling strategies, such as minimal, i.e., as many observations per individual as parameters in the model, and intensive on sample size. The proposed sample size computation method can produce estimates of minimum sample size to achieve the desired power in hypothesis testing in a greatly reduced time than currently available simulation-based methods. The method is rapid and efficient for sample size computation in population PK/PD study using nonlinear mixed effect models. The method is general and can accommodate any type of hierarchical models. Simulation results suggest that intensive sampling allows the reduction of the number of patients enrolled in a clinical study.     

Automated covariate selection and Bayesian model averaging in population PK/PD models

We illustrate the use of ‘reversible jump’ MCMC to automate the process of covariate selection in population PK/PD analyses. The output from such an approach can be used not only to determine the ‘best’ covariate model for each parameter, but also to formally measure the spread of uncertainty across all possible models, and to average inferences across a range of ‘good’ models. We examine the substantive impact of such model averaging compared to conditioning inferences on the ‘best’ model alone, and conclude that clinically significant differences between the two approaches can arise. The illustrative data that we consider pertain to the drug vancomycin in 59 neonates and infants, and all analyses are conducted using the WinBUGS software with newly developed ‘Jump’ interface installed.     

Pharmacodynamics of piperacillin in severely ill patients evaluated by using a PK/PD model

Penetration of antiinfective drugs into soft tissues is essential for antimicrobial killing at the target site, but is substantially lower in severely ill patients compared with healthy subjects. The present study was conducted to assess the antimicrobial effect of piperacillin in severely ill patients. Strains of Staphylococcus aureus and Pseudomonas aeruginosa were exposed in vitro to concentrations of piperacillin, simulating the pharmacokinetic profiles measured in soft tissue of patients and healthy subjects. The simulation for patients resulted in effective killing, whereas bacterial regrowth was detected for healthy subjects. Our in vitro simulation showed that bacterial killing may be effective in severely ill patients despite relatively low concentrations of piperacillin at the target site. This finding is due to impaired renal function and subsequently prolonged tissue and plasma half-lives of piperacillin in intensive care patients.     

Modeling receptor/gene-mediated effects of corticosteroids on hepatic tyrosine aminotransferase dynamics in rats: dual regulation by endogenous and exogenous corticosteroids

Receptor/gene-mediated effects of corticosteroids on hepatic tyrosine aminotransferase (TAT) were evaluated in normal rats. A group of normal male Wistar rats were injected with 50 mg/kg methylprednisolone (MPL) intramuscularly at the nadir of their plasma corticosterone (CST) rhythm (early light cycle) and sacrificed at various time points up to 96 h post-treatment. Blood and livers were collected to measure plasma MPL, CST, hepatic glucocorticoid receptor (GR) mRNA, cytosolic GR density, TAT mRNA, and TAT activity. The pharmacokinetics of MPL showed bi-exponential disposition with two first-order absorption components from the injection site and bioavailability was 21%. Plasma CST was reduced after MPL dosing, but resumed its daily circadian pattern within 36 h. Cytosolic receptor density was significantly suppressed (90%) and returned to baseline by 72 h resuming its biphasic pattern. Hepatic GR mRNA follows a circadian pattern which was disrupted by MPL and did not return during the study. MPL caused significant down-regulation (50%) in GR mRNA which was followed by a delayed rebound phase (60-70 h). Hepatic TAT mRNA and activity showed up-regulation as a consequence of MPL, and returned to their circadian baseline within 72 and 24 h of treatment. A mechanistic receptor/gene-mediated pharmacokinetic/pharmacodynamic model was able to satisfactorily describe the complex interplay of exogenous and endogenous corticosteroid effects on hepatic GR mRNA, cytosolic free GR, TAT mRNA, and TAT activity in normal rats.     

PK/PD: new insights for antibacterial and antiviral applications

The path of new compounds from discovery to bedside is long and costly and a large majority of compounds never make it to the market. To improve drug development, better tools are needed to assess efficacy and safety early in the process. One approach that has been suggested by the FDA to help streamlining the drug development process is pharmacokinetic/pharmacodynamic (PK/PD) modeling and simulation. In this approach, a model-based link between PK profiles and corresponding PD is established. Once a suitable model is identified and validated, predictions about efficacy and safety of different dosing regimens can be made. The goal of this review is to examine the current state of PK, PD, and PK/PD in antibiotic and antiviral research and development.     

Using Stochastic Differential Equations for PK/PD Model Development

A method for PK/PD model development based on stochastic differential equation models is proposed. The new method has a number of advantages compared to conventional methods. In particular, the new method avoids the exhaustive trial-and-error based search often conducted to determine the most appropriate model structure, because it allows information about the appropriate model structure to be extracted directly from data. This is accomplished through quantification of the uncertainty of the individual parts of an initial model, by means of which tools for performing model diagnostics can be constructed and guidelines for model improvement provided. Furthermore, the new method allows time-variations in key parameters to be tracked and visualized graphically, which allows important functional relationships to be revealed. Using simulated data, the performance of the new method is demonstrated by means of two examples. The first example shows how, starting from a simple assumption of linear PK, the method can be used to determine the correct nonlinear model for describing the PK of a drug following an oral dose. The second example shows how, starting from a simple assumption of no drug effect, the method can be used to determine the correct model for the nonlinear effect of a drug with known PK in an indirect response model.     

A Mechanism-Based PK/PD Model for Hematological Toxicities Induced by Antibody-Drug Conjugates

Antibody-drug conjugates (ADCs) are complex drug platforms composed of monoclonal antibodies (mAbs) conjugated to potent cytotoxic drugs (payloads) via chemical linkers, enabling selective payload delivery to neoplastic cells, resulting in improved efficacy and reduced toxicity. Brentuximab vedotin (Adcetris®, SGN-35) and adotrastuzumab emtansine (Kadcyla®, T-DM1) are the two FDA-approved and commercially available ADCs, and both drugs exhibit ADC-related thrombocytopenia and neutropenia. A pharmacokinetic/pharmacodynamic (PK/PD) model for ADCs was developed to identify the analyte from each ADC that is most associated with the observed hematopoietic toxicities and to determine the role of the apparent in vivo payload release rate on the severity of thrombocytopenia and neutropenia. Murine xenograft experiments and data from literature were combined, and the PK of both ADCs and their analytes were described with two-compartment models, with linear elimination and first-order payload release rate constants (k _rel). ADC-associated hematotoxicities were captured with a previously published PD model for myelosuppression driven by various analytes. ADC half-lives were about 5 days, and k _rel values were 0.46 (T-DM1) and 0.12 h^?1 (SGN-35). The lifespans of platelets following T-DM1 and neutrophils following SGN-35 were 3.73 and 4.72 days. Comparison of alternate model structures suggested that mechanisms of myelosuppression are payload-driven for SGN-35 and ADC pinocytosis-dependent for T-DM1. Model simulations suggested that a 4-fold increase (T-DM1) and 70% decrease (SGN-35) in k _rel would improve hematotoxicity to grade 1. The proposed model successfully captured the PK and associated myelosuppression of both ADCs and might serve as a general PK/PD platform for assessing hematological toxicities to ADCs.     

PK/PD参数与抗菌药物的优化用药

反映时间依赖性抗菌药物的PK/PD参数为t>MIC,反映浓度依赖性抗菌药物的PK/PD参数为cmax/MIC或AUC/MIC。时间依赖性与浓度依赖性抗菌药物都与抗菌药物后效应(PAE)和半衰期(t1/2)密切相关。运用PK/PD参数优化抗菌药物的合理用药,叙述了时间依赖性和浓度依赖性抗菌药物及其运用PK/PD参数优化用药的注意点。     

Brain microdialysis and PK/PD correlation of pregabalin in rats.

Pregabalin [PGB, (S)-3-isobutyl GABA, CI-1008] is a derivative of the inhibitory neurotransmitter g-aminobutyric acid (GABA). It has shown anticonvulsant, analgesia and anxiety activity in animal models. In this report, blood-brain barrier (BBB) influx and efflux of PGB were investigated with microdialysis at efficacious doses in rats. BBB influx (CLin) and efflux (CLout) permeability for pregabalin were 4.8 and 37.2 microL/min/g brain, respectively, following an intravenous infusion to rats. The results indicate that PGB is brain penetrable, supporting its anti-epilepsy and other CNS pharmacology. Significant anticonvulsant action of PGB was detected between 2 and 8 hr post oral dose, which is lag behind ECF drug concentrations lees. A PK/PD link model was used to describe the counter-clockwise hysteresis relationship between pregabalin brain ECF concentration and the anticonvulsant effect in rats. The resulting Ce (concentration in effect compartment) versus effect profile exhibits a sigmoidal curve and the calculated ECe50 and Keo values were 95.3 ng/mL and 0.0092 min-1, respectively. The small Keo value suggests that the effect is not directly proportional to the amount of pregabalin in the ECF compartment possibly due to inherent delay.     

Population PK and PK/PD modelling of microencapsulated octreotide acetate in healthy subjects

AIMS: To develop a population model that can describe the pharmacokinetic profile of microencapsulated octreotide acetate in healthy cholecystectomized subjects. To investigate the correlation between serum IGF-1 and octreotide concentration. METHODS: A population pharmacokinetic analysis was performed on octreotide data obtained following a single dose of 30 mg microencapsulated octreotide acetate intramuscularly. The relationship between serum IGF-1 concentration and octreotide concentration was effectively described by a population pharmacokinetic/pharmacodynamic model. RESULTS: The pharmacokinetic profile of octreotide was characterized by an initial peak of octreotide followed by a sustained-release of drug. Plateau concentration were sustained up to day 70, and gradually declined to below the detection limit by day 112. A one-compartment linear model was constructed which consisted of two absorption processes, characterized by KIR and KSR, rate constants for immediate-release and sustained-release, respectively, with first-order elimination (Ke; 1.05 h-1). The surface, unencapsulated drug was immediately absorbed into the central compartment with first-order absorption (KIR; 0.0312 h-1), while the microencapsulated drug was first released in a zero-order fashion into a depot before being absorbed into the central compartment with first-order absorption (KSR; 0.00469 h-1) during a period of tau (1680 h). Body weight and gender were important covariates for the apparent volume of distribution. The type of formulation was an important covariate for KIR but had no effect on KSR. An inhibitory Emax population pharmacokinetic/pharmacodynamic model could adequately describe the relationship between IGF-1 (expressed as percent baseline) and octreotide concentration. Baseline IGF-1 concentration was found to be a significant covariate for the baseline effect (E0). A relationship between GH concentration and octreotide concentration was not established. CONCLUSIONS: The pharmacokinetic profile of microencapsulated octreotide acetate was effectively described by the derived population model. The relationship between IGF-1 and drug concentration could be used to guide optimization of therapeutic octreotide dosage regimens.     

From Target Selection to the Minimum Acceptable Biological Effect Level for Human Study: Use of Mechanism-based PK/PD Modeling to Design Safe and Efficacious Biologics

In this paper, two applications of mechanism-based modeling are presented with their utility from candidate selection to first-in-human dosage selection. The first example is for a monoclonal antibody against a cytomegalovirus glycoprotein complex, which involves an antibody binding model and a viral load model. The model was used as part of a feasibility analysis prior to antibody generation, setting the specifications for the affinity needed to achieve a desired level of clinical efficacy. The second example is a pharmacokinetic-pharmacodynamic model based on a single-dose pharmacology study in cynomolgus monkey using data on pharmacokinetics, receptor occupancy, and the dynamics of target cell depletion and recovery. The model was used to estimate the MABEL, here defined as the minimum acceptable biological effect level against which a dose is selected for a first-in-human study. From these applications, we demonstrate that mechanism-based PK/PD binding models are useful for predicting human response to biologics compounds. Especially, such models have the ability to integrate preclinical and clinical, in vitro and in vivo information and facilitate rational decision making during various stages of drug discovery and translational research.     

抗厌氧菌药物PK/PD研究方法概述

随着抗菌药物药动学(PK)和药效学(PD)的不断发展,PK/PD研究在抗菌药的药效学评价、给药方案的制定和优化以及细菌耐药性等方面的作用日趋重要,必不可少.目前国内外发表了大量抗菌药物PK/PD的研究文献,但由于厌氧菌培养条件的苛刻性,限制了抗厌氧菌药物的PK/PD研究.本文综述近年来发表的为数不多的有关抗厌氧菌药物的PK/PD研究文献,介绍该类药物PK/PD体外研究、动物和人体内研究方法,为国内今后开展此方面的研究提供参考.     

Three new residual error models for population PK/PD analyses

Residual error models, traditionally used in population pharmacokinetic analyses, have been developed as if all sources of error have properties similar to those of assay error. Since assay error often is only a minor part of the difference between predicted and observed concentrations, other sources, with potentially other properties, should be considered. We have simulated three complex error structures. The first model acknowledges two separate sources of residual error, replication error plus pure residual (assay) error. Simulation results for this case suggest that ignoring these separate sources of error does not adversely affect parameter estimates. The second model allows serially correlated errors, as may occur with structural model misspecification. Ignoring this error structure leads to biased random-effect parameter estimates. A simple autocorrelation model, where the correlation between two errors is assumed to decrease exponentially with the time between them, provides more accurate estimates of the variability parameters in this case. The third model allows time-dependent error magnitude. This may be caused, for example, by inaccurate sample timing. A time-constant error model fit to time-varying error data can lead to bias in all population parameter estimates. A simple two-step time-dependent error model is sufficient to improve parameter estimates, even when the true time dependence is more complex. Using a real data set, we also illustrate the use of the different error models to facilitate the model building process, to provide information about error sources, and to provide more accurate parameter estimates. This work was supported by grants GM26676 and GM2669