Pharmacodynamic parameter estimation: population size versus number of samples

Predicting Antibiotic Effect of Vancomycin Using Pharmacokinetic/Pharmacodynamic Modeling and Simulation: Dense Sampling versus Sparse Sampling

This study aimed to investigate the effect of a structural pharmacokinetic (PK) model with fewer compartments developed following sparse sampling on the PK parameter estimation and the probability of target attainment (PTA) prediction of vancomycin. Two- and three-compartment PK models of vancomycin were used for the virtual concentration–time profile simulation. Datasets with reduced blood sampling times were generated to support a model with a lesser number of compartments. Monte Carlo simulation was conducted to evaluate the PTA. For the two-compartment PK profile, the total clearance (CL) of the reduced one-compartment model showed a relative bias (RBias) and relative root mean square error (RRMSE) over 90%. For the three-compartment PK profile, the CL of the reduced one-compartment model represented the largest RBias and RRMSE, while the steady-state volume of distribution of the reduced two-compartment model represented the largest absolute RBias and RRMSE. A lesser number of compartments corresponded to a lower predicted area under the concentration–time curve of vancomycin. The estimated PK parameters and predicted PK/PD index from models built with sparse sampling designs that cannot support the PK profile can be significantly inaccurate and unprecise. This might lead to the misprediction of the PTA and selection of improper dosage regimens when clinicians prescribe antibiotics.

Population Pharmacodynamic Modeling Using the Sigmoid Emax Model: Influence of Inter-individual Variability on the Steepness of the Concentration-Effect Relationship. a Simulation Study

The relationship between the concentration of a drug and its pharmacological effect is often described by empirical mathematical models. We investigated the relationship between the steepness of the concentration–effect relationship and inter-individual variability (IIV) of the parameters of the sigmoid E_max model, using the similarity between the sigmoid E_max model and the cumulative log-normal distribution. In addition, it is investigated whether IIV in the model parameters can be estimated accurately by population modeling. Multiple data sets, consisting of 40 individuals with 4 binary observations in each individual, were simulated with varying values for the model parameters and their IIV. The data sets were analyzed using Excel Solver and NONMEM. An empirical equation (Eq. (11)) was derived describing the steepness of the population-predicted concentration–effect profile (γ*) as a function of γ and IIV in C50 and γ, and was validated for both binary and continuous data. The tested study design is not suited to estimate the IIV in C50 and γ with reasonable precision. Using a naive pooling procedure, the population estimates γ* are significantly lower than the value of γ used for simulation. The steepness of the population-predicted concentration–effect relationship (γ*) is less than that of the individuals (γ). Using γ*, the population-predicted drug effect represents the drug effect, for binary data the probability of drug effect, at a given concentration for an arbitrary individual.

Impact of Sampling Period on Population Pharmacokinetic Analysis of Antibiotics: Why do You Take Blood Samples Following the Fourth Dose?

To date, many population pharmacokinetic models of antibiotics have been developed using blood sampling data after the fourth or fifth dose, which represents steady-state levels. However, if a model developed using blood sampled after the first dose is equivalent to that using blood sampled after the fourth dose, it would be advantageous to utilize the former. The aim of this study was to investigate the effect of blood sampling after the first and/or fourth drug administration on the accuracy and precision of parameter estimates. A previously reported robust, two-compartment model of vancomycin was used for simulation to evaluate the performances of the parameter estimates. The parameter estimation performances were assessed using relative bias and relative root mean square error. Performance was investigated in 72 scenarios consisting of a combination of two blood sampling periods (the first and fourth dose), two total clearances, three infusion times, and four sample sizes. The population pharmacokinetic models from data collected at the first dose and those collected at the fourth dose produced parameter estimates that were similar in accuracy and precision. This study will contribute to increasing the efficiency and simplicity of antibiotic pharmacokinetic studies.

Modelling performance and skeletal muscle adaptations with exponential growth functions during resistance training

System theory is classically applied to describe and to predict the effects of training load on performance. The classic models are structured by impulse-type transfer functions, nevertheless, most biological adaptations display exponential growth kinetics. The aim of this study was to propose an extension of the model structure taking into account the exponential nature of skeletal muscle adaptations by using a genetic algorithm. Thus, the conventional impulse-type model was applied in 15 resistance trained rodents and compared with exponential growth-type models. Even if we obtained a significant correlation between actual and modelled performances for all the models, our data indicated that an exponential model is associated with more suitable parameters values, especially the time constants that correspond to the positive response to training. Moreover, positive adaptations predicted with an exponential component showed a strong correlation with the main structural adaptations examined in skeletal muscles, i.e. hypertrophy (R² = 0.87, 0.96 and 0.99, for type 1, 2A and 2X cross-sectional area fibers, respectively) and changes in fiber-type composition (R² = 0.81 and 0.79, for type 1 and 2A fibers, respectively). Thus, an exponential model succeeds to describe both performance variations with relevant time constants and physiological adaptations that take place during resistance training.

Feasibility of Exposure-Response Analyses for Clinical Dose-Ranging Studies of Drug Combinations

The exposure-response relationship of combinatory drug effects can be quantitatively described using pharmacodynamic interaction models, which can be used for the selection of optimal dose combinations. The aim of this simulation study was to evaluate the reliability of parameter estimates and the probability for accurate dose identification for various underlying exposure-response profiles, under a number of different phase II designs. An efficacy variable driven by the combined exposure of two theoretical compounds was simulated and model parameters were estimated using two different models, one estimating all parameters and one assuming that adequate previous knowledge for one drug is readily available. Estimation of all pharmacodynamic parameters under a realistic, in terms of sample size and study design, phase II trial, proved to be challenging. Inaccurate estimates were found in all exposure-response scenarios, except for situations where no pharmacodynamic interaction was present, with the drug potency and interaction parameters being the hardest to estimate. When previous knowledge of the exposure-response relationship of one of the monocomponents is available, such information should be utilized, as it enabled relevant improvements in parameter estimation and in correct dose identification. No general trends for classification of the performance of the tested study designs across different scenarios could be identified. This study shows that pharmacodynamic interactions models can be used for the exposure-response analysis of clinical endpoints especially when accompanied by appropriate dose selection in regard to the expected drug potencies and appropriate trial size and if information regarding the exposure-response profile of one monocomponent is available.

Parameter estimation for sigmoid Emax models in exposure-response relationship

The purpose of this simulation study is to explore the limitation of the population PK/PD analysis using data from a clinical study and to help to construct an appropriate PK/PD design that enable precise and unbiased estimation of both fixed and random PD parameters in PK/PD analysis under different doses and Hill coefficients. Seven escalating doses of virtual drugs with equal potency and efficacy but with five different Hill coefficients were used in simulations of single and multiple dose scenarios with dense sampling design. A total of 70 scenarios with 100 subjects were simulated and estimated 100 times applying 1-compartment PK model and sigmoid E_max model. The bias and precision of the parameter estimates in each scenario were assessed using relative bias and relative root mean square error. For the single dose scenarios, most PD parameters of sigmoid E_max model were accurately and precisely estimated when the C_max was more than 85% of EC₅₀, except for typical value and inter-individual variability of EC₅₀ which were poorly estimated at low Hill coefficients. For the multiple dose studies, the parameter estimation performance was not good. This simulation study demonstrated the effect of the relative range of sampled concentrations to EC₅₀ and sigmoidicity on the parameter estimation performance using dense sampling design.

Combined Use of Etomidate and Dexmedetomidine Produces an Additive Effect in Inhibiting the Secretion of Human Adrenocortical Hormones

Background

The direct effects of etomidate were investigated on the secretion of cortisol and its precursors by dispersed cells from the adrenal cortex of human of animals. Dexmedetomidine (DEX) is an anesthetic agent that may interfere with cortisol secretion via an unknown mechanism, such as involving inhibition of 11β-hydroxylase and the cholesterol side-chain cleavage enzyme system. The aim of this study was to determine whether dexmedetomidine (DEX) has a similar inhibitory effect on adrenocortical function, and whether combined use of etomidate (ETO) and DEX could produce a synergistic action in inhibiting the secretion of human adrenocortical hormones.

Material/Methods

Human adrenocortical cells were exposed to different concentrations of ETO and DEX. The dose-effect model between the ETO concentration and the mean secretion of cortisone (CORT) and aldosterone (ALDO) per hour was estimated.

Results

Hill’s equation well-described the dose-effect correlation between the ETO concentration and the amount of ALDO and CORT secretion. When the DEX concentration was introduced into the model by using E₀ (basal secretion) as the covariate, the goodness of fit of the ETO-CORT dose-effect model was improved significantly and the objective function value was reduced by 4.55 points (P<0.05). The parameters of the final ETO-ALDO pharmacodynamics model were EC₅₀=9.74, E_max=1.20, E₀=1.33, and γ=18.5; the parameters of the final ETO-CORT pharmacodynamics model were EC₅₀=9.49, E_max=8.16, E₀=8.57, and γ=37.0. In the presence of DEX, E₀ was 8.57–0.0247×(CDEX–4.6), and the other parameters remained unchanged. All parameters but γ were natural logarithm conversion values.

Conclusions

Combined use of DEX and ETO reduced ETO’s inhibitory E₀ (basal secretion) of CORT from human adrenocortical cells in a dose-dependent manner, suggesting that combined use of ETO and DEX produced an additive effect in inhibiting the secretion of human adrenocortical hormones.

Modeling the responses to resistance training in an animal experiment study

The aim of the present study was to test whether systems models of training effects on performance in athletes can be used to explore the responses to resistance training in rats. 11 Wistar Han rats (277 ± 15 g) underwent 4 weeks of resistance training consisting in climbing a ladder with progressive loads. Training amount and performance were computed from total work and mean power during each training session. Three systems models relating performance to cumulated training bouts have been tested: (i) with a single component for adaptation to training, (ii) with two components to distinguish the adaptation and fatigue produced by exercise bouts, and (iii) with an additional component to account for training-related changes in exercise-induced fatigue. Model parameters were fitted using a mixed-effects modeling approach. The model with two components was found to be the most suitable to analyze the training responses (R(2) = 0.53; P < 0.001). In conclusion, the accuracy in quantifying training loads and performance in a rodent experiment makes it possible to model the responses to resistance training. This modeling in rodents could be used in future studies in combination with biological tools for enhancing our understanding of the adaptive processes that occur during physical training.

A mixed-effects model of the dynamic response of muscle gene transcript expression to endurance exercise

Altered expression of a broad range of gene transcripts after exercise reflects the specific adjustment of skeletal muscle makeup to endurance training. Towards a quantitative understanding of this molecular regulation, we aimed to build a mixed-effects model of the dynamics of co-related transcript responses to exercise. It was built on the assumption that transcript levels after exercise varied because of changes in the balance between transcript synthesis and degradation. It was applied to microarray data of 231 gene transcripts in vastus lateralis muscle of six subjects 1, 8 and 24 h after endurance exercise and 6-week training on a stationary bicycle. Cluster analysis was used to select groups of transcripts having highest co-correlation of their expression (r > 0.70): Group 1 comprised 45 transcripts including factors defining the oxidative and contractile phenotype and Group 2 included 39 transcripts mainly defined by factors found at the cell periphery and the extracellular space. Data from six subjects were pooled to filter experimental noise. The model fitted satisfactorily the responses of Group 1 (r (2) = 0.62 before and 0.85 after training, P < 0.001) and Group 2 (r (2) = 0.75 and 0.79, P < 0.001). Predicted variation in transcription rate induced by exercise yielded a difference in amplitude and time-to-peak response of gene transcripts between the two groups before training and with training in Group 2. The findings illustrate that a mixed-effects model of transcript responses to exercise is suitable to explore the regulation of muscle plasticity by training at the transcriptional level and indicate critical experiments needed to consolidate model parameters empirically.

Random serial sampling to evaluate efficacy of iron fortification: a randomized controlled trial of margarine fortification with ferric pyrophosphate or sodium iron edetate

BACKGROUND

Random serial sampling is widely used in population pharmacokinetic studies and may have advantages compared with conventional fixed time-point evaluation of iron fortification.

OBJECTIVE

Our objective was to validate random serial sampling to judge the efficacy of iron fortification of a low-fat margarine.

DESIGN

We conducted a 32-wk placebo-controlled, double-blind, iron-intervention trial in 18-40-y-old Swiss women (n = 142) with serum ferritin (SF) concentrations <25 μg/L. Women were randomly assigned to 3 groups to receive 20 g margarine, with 14 mg added iron as either micronized ground ferric pyrophosphate (MGFePP) or sodium iron edetate (NaFeEDTA), or placebo daily. We measured hemoglobin and iron status of subjects at 2 fixed time points (at baseline and the endpoint) plus 3 randomly assigned time points between 4 and 28 wk. With the use of bootstrapping, the number of observations per individual was reduced to 3 and then compared with the 5-time-point data. Mixed-effects models were used to estimate iron repletion over time for random sampling, and analysis of covariance was used for fixed time-point sampling.

RESULTS

Body iron stores increased in women who received MGFePP or NaFeEDTA compared with women who received placebo (P < 0.05). The increase in body iron stores with NaFeEDTA fortification was 2-3 times the increase with MGFePP fortification (P < 0.05); the difference was more marked in women with baseline SF concentrations <15 μg/L (P < 0.05). Random serial sampling reduced the required sample size per group to one-tenth of that for 2 fixed time points. Compared with the 5-time-point analysis, the 3-time-point sparse sampling generated comparable estimates of efficacy.

CONCLUSIONS

When used to evaluate the efficacy of iron fortificants, random serial sampling can reduce the sample size, invasiveness, and costs while increasing sensitivity. Random serial sampling more clearly describes the pattern of iron repletion and may prove useful in evaluating other micronutrient interventions.

The effects of obstructive jaundice on the pharmacodynamics of propofol: does the sensitivity of intravenous anesthetics change among icteric patients?

BACKGROUND

Some studies suggest that certain clinical symptoms of cholestasis, such as fatigue and pruritus, result from altered neurotransmission. Patients with obstructive jaundice also have labile blood pressure and heart rate. In the present study, the authors investigated whether obstructive jaundice affects a patient's sensitivity to hypnotics and the haemodynamic profile of propofol.

METHODS

Thirty-six ASA physical status I/II/III patients with serum total bilirubin (TBL) from 7.8 to 362.7 micromol/l scheduled for bile duct surgery were recruited. A computer-controlled propofol infusion programmed for effect site target was used to rapidly attain and maintain sequential increase of the compartment concentration (from 1 to 3 microg/ml). Each target-controlled concentration was maintained for about 12 min, and arterial blood samples were drawn for propofol concentration determination. The bispectral index (BIS) and mean arterial pressures (MAP) were used as indices of the propofol effect. The relation between the concentration and the effects was described by the Hill equation. The pharmacodynamic parameters were optimized using a nonlinear mixed-effect model.

RESULTS

TBL was not a significant covariate of EC(50) for the pharmacodynamic model. For BIS and MAP, the parameters of the pharmacodynamic model were E(max)=75.77%, EC(50)=2.34 microg/ml, and gamma=1.82, and E(max)=47.83%, EC(50)=1.49 microg/ml, and gamma=1.88, respectively.

CONCLUSIONS

We demonstrated that obstructive jaundice with serum TBL from 7.8 to 362.7 micromol/l had no effect on propofol pharmacodynamics observed by BIS and MAP.

Population pharmacodynamic parameter estimation from sparse sampling: effect of sigmoidicity on parameter estimates

The objective of this stimulation study was to evaluate effect of simoidicity of the concentration-effect (C-E) relationship on the efficiency of population parameter estimation from sparse sampling and is a continuation of previous work that addressed the effect of sample size and number of samples on parameters estimation from sparse sampling for drugs with C-E relationship characterized by high sigmoidicity (gamma > 5). The findings are based on observed C-E relationships for two drugs, octreotide and remifentanil, characterized by simple E (max) and sigmoid E (max) models (gamma = ~2.5), respectively. For each model, C-E profiles (100 replicates of 100 subjects each) were simulated for several sampling designs, with four or five samples/individual randomly obtained from within sampling windows based on EC(50)-normalized plasma drug concentrations, PD parameters based on observed population mean values, and inter-individual and residual variability of 30% and 25%, respectively. The C-E profiles were fitted using non-linear mixed effect modeling with the first-order conditional estimation method; variability parameters were described by an exponential error model. The results showed that, for the sigmoid E (max) model, designs with four or five samples reliably estimated the PD parameters (EC(50), E (max), E (0), and gamma), whereas the five-sample design, with two samples in the 2-3 E (max) region, provided in addition more reliable estimates of inter-individual variability; increasing the information content of the EC(50) region was not critical as long as this region was covered by a single sample in the 0.5-1.5 EC(50) window. For the simple E (max) model, because of the shallower profile, enriching the EC(50) region was more important. The impact of enrichment of appropriate regions for the two models can be explained based on the shape (sigmoidicity) of the concentration-effect relationships, with shallower C-E profiles requiring data enrichment in the EC(50) region and steeper curves less so; in both cases, the E (max) region needs to be adequately delineated, however. The results provide a general framework for population parameter estimation from sparse sampling in clinical trials when the underlying C-E profiles have different degrees of sigmoidicity.