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Taking parameter uncertainty into account is key to make drug development decisions such as testing whether trial endpoints meet defined criteria. Currently used methods for assessing parameter uncertainty in NLMEM have limitations, and there is a lack of diagnostics for when these limitations occur. In this work, a method based on sampling importance resampling (SIR) is proposed, which has the advantage of being free of distributional assumptions and does not require repeated parameter estimation. To perform SIR, a high number of parameter vectors are simulated from a given proposal uncertainty distribution. Their likelihood given the true uncertainty is then approximated by the ratio between the likelihood of the data given each vector and the likelihood of each vector given the proposal distribution, called the importance ratio. Non-parametric uncertainty distributions are obtained by resampling parameter vectors according to probabilities proportional to their importance ratios. Two simulation examples and three real data examples were used to define how SIR should be performed with NLMEM and to investigate the performance of the method. The simulation examples showed that SIR was able to recover the true parameter uncertainty. The real data examples showed that parameter 95 % confidence intervals (CI) obtained with SIR, the covariance matrix, bootstrap and log-likelihood profiling were generally in agreement when 95 % CI were symmetric. For parameters showing asymmetric 95 % CI, SIR 95 % CI provided a close agreement with log-likelihood profiling but often differed from bootstrap 95 % CI which had been shown to be suboptimal for the chosen examples. This work also provides guidance towards the SIR workflow, i.e.,which proposal distribution to choose and how many parameter vectors to sample when performing SIR, using diagnostics developed for this purpose. SIR is a promising approach for assessing parameter uncertainty as it is applicable in many situations where other methods for assessing parameter uncertainty fail, such as in the presence of small datasets, highly nonlinear models or meta-analysis.

The aim of this investigation is to identify, by in silico and in vitro methods, the molecular determinants, e.g., solubility in an aqueous medium and lipophilic properties, which have an effect on the bioavailability of five selected fluoroquinolones. These properties were estimated by analysis of the electrostatic potential pattern and values of free energy of solvation as well as the partition coefficients of the studied compounds. The study is based on theoretical quantum-chemical methods and a simple experimental shake-flask technique with two immiscible phases, n -octanol and phosphate buffer. The solvation free energy values of compounds in both environments appeared to be negative. The wide range of electrostatic potential from negative to positive demonstrates the presence of dipole–dipole intermolecular interactions, while the high electron density at various sites indicates the possibility of hydrogen bond formation with solvent molecules. High partition coefficient values, obtained by summing the atomic contributions, did not take various correction factors into account and therefore were not accurate. Theoretical partition coefficient values based on more accurate algorithms, which included these correction factors (fragmental methods), yielded more accurate values. Theoretical methods are useful tools for predicting the bioavailability of fluoroquinolones.

Knowledge of the uncertainty in model parameters is essential for decision-making in drug development. Contrarily to other aspects of nonlinear mixed effects models (NLMEM), scrutiny towards assumptions around parameter uncertainty is low, and no diagnostic exists to judge whether the estimated uncertainty is appropriate. This work aims at introducing a diagnostic capable of assessing the appropriateness of a given parameter uncertainty distribution. The new diagnostic was applied to case bootstrap examples in order to investigate for which dataset sizes case bootstrap is appropriate for NLMEM. The proposed diagnostic is a plot comparing the distribution of differences in objective function values (dOFV) of the proposed uncertainty distribution to a theoretical Chi square distribution with degrees of freedom equal to the number of estimated model parameters. The uncertainty distribution was deemed appropriate if its dOFV distribution was overlaid with or below the theoretical distribution. The diagnostic was applied to the bootstrap of two real data and two simulated data examples, featuring pharmacokinetic and pharmacodynamic models and datasets of 20–200 individuals with between 2 and 5 observations on average per individual. In the real data examples, the diagnostic indicated that case bootstrap was unsuitable for NLMEM analyses with around 70 individuals. A measure of parameter-specific “effective” sample size was proposed as a potentially better indicator of bootstrap adequacy than overall sample size. In the simulation examples, bootstrap confidence intervals were shown to underestimate inter-individual variability at low sample sizes. The proposed diagnostic proved a relevant tool for assessing the appropriateness of a given parameter uncertainty distribution and as such it should be routinely used.

When performing a population pharmacokinetic modelling analysis covariates are often added to the model. Such additions are often justified by improved goodness of fit and/or decreased in unexplained (random) parameter variability. Increased goodness of fit is most commonly measured by the decrease in the objective function value. Parameter variability can be defined as the sum of unexplained (random) and explained (predictable) variability. Increase in magnitude of explained parameter variability could be another possible criterion for judging improvement in the model. The agreement between these three criteria in diagnosing covariate-parameter relationships of different strengths and nature using stochastic simulations and estimations as well as assessing covariate-parameter relationships in four previously published real data examples were explored. Total estimated parameter variability was found to vary with the number of covariates introduced on the parameter. In the simulated examples and two real examples, the parameter variability increased with increasing number of included covariates. For the other real examples parameter variability decreased or did not change systematically with the addition of covariates. The three criteria were highly correlated, with the decrease in unexplained variability being more closely associated with changes in objective function values than increases in explained parameter variability were. The often used assumption that inclusion of covariates in models only shifts unexplained parameter variability to explained parameter variability appears not to be true, which may have implications for modelling decisions.

The objective of this work was to facilitate the development of nonlinear mixed effects models by establishing a diagnostic method for evaluation of stochastic model components. The random effects investigated were between subject, between occasion and residual variability. The method was based on a first-order conditional estimates linear approximation and evaluated on three real datasets with previously developed population pharmacokinetic models. The results were assessed based on the agreement in difference in objective function value between a basic model and extended models for the standard nonlinear and linearized approach respectively. The linearization was found to accurately identify significant extensions of the model’s stochastic components with notably decreased runtimes as compared to the standard nonlinear analysis. The observed gain in runtimes varied between four to more than 50-fold and the largest gains were seen for models with originally long runtimes. This method may be especially useful as a screening tool to detect correlations between random effects since it substantially quickens the estimation of large variance–covariance blocks. To expedite the application of this diagnostic tool, the linearization procedure has been automated and implemented in the software package PsN.

In vivo microdialysis with HPLC was used to investigate the pharmacokinetics of pefloxacin and its interaction with cyclosporin A. Microdialysis probes were inserted into the jugular vein/right atrium, the striatum and the bile duct of male Sprague‐Dawley rats. Biological fluid sampling thereby allowed the simultaneous determination of pefloxacin levels in blood, brain and bile. Following pefloxacin administration, the brain‐to‐blood coefficient of distribution was 0.036. This was calculated by dividing the area under the concentration curve (AUC) of pefloxacin in brain by its AUC in blood (k=AUCbrain/AUCblood). When the P‐glycoprotein cyclosporin A (10 mg kg−1) was co‐administered with pefloxacin (10 mg kg−1), the AUC and the mean residence time in rat blood did not differ significantly (P>0.05). Similarly, the pharmacokinetics of pefloxacin in rat brain was not affected by the presence of cyclosporin A. The AUC of unbound pefloxacin in bile was significantly greater than that in blood. The disposition of pefloxacin in rat bile shows a slow elimination phase following a peak concentration 30 min after pefloxacin administration (10 mg kg−1, i.v.). The bile‐to‐blood coefficient of distribution (k=AUCbile/AUCblood) was 1.53. The results indicated that pefloxacin was able to penetrate the blood‐brain barrier and that the concentration in bile was greater than that in the blood, suggesting active biliary excretion of pefloxacin. Current data obtained from rats show no significant impact of cyclosporin A on the pharmacokinetics of pefloxacin in rat blood and brain when administered by concomitant i.v. bolus. British Journal of Pharmacology (2001) 132, 1310–1316; doi:10.1038/sj.bjp.0703927

The aim of this study was to elucidate some of the pharmacokinetic parameters of pefloxacin in lactating goats (n = 5) following intravenous (i.v.) or intramuscular (i.m.) injections of 10 mg/kg bw. Serially obtained serum, milk and urine samples were collected at precise time intervals, and the drug concentrations were assayed using a microbiological assay. A two-compartment open model best described the decrease of pefloxacin concentration in the serum after intravenous administration. The maximum serum concentration (C0(p)) was 8.4 +/- 0.48 microg/ml; elimination half-life (t 1/2 beta) was 1.6 +/- 0.3 h; total body clearance (Cl(tot) was 3.6 +/- 0.3 L/kg/h; steady-state volume of distribution (V(dss)) was 5.14 +/- 0.21 L/kg; and the area under the curve (AUC) was 2.78 +/- 0.22 microg.ml/h. Pefloxacin was absorbed rapidly after i.m. injection with an absorption half-life (t 1/2 ab) of 0.32 +/- 0.02 h. The peak serum concentration (Cmax) of 0.86 +/- 0.08 microg/ml was attained at 0.75 h (Tmax). The absolute bioavailability after i.m. administration was 70.63 +/- 1.13% and the serum protein-bound fraction ranged from 7.2% to 14.3%, with an average value of 9.8 +/- 1.6%. Penetration of pefloxacin from the blood into the milk was rapid and extensive, and the pefloxacin concentration in milk exceeded that in serum from 1 h after administration. The drug was detected in milk and urine for 10 and 72 h, respectively; no samples were taken after 72 h.

The plasma concentrations and pharmacokinetics of the fluoroquinolone antimicrobial agent pefloxacin, following the administration of a single intravenous (10 mg/kg) or oral (20 mg/kg) dose, were investigated in healthy female goats. The antimicrobial activity in plasma was measured at predetermined times after drug administration by an agar well diffusion microbiological assay, using Escherichia coli (ATCC 25922) as the test organism. Concentrations of the drug > or = 0.25 microg/ml were maintained in plasma for up to 6 and 10 h after intravenous (i.v.) or oral administration of pefloxacin, respectively. The concentration time data for pefloxacin in plasma after i.v. or oral administration conformed to two- and one-compartment open models, respectively. Plasma pefloxacin concentrations decreased rapidly during the initial phase after i.v. injection, with a distribution half-life (t(1/2alpha)) of 0.10 +/- 0.01 h. The terminal phase had a half-life (t(1/2beta)) of 1.12 +/- 0.21 h. The volume of distribution at steady state (Vdss), mean residence time (MRT) and total systemic clearance (ClB) of pefloxacin were 1.08 +/- 0.09 L/kg, 1.39 +/- 0.23 h and 821 +/- 88 (ml/h)/kg, respectively. Following oral administration of pefloxacin, the maximum concentration in the plasma (Cmax) was 2.22 +/- 0.48 microg/ml and the interval from administration until maximum concentration (tmax) was 2.3 +/- 0.7 h. The absorption half-life (t(1/2ka)) mean absorption time (MAT) and elimination half-life of pefloxacin were 0.82 +/- 0.40, 4.2 +/- 1.0 and 2.91 +/- 0.50 h, respectively. The oral bioavailability of pefloxacin was 42% +/- 5.8%. On the basis of the pharmacokinetic data, a dosage regimen of 20 mg/kg, i.v. at 8 h intervals or orally twice daily, is suggested for treating infections caused by drug-sensitive pathogens in goats.

A new mathematical approach was developed to quantify convulsant interaction between pefloxacin and theophylline in rats. Animals received each compound separately or in different combination ratios. Infusion was stopped at the onset of maximal seizures. Cerebrospinal fluid (CSF) and plasma samples were collected for HPLC drug determination. The nature and intensity of the pharmacodynamic (PD) interaction between drugs was assessed with a new modeling approach which includes (a) data transformation to create an essentially error-free X-variable and (b) estimation of an interaction parameter a by fitting a nonlinear hyperbolic model to the combination data with unweighted nonlinear regression. Drug disposition to the biophase was linear within the range of administered doses. The estimates of a suggested a Loewe antagonistic interaction between pefloxacin and theophylline at the induction of maximal seizures in rats. Similar intensity of PD interaction was observed at the dose and biophase level (alpha was -0.415 +/- 0.069 and -0.567 +/- 0.079, respectively). The suitability of the proposed model was assessed by Monte Carlo simulation. This new mathematical approach enabled the characterization of the Loewe antagonistic nature of the PD (convulsant) interaction between pefloxacin and theophylline, whereas previously used methodologies failed to do so.