Semiparametric analysis of non-steady-state pharmacodynamic data

Drug Exposure to Establish Pharmacokinetic-Response Relationships in Oncology

In the oncology field, understanding the relationship between the dose administered and the exerted effect is particularly important because of the narrow therapeutic index associated with anti-cancer drugs and the high interpatient variability. Therefore, in this review, we provide a critical perspective of the different methods of characterising treatment exposure in the oncology setting. The increasing number of modelling applications in oncology reflects the applicability and the impact of pharmacometrics on all phases of the drug development process and patient management as well. Pharmacometric modelling is a worthy component within the current paradigm of model-based drug development, but pharmacometric modelling techniques are also accessible for the clinician in the optimisation of current oncology therapies. Consequently, the application of population models in a hospital setting by generating close collaborations between physicians and pharmacometricians is highly recommended, providing a systematic means of developing and assessing model-based metrics as 'drivers' for various responses to treatments, which can then be evaluated as predictors for treatment success. Characterising the key determinants of variability in exposure is of particular importance for anticancer agents, as efficacy and toxicity are associated with exposure. We present the different strategies to describe and predict drug exposure that can be applied depending on the data available, with the objective of obtaining the most useful information in the patients' favour throughout the full drug cycle. Therefore, the objective of the present article is to review the different approaches used to characterise a patient's exposure to oncology drugs, which will result in a better understanding of the time course of the response and the magnitude of interpatient variability.

Modelling the dose-response relationship: the fair share of pharmacokinetic and pharmacodynamic information

AIMS

The aim of this paper is to investigate the role of drug concentration samplings in the modelling of the dose-response relationship.

METHODS

Using an initial PK/PD model, a reference dataset was simulated. PK and PD samples were extracted to create reduced datasets. PK/PD and K-PD models were fitted to theses reduced datasets. Post hoc estimates from both types of models were compared to the initial PK/PD model and performance was assessed.

RESULTS

K-PD models were largely biased when the drug has a nonlinear elimination. PK/PD models with 1 PK and 2 PD samples were superior to K-PD models with 3 PD samples. PK/PD models with 1 or 2 PK samples and 3 PD samples proved to be superior to K-PD models with 4 PD samples.

CONCLUSIONS

K-PD models should not be used when the drug has nonlinear elimination. K-PD models should not replace PK/PD modelling but are an alternative approach if the PD information is large enough.

Evaluation of drugs in pediatrics using K-PD models: perspectives

Some pharmacodynamic (PD) models, called K-PD models, have been developed for the description of drug action kinetics in the absence of drug concentration measurements. Because blood samples for drug measurements are not needed, these models may be very useful in pediatric studies, by reducing their invasiveness. In addition, a number of PD measurements are also non-invasive and specific devices exist for measures in children. Therefore, the kinetics of drug action may be characterized with minimal invasiveness. A brief description of the key features of these models is given, and a number of examples of application are presented. K-PD models are expected to be most useful when the drug kinetics is simple (i.e. when the one-compartment model is a reasonable description), or when the response kinetics is slow compared with drug kinetics. K-PD models have already demonstrated their usefulness in animal and adult studies. They are very attractive for pediatric studies and they should facilitate the assessment of drug efficacy and safety.

Pharmacokinetic/pharmacodynamic modeling of anesthetics in children: therapeutic implications

Modeling the pharmacokinetics and pharmacodynamics of anesthetics in children is performed as a response to the clinical need for safe and efficacious administration of drugs with a low therapeutic index. Rates and concentrations of these drugs, which are the primary parameters used by anesthesiologists, depend on physiologic parameters that are markedly affected by development. Volatile anesthetics have been used for >50 years in pediatric patients. The pharmacokinetics of inhalation agents are context sensitive, but little difference between age groups has been described. These agents are not only eliminated unchanged by the lung but they are also metabolized by the liver. Halothane has Michaelis-Menten kinetics, with up to 40% of the administered dose metabolized by the liver. For volatile anesthetics, the effect measured is the minimum alveolar concentration (MAC) that leads to movement of the limb in response to skin incision in 50% of the patients studied. The MAC is higher in infants than in children and adults. Infants aged 6 months have a MAC 1.5-1.8 times the MAC observed in adults aged 40 years. Children have a greater clearance and volume of distribution of propofol than adults. In order to achieve similar plasma concentrations, children require three times the initial dose used in adults. In adults, an increased sensitivity to propofol has been demonstrated with aging, but nothing is known about the effects in children. However, it is clear that equipotent doses of propofol induce marked deleterious hemodynamic effects in infants compared with children. Regional anesthesia is used in pediatrics, both in combination with general anesthesia during surgery or alone for postoperative analgesia. A marked decrease in protein binding has been described in infants. In the postoperative period, a rapid increase in binding because of inflammation decreases the free fraction, but the free drug concentration remains constant because of the resulting decrease in total clearance. A low clearance because of liver function immaturity has been observed during the first year(s) of life for bupivacaine and ropivacaine. Pharmacodynamic interactions between general anesthesia and regional anesthesia need to be modeled. This is one of the future tasks for pharmacokineticists. Methods such as the Dixon up-and-down allocation and the isobolographic technique are promising in this field.

Modelling response time profiles in the absence of drug concentrations: definition and performance evaluation of the K-PD model

The plasma concentration-time profile of a drug is essential to explain the relationship between the administered dose and the kinetics of drug action. However, in some cases such as in pre-clinical pharmacology or phase-III clinical studies where it is not always possible to collect all the required PK information, this relationship can be difficult to establish. In these circumstances several authors have proposed simple models that can analyse and simulate the kinetics of the drug action in the absence of PK data. The present work further develops and evaluates the performance of such an approach. A virtual compartment representing the biophase in which the concentration is in equilibrium with the observed effect is used to extract the (pharmaco)kinetic component from the pharmacodynamic data alone. Parameters of this model are the elimination rate constant from the virtual compartment (KDE), which describes the equilibrium between the rate of dose administration and the observed effect, and the second parameter, named EDK(50) which is the apparent in vivo potency of the drug at steady state, analogous to the product of EC(50), the pharmacodynamic potency, and clearance, the PK "potency" at steady state. Using population simulation and subsequent (blinded) analysis to evaluate this approach, it is demonstrated that the proposed model usually performs well and can be used for predictive simulations in drug development. However, there are several important limitations to this approach. For example, the investigated doses should extend from those producing responses well below the EC(50) to those producing ones close to the maximum response, optimally reach steady state response and followed until the response returns to baseline. It is shown that large inter-individual variability on PK-PD parameters will produce biases as well as large imprecision on parameter estimates. It is also clear that extrapolations to dosage routes or schedules other than those used to estimate the parameters should be undertaken with great caution (e.g., in case of non-linearity or complex drug distribution). Consequently, it is advised to apply this approach only when the underlying structural PD and PK are well understood. In any case, K-PD model should definitively not be substituted for the gold standard PK-PD model when correct full model can and should be identified.

Pharmacokinetic-pharmacodynamic modelling: history and perspectives

A major goal in clinical pharmacology is the quantitative prediction of drug effects. The field of pharmacokinetic-pharmacodynamic (PK/PD) modelling has made many advances from the basic concept of the dose-response relationship to extended mechanism-based models. The purpose of this article is to review, from a historical perspective, the progression of the modelling of the concentration-response relationship from the first classic models developed in the mid-1960s to some of the more sophisticated current approaches. The emphasis is on general models describing key PD relationships, such as: simple models relating drug dose or concentration in plasma to effect, biophase distribution models and in particular effect compartment models, models for indirect mechanism of action that involve primarily the modulation of endogenous factors, models for cell trafficking and transduction systems. We show the evolution of tolerance and time-variant models, non- and semi-parametric models, and briefly discuss population PK/PD modelling, together with some example of more recent and complex pharmacodynamic models for control system and nonlinear HIV-1 dynamics. We also discuss some future possible directions for PK/PD modelling, report equations for general classes of novel semi-parametric models, as well as describing two new classes, additive or set-point, of regulatory, additive feedback models in their direct and indirect action variants.

Spontaneous ventilation with remifentanil in children

BACKGROUND

Remifentanil is a short-acting drug that allows us to study the specific respiratory effects of potent opioid analgesics. The purpose of this study is to describe the effects of a remifentanil infusion during spontaneous ventilation in children. Pharmacokinetic studies provide useful information on the time course of opioid blood concentrations; however, they cannot be easily translated into infusion administration guidelines for pediatric clinical practice.

METHODS

A total of 32 children, aged 2-7 years, undergoing restorative dentistry, spontaneously breathing under sevoflurane anesthesia were enrolled in the study. After an initial bolus dose of remifentanil, an infusion was administered in ascending logarithmic increments at 10 min intervals. Increments were discontinued when endtidal carbon dioxide exceeded 9 kPa (70 mmHg), desaturation occurred (SpO2 < 94%) or with the onset of apnea (>5 s). The maximum tolerated dose was determined for each subject. Endtidal carbon dioxide, minute ventilation and respiratory rate were continuously recorded.

RESULTS

The median tolerated dose of remifentanil was 0.127 microg.kg(-1).min(-1) (range: 0.053-0.3 microg.kg(-1).min(-1)). When comparing the last four incremental increases in each subject, 35% change in respiratory rate occurred in the last 10 min period while changes in endtidal carbon dioxide and minute ventilation were gradual and of less magnitude. There was no correlation between age and respiratory rate.

CONCLUSIONS

There is a large variation in the dose of remifentanil tolerated by children while breathing spontaneously under anesthesia. A respiratory rate of <10 b.min(-1) appears to be the best predictor of the maximum tolerated dose.

Mixed-effects modeling of the pharmacodynamic response to the calcimimetic agent R-568

OBJECTIVE

The parathyroid cell calcium receptor is a novel drug target for affecting parathyroid hormone (PTH) secretion and for treating hyperparathyroidism. R-568 is a calcium receptor agonist that inhibits PTH secretion and increases calcitonin release in preclinical studies. The objective of this study was to evaluate the effect of R-568 on PTH plasma concentrations in humans.

METHODS

Eighteen healthy postmenopausal women were included in the study. Single ascending oral doses of 10 to 400 mg were administered in a randomized, placebo-controlled double-blind trial. PTH plasma concentrations were measured for up to 120 hours after each dose.

RESULTS

R-568 caused a dose-dependent decrease in plasma PTH, with peak effect observed within 1/2 to 2 hours after dosing. The maximum effect did not increase beyond doses from 80 to 160 mg, but duration of response increased at higher doses. An indirect-response model was developed to estimate the rates of input and output of the active moiety(ies), the inhibitory effect on PTH secretion, and the circadian variability in PTH. Population parameter estimates were 3.02 hour-1 and 0.49 hour-1 for rates of input and output of the active moiety(ies), respectively, IA50 (the unscaled amount of R-568 associated with 50% of Emax) was 16.3 mg, Emax (the maximum effect caused by R-568 expressed as a fraction of the rate of PTH secretion in the absence of any drug effect) was 89%, CPTH(baseline) (the baseline PTH plasma concentration in the absence of any drug effect) was 34.6 pg/mL, KePTH (the elimination rate constant for PTH) was 1.73 hour-1, amplitude of the circadian variability in PTH secretion was 5.8%, and the time of peak PTH secretion occurred at about 6 PM. Intersubject variability in parameter estimates ranged from 7% to 121%, and residual variability was 22%.

CONCLUSION

The model correctly described the onset, extent, and duration of effect on PTH after a wide range of doses of R-568.

New mathematical implementation of generalized pharmacodynamic models: method and clinical evaluation

A new method and experimental design are presented to unambiguously estimate the transduction function (phi) and the conduction function (psi) of the generalized pharmacodynamic model: E = phi (psi * r), when measured pharmacokinetic response r is (i) drug plasma concentration and (ii) drug input rate into the systemic circulation. phi relates the observed pharmacologic effect E to the concentration at the effect site: ce = (psi * r), psi defines transfer of drug from plasma site to effect site or from input site to effect site, and * represents the convolution integral. The model functions psi and phi were expressed as cubic splines giving a very flexible description of those processes which is not biased by the structured assumptions of more conventional models, e.g., effect compartment models. The experimental design proposed addresses the problem of ambiguous identification of the model functions typical of these models; that is, there is more than one pair of very different functions describing the effect data collected after a single drug administration. We tested the hypothesis that the simultaneous fitting of at least two administrations allows the unambiguous identification of the model functions without the need for unlikely or cumbersome constraints. The performance of the mathematical implementation and the robustness of the methods with respect to measurement noise and possible failure of some assumptions, such as intraindividual variability, were tested by computer simulations. The method was then applied to the results of a clinical study of verapamil pharmacodynamics in 6 healthy subjects. Results of these studies demonstrated that the mathematical implementation does not introduce bias or artifact into the estimated functions and that the models and the proposed methods are suitable for application to clinical research. Two drug administrations were sufficient to unambiguously describe verapamil pharmacodynamics in the 6 human subjects studied.

Pharmacodynamic modeling of the electroencephalographic effects of flumazenil in healthy volunteers sedated with midazolam

The purpose of this study was to model pharmacodynamically the reversal of midazolam sedation with flumazenil. Ten human volunteers underwent four different sessions. In session 1, individual midazolam pharmacokinetics and electroencephalographic pharmacodynamics were determined. In sessions 2 and 3, a computer-controlled infusion of midazolam with individual volunteer pharmacokinetic data was administered, targeting a plasma concentration corresponding to a light or deep level of sedation (20% or 80% of the maximal midazolam electroencephalographic effect) for a period of 210 minutes. After obtaining a stable electroencephalographic effect and constant midazolam plasma concentrations, a zero-order infusion of flumazenil was started until complete reversal of midazolam electroencephalographic effect was obtained. The flumazenil infusion was then stopped and the volunteer was allowed to resedate because of the constant midazolam drug effect. The electroencephalographic response was measured during a 180-minute period and analyzed by aperiodic analysis and fast-Fourier transforms. In session 4, a midazolam plasma concentration corresponding to a deep level of sedation was targeted for 210 minutes to examine for the possible development of acute tolerance. No flumazenil was given in session 4. For a light sedation level, with a mean midazolam plasma concentration of 160 +/- 64 ng/ml, the mean half-life of the equilibration rate constant of flumazenil reversal is 5.0 +/- 2.5 minutes, and the mean effect site concentration causing 50% of Emax is 13.7 +/- 5.8 ng/ml. For a deep level of sedation, with a mean midazolam plasma concentration of 551 +/- 196 ng/ml, the mean half-life of the equilibration rate constant is 3.9 +/- 1.5 minutes, and the mean effect site concentration causing 50% of Emax is 20.6 +/- 6.8 ng/ml. This study provides an estimate of the magnitude of the blood/central nervous system equilibration delay for flumazenil antagonism of midazolam sedation and further defines the usefulness of the electroencephalogram as a measure of midazolam pharmacodynamic effect.

Pharmacokinetic analysis of the time course of effect of atracurium

OBJECTIVE

To examine the ability to determine clinically important pharmacokinetic and pharmacodynamic parameters of atracurium by the analysis of the time course of effect without the use of plasma concentration data.

DESIGN

Neuromuscular transmission was monitored with train-of-four stimulation and electromyographic quantitation of the first (T1) and fourth (T4) responses in eight anesthetized patients undergoing elective surgery. The time course of onset and recovery of neuromuscular blockade by three successive bolus doses of atracurium was recorded. Equations describing the theoretic time course of concentrations in the effect compartment and the dose-response relationship were fitted simultaneously to these data; the parameters of these equations derived from the fit of two doses were used to predict the response to a third dose. Fitting the equations to all three doses was also performed to assess the accuracy of predictions for atracurium.

RESULTS

From the depression of the first twitch after three consecutive doses in eight patients, the half-lives of uptake into and elimination from the effect compartment were 2.1 +/- 0.2 minutes (mean +/- SEM) and 25.8 +/- 2.3 minutes (n = 8). The doses producing 50% and 95% depression of the first twitch (ED50 and ED95) were 168 +/- 15 and 280 +/- 25 micrograms/kg, respectively, with a Hill coefficient of 6.1 +/- 0.5. The half-life of elimination estimated from the fourth twitch was similar to that from the first twitch.

CONCLUSIONS

The analysis of high-resolution effect data is capable of giving pharmacokinetic and pharmacodynamic parameters with clinically acceptable accuracy within a short sampling time, without resorting to laboratory analysis. This method is specific for active drug and would be of value for individualization of administration for short-term treatment.

Pharmacokinetic-pharmacodynamic (PK-PD) modelling in non-steady-state studies and arterio-venous drug concentration differences

In conducting a non-steady-state pharmacokinetic (PK)-pharmacodynamic (PD) study there is potential for the observed effect (E) vs time, and venous plasma drug concentration (C) vs time, profiles to display temporal displacement with respect to each other. This is most frequently observed when there exists a distributional nonequilibrium across the effect organ giving rise to hysteresis, i.e. observed C preceding E in the time domain, with the resulting potential for a counterclockwise loop to be generated in the observed E vs C plot (when data are connected in time-order). Such temporal displacement does not afford direct prediction of the steady-state E vs C PD relationship. When an arterio-venous (A-V) difference exists across the tissues of the blood sampling compartment (i.e. the arm), and this arises solely from an elimination process then drug concentration in the respective peripheral arterial plasma and venous plasma compartments will be in equilibrium at all times during a non-steady-state PK experiment. If there are no other sources of temporal displacement in the relationship between E and C then the observed E vs C plot will be a direct predictor of the steady-state E vs C PD relationship. In contrast when the A-V difference is of a distributional nature then proteresis, i.e. observed E preceding C in the time domain, will arise with the potential for the generation of a clockwise loop in the observed E vs C relationship. Simulated error-incorporated E vs time, and C vs time, data was analysed by semi-parametric implementation of an effect-compartment link-model that affords accurate steady-state E vs C PD predictions (without the requirement of sampling arterial blood) from data that incorporates the concurrent presence of: (i) distributional nonequilibrium across the effect organ, and (ii) distributional A-V non-equilibrium. Accurate steady-state E vs C PD predictions were achieved irrespective of the comparative magnitudes of the two nonequilibria, i.e. whether the rate of equilibration across the effect organ was faster than, or slower than, the rate of equilibration across the arm (resulting in a clockwise or counterclockwise loop in the observed E vs C plot, respectively), or indeed if one or other of the nonequilibria is essentially absent. When the rate of equilibration across the effect organ is slower than the rate of A-V equilibration (i.e. counterclockwise loop generated in the observed E vs C plot) then the need to model for the underlying A-V nonequilibrium is redundant, i.e. accurate steady-state E vs C PD predictions can be achieved with implementation (strictly incorrectly) of a more simple link parameterised solely to model for distributional nonequilibrium across the effect organ.(ABSTRACT TRUNCATED AT 400 WORDS)

Application of a variable direction hysteresis minimization approach in describing the central nervous system pharmacodynamic effects of alfentanil in rabbits

The relationship between the concentration of a drug and its pharmacologic effect is of central interest in pharmacodynamics. Various compartmental and noncompartmental methods have been proposed for elucidating this relationship when the plasma drug concentration and effects are both measured. Although the relationship between drug input and the pharmacologic effect is equally useful, it has not received as much attention. A system analysis hysteresis minimization pharmacodynamic method was developed to describe the central nervous system effects of alfentanil in rabbits. The spectral edge frequency (SEF) was used as the effect measure and the infusion rate as the pharmacokinetic variable. The sigmoid Emax and cubic polynomial representations of the transduction relationship were investigated in modeling the collapsed hysteresis loop. The results indicated that alfentanil has a relatively rapid biophase equilibration time (t50 = 6 min). Both the sigmoid Emax and cubic polynomial transduction relationships were equally effective in describing the observed effect data and gave similar predictions. The proposed approach has the advantage of not assuming a specific compartmental structure for the pharmacokinetic-pharmacodynamic link. A particular advantage of the method is that no functional relationship is assumed a priori for the transduction relationship, and errors in both regression variables are considered in the optimization. The system analysis pharmacodynamic approach assumes linear disposition pharmacokinetics, an instantaneous and time-invariant transduction, and that inductive effects like tolerance or sensitization do not develop significantly in the time frame studied.

Validation of a variable direction hysteresis minimization pharmacodynamic approach: cardiovascular effects of alfentanil

An important goal in therapeutics is the quantitative prediction of drug effects. Although several comprehensive pharmacodynamic models have been proposed, relatively few of these have attempted to assess objectively the application of the models to predict pharmacologic responses. A variable-direction hysteresis minimization approach was proposed recently that allowed the pharmacodynamics of drugs to be modeled using information about drug input. The application and validation of this approach are demonstrated using the pharmacodynamic effect of alfentanil, a short-acting narcotic analgesic agent, in New Zealand White rabbits. A parameter is proposed to assess the ability of the pharmacodynamic model to predict responses.

Pharmacokinetic and pharmacodynamic data and models in clinical trials

There is current emphasis for extended integration of pharmacokinetics (PK) and pharmacodynamics (PD) into all phases of new drug development, including large-scale clinical trials. In this paper, we focus on study design and data analysis issues for the investigation of pharmacokinetic/pharmacodynamic and blood level/effect relationships in patients. The application of descriptive and model-based regression statistical methodology for including sparse drug systemic concentration data in the analysis of efficacy and safety is illustrated by examples chosen from diverse therapeutic areas. The population approach, based on mixed-effects modelling, is one such methodology, which also provides new tools for analysis of response vs dose and response vs time data. The existence of a variety of statistical techniques for handling complex PK/PD time-varying data should increase the impact of such data analysis on future drug development.