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.     

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.     

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.     

Optimal Design of Mixed-Effects PK/PD Models Based on Differential Equations

There is a vast literature on the analysis of optimal design of nonlinear mixed-effects models (NLMMs) described by ordinary differential equations (ODEs) with analytic solution. However, much less has been published on the design of trials to fit such models with nonanalytic solution. In this article, we use the “direct” method to find parameter sensitivities, which are required during the optimization of models defined as ODEs, and apply them to find D-optimal designs for various specific situations relevant to population pharmacokinetic studies using a particular model with first-order absorption and elimination. In addition, we perform two simulation studies. The first one aims to show that the criterion computed from the development of the Fisher information matrix expression is a good measure to compare and optimize population designs, thus avoiding a large number of simulations; In the second one, a sensitivity analysis with respect to parameter misspecification allows us to compare the robustness of different population designs constructed in this article.     

Simultaneous vs. Sequential Analysis for Population PK/PD Data I: Best-Case Performance

Dose [-concentration]-effect relationships can be obtained by fitting a predictive pharmacokinetic (PK)-pharmacodynamic (PD) model to both concentration and effect observations. Either a model can befit simultaneously to all the data ("simultaneous" method), or first a model can befit to the PK data and then a model can be fit to the PD data, conditioning in some way on the PK data or on the estimates of the PK parameters ("sequential" method). Using simulated data, we compare the performance of the simultaneous method with that of three sequential method variants with respect to computation time, estimation precision, and inference. Using NONMEM, under various study designs, observations of one type of PK and one type of PD response from different numbers of individuals were simulated according to a one-compartment PK model and direct Emax PD model, with parameters drawn from an appropriate population distribution. The same PK and PD models were fit to these observations using simultaneous and sequential methods. Performance measures include computation time,fraction of cases for which estimates are successfully obtained, precision of PD parameter estimates, precision of PD parameter standard error estimates, and type-I error rates of a likelihood ratio test. With the sequential method, computation time is less, and estimates are more likely to be obtained. Using the First Order Conditional Estimation (FOCE) method, a sequential approach that conditions on both population PK parameter estimates and PK data, estimates PD parameters and their standard errors about as well as the "gold standard" simultaneous method, and saves about 40% computation time. Type-I error rates of likelihood ratio test for both simultaneous and sequential approaches are close to the nominal rates.     

Simultaneous vs. Sequential Analysis for Population PK/PD Data II: Robustness of Methods

A model can be fit to joint PK/PD data (concentration and effect) either simultaneously or sequentially. The results of a companion paper suggested that when the data-analytic and true models agree, a particular sequential approach is computationally faster than the simultaneous one, yet produces hardly less precise PD parameter estimates, and for suitable designs, about as accurate PD standard error estimates. In this paper, we compare the performance of various methods for the case that the data-analytic model is misspecified. We illustrate these methods by applying them to a set of real data. Using NONMEM, population PK/PD observations were simulated under various study designs according to a one- or two-compartment PK model and direct Emax or sigmoid Emax model. A one-compartment PK model and Emax PD model were fit to the simulated observations by simultaneous and sequential methods. Predictive performance (interpolation and extrapolation) of PD and the type-I error rate of a likelihood ratio test are compared. The real data set consists of PK and (more frequent) PD observations after administration of the muscle relaxant vecuronium. When only the PK data-analytic model is misspecified, the simultaneous method has greater precision than the sequential methods. However a sequential method that uses a non-parametric PK model performs better than both other methods when PK model misspecification is severe. When the PD data-analytic model is misspecified, sequential and simultaneous methods perform similarly. The analysis of the real data shows that the PK fitted with the simultaneous method can be quite sensitive to PD model misspecification, yielding a possible diagnostic for this type of misspecification.     

抗真菌药PK/PD研究进展

药代动力学/药效学(PK/PD)结合了PK与PD的研究方法,同步研究药代动力学特征及与药效和疗效的关系,定量描述药物的效应-时间过程。PK/PD研究有利于更有效地利用现有的抗真菌药物和提高其在许多严重真菌感染时的抗菌效果。本文就抗真菌药的PK/PD研究进展进行综述。     

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.     

Physiologically-Based PK/PD Modelling of Therapeutic Macromolecules

Therapeutic proteins are a diverse class of drugs consisting of naturally occurring or modified proteins, and due to their size and physico-chemical properties, they can pose challenges for the pharmacokinetic and pharmacodynamic studies. Physiologically-based pharmacokinetics (PBPK) modelling has been effective for early in silico prediction of pharmacokinetic properties of new drugs. The aim of the present workshop was to discuss the feasibility of PBPK modelling of macromolecules. The classical PBPK approach was discussed with a presentation of the successful example of PBPK modelling of cyclosporine A. PBPK model was performed with transport of the cyclosporine across cell membranes, affinity to plasma proteins and active membrane transporters included to describe drug transport between physiological compartments. For macromolecules, complex PBPK modelling or permeability-limited and/or target-mediated distribution was discussed. It was generally agreed that PBPK modelling was feasible and desirable. The role of the lymphatic system should be considered when absorption after extravascular administration is modelled. Target-mediated drug disposition was regarded as an important feature for generation of PK models. Complex PK-models may not be necessary when a limited number of organs are affected. More mechanistic PK/PD models will be relevant when adverse events/toxicity are included in the PK/PD modelling.     

Dosing of colistin-back to basic PK/PD

The increasing prevalence of multidrug-resistant Gram-negative bacteria worldwide has led to a re-evaluation of the previously discarded antibiotic, colistin. Despite its important role as salvage therapy for otherwise untreatable infections, dosage guidelines for the prodrug colistin methanesulfonate (CMS) are not scientifically based and have led to treatment failure and increased colistin resistance. In this review we summarise the recent progress made in the understanding of the pharmacokinetics of CMS and formed colistin with an emphasis on critically ill patients. The pharmacodynamics of colistin is also reviewed, with special attention given to the relationship between pharmacokinetics and pharmacodynamics and how the emerging data can be used to inform design of optimal dosage regimens. Recent data suggest the current dosage regimens of CMS are suboptimal in many critically ill patients.     

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     

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.     

A Novel Oral Vehicle for Poorly Soluble HSV-Helicase Inhibitors: PK/PD Validations

PURPOSE: The current study describes the design and validation of a novel oral vehicle for delivering poorly water-soluble herpes simplex virus (HSV)-helicase inhibitors in preclinical pharmacokinetic (PK) and pharmacodynamic (PD) evaluations. METHODS: Poorly water-soluble compounds were used in solubility and drinking compliance tests in mice. A preferred vehicle containing 0.1% bovine serum albumin (BSA), 3% dextrose, 5% polyethylene glycol (PEG) 400, and 2% peanut oil, pH 2.8 with HCL (BDPP) was selected. This vehicle was further validated with oral PK and in vivo antiviral PD studies using BILS 45 BS. RESULTS: Solubility screen and drinking compliance tests revealed that the BDPP vehicle could solubilize BILS compounds at 0.5-3 mg/ml concentration range and could be administered to mice without reducing water consumption. Comparative oral PK of BILS 45 BS in HCL or BDPP by gavage at 40 mg/kg showed overlapping PK profiles. In vivo antiviral efficacy and potency of BILS 45 BS in BDPP by oral gavages or in drinking water were confirmed to be comparable as that achieved by gavage in HCL solution. CONCLUSIONS: These results provide a protein-enriched novel oral vehicle for delivering poorly water-soluble antiviral compounds in a continuous administration mode. Similar approaches may be applicable to other poorly soluble compounds by gavage or in drinking solution.     

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.     

Comparison of some control strategies for three-compartment PK/PD models

In drug therapy, effective dosage strategies are needed to maintain target drug effects. The relationship between drug dose and drug effect is often described by pharmacokinetic/pharmacodynamic (PK/PD) models where typically the PK model has a multicompartment form and the PD model is the sigmoidal Emax model. The parameters in the PK/PD model are generally unknown in the individual patient, although prior knowledge may be available and can be updated after measurements of drug effect are taken during the therapy. This fact, together with the complexity of the PK/PD model, makes the control problem complex. This paper investigates several control strategies in the framework of a three-compartment PK model plus an effect site with a PD model. Using computer simulations under different assumptions, we show that a MAP (maximum a posteriori) Bayesian type of strategy is effective, nevertheless in high-risk situations a stochastic control strategy hedging against estimation errors provides better performance at computational cost. Partially funded by Palo Alto Institute for Research and Education Inc., and the Veterans Administration Merit Review Program.