Extensions to the Visual Predictive Check to facilitate model performance evaluation

The Visual Predictive Check (VPC) is a valuable and supportive instrument for evaluating model performance. However in its most commonly applied form, the method largely depends on a subjective comparison of the distribution of the simulated data with the observed data, without explicitly quantifying and relating the information in both. In recent adaptations to the VPC this drawback is taken into consideration by presenting the observed and predicted data as percentiles. In addition, in some of these adaptations the uncertainty in the predictions is represented visually. However, it is not assessed whether the expected random distribution of the observations around the predicted median trend is realised in relation to the number of observations. Moreover the influence of and the information residing in missing data at each time point is not taken into consideration. Therefore, in this investigation the VPC is extended with two methods to support a less subjective and thereby more adequate evaluation of model performance: (i) the Quantified Visual Predictive Check (QVPC) and (ii) the Bootstrap Visual Predictive Check (BVPC). The QVPC presents the distribution of the observations as a percentage, thus regardless the density of the data, above and below the predicted median at each time point, while also visualising the percentage of unavailable data. The BVPC weighs the predicted median against the 5th, 50th and 95th percentiles resulting from a bootstrap of the observed data median at each time point, while accounting for the number and the theoretical position of unavailable data. The proposed extensions to the VPC are illustrated by a pharmacokinetic simulation example and applied to a pharmacodynamic disease progression example

Nonlinear pharmacokinetics of therapeutic proteins resulting from receptor mediated endocytosis

Receptor mediated endocytosis (RME) plays a major role in the disposition of therapeutic protein drugs in the body. It is suspected to be a major source of nonlinear pharmacokinetic behavior observed in clinical pharmacokinetic data. So far, mostly empirical or semi-mechanistic approaches have been used to represent RME. A thorough understanding of the impact of the properties of the drug and of the receptor system on the resulting nonlinear disposition is still missing, as is how to best represent RME in pharmacokinetic models. In this article, we present a detailed mechanistic model of RME that explicitly takes into account receptor binding and trafficking inside the cell and that is used to derive reduced models of RME which retain a mechanistic interpretation. We find that RME can be described by an extended Michaelis–Menten model that accounts for both the distribution and the elimination aspect of RME. If the amount of drug in the receptor system is negligible a standard Michaelis–Menten model is capable of describing the elimination by RME. Notably, a receptor system can efficiently eliminate drug from the extracellular space even if the total number of receptors is small. We find that drug elimination by RME can result in substantial nonlinear pharmacokinetics. The extent of nonlinearity is higher for drug/receptor systems with higher receptor availability at the membrane, or faster internalization and degradation of extracellular drug. Our approach is exemplified for the epidermal growth factor receptor system

Pharmacokinetic and pharmacodynamic modelling after subcutaneous, intravenous and buccal administration of a high-concentration formulation of buprenorphine in conscious cats

The aim of this study was to describe the joint pharmacokinetic-pharmacodynamic model and evaluate thermal antinociception of a high-concentration formulation of buprenorphine (Simbadol™) in cats

The Paired Availability Design for Historical Controls

BACKGROUND: Although a randomized trial represents the most rigorous method of evaluating a medical intervention, some interventions would be extremely difficult to evaluate using this study design. One alternative, an observational cohort study, can give biased results if it is not possible to adjust for all relevant risk factors. METHODS: A recently developed and less well-known alternative is the paired availability design for historical controls. The paired availability design requires at least 10 hospitals or medical centers in which there is a change in the availability of the medical intervention. The statistical analysis involves a weighted average of a simple "before" versus "after" comparison from each hospital or medical center that adjusts for the change in availability. RESULTS: We expanded requirements for the paired availability design to yield valid inference. (1) The hospitals or medical centers serve a stable population. (2) Other aspects of patient management remain constant over time. (3) Criteria for outcome evaluation are constant over time. (4) Patient preferences for the medical intervention are constant over time. (5) For hospitals where the intervention was available in the "before" group, a change in availability in the "after group" does not change the effect of the intervention on outcome. CONCLUSION: The paired availability design has promise for evaluating medical versus surgical interventions, in which it is difficult to recruit patients to a randomized trial

Pharmacokinetics of Teriparatide (rhPTH[1–34]) and Calcium Pharmacodynamics in Postmenopausal Women with Osteoporosis

Teriparatide (rhPTH[1–34]) affects calcium metabolism in a pattern consistent with the known actions of endogenous parathyroid hormone (PTH). This report describes the pharmacokinetics and resulting serum calcium response to teriparatide in postmenopausal women with osteoporosis. Pharmacokinetic samples for this analysis were obtained from 360 women who participated in the Fracture Prevention Trial. Postmenopausal women with osteoporosis received daily subcutaneous injections of either teriparatide 20 μg (4.86 μmol) or placebo, median 21 months’ treatment. Serum teriparatide and calcium concentrations were measured throughout the study. An indirect-response model was developed to describe the pharmacokinetic–pharmacodynamic relationship between teriparatide concentrations and serum calcium response. The pharmacokinetics of teriparatide were characterized by rapid absorption (maximum concentration achieved within 30 min) and rapid elimination (half-life of 1 h), resulting in a total duration of exposure to the peptide of approximately 4 h. Teriparatide transiently increased serum calcium, with the maximum effect observed at approximately 4.25 h (median increase 0.4 mg/dl [0.1 mmol/l]). Calcium concentrations returned to predose levels by 16–24 h after each dose. Persistent hypercalcemia was not observed; one teriparatide 20 μg-treated patient had a predose serum calcium value above the normal range but <11.0 mg/dl (2.75 mmol/l). Following once-daily subcutaneous administration, teriparatide produces a modest but transient increase in serum calcium, consistent with the known effects of endogenous PTH on mineral metabolism. The excursion in serum calcium is brief, due to the short length of time that teriparatide concentrations are elevated

Estimation of tulathromycin depletion in plasma and milk after subcutaneous injection in lactating goats using a nonlinear mixed-effects pharmacokinetic modeling approach

Citation: Lin, Z. M., Cuneo, M., Rowe, J. D., Li, M. J., Tell, L. A., Allison, S., . . . Gehring, R. (2016). Estimation of tulathromycin depletion in plasma and milk after subcutaneous injection in lactating goats using a nonlinear mixed-effects pharmacokinetic modeling approach. Bmc Veterinary Research, 12, 10. https://doi.org/10.1186/s12917-016-0884-4Background: Extra-label use of tulathromycin in lactating goats is common and may cause violative residues in milk. The objective of this study was to develop a nonlinear mixed-effects pharmacokinetic (NLME-PK) model to estimate tulathromycin depletion in plasma and milk of lactating goats. Eight lactating goats received two subcutaneous injections of 2.5 mg/kg tulathromycin 7 days apart; blood and milk samples were analyzed for concentrations of tulathromycin and the common fragment of tulathromycin (i.e., the marker residue CP-60,300), respectively, using liquid chromatography mass spectrometry. Based on these new data and related literature data, a NLME-PK compartmental model with first-order absorption and elimination was used to model plasma concentrations and cumulative excreted amount in milk. Monte Carlo simulations with 100 replicates were performed to predict the time when the upper limit of the 95% confidence interval of milk concentrations was below the tolerance. Results: All animals were healthy throughout the study with normal appetite and milk production levels, and with mild-moderate injection-site reactions that diminished by the end of the study. The measured data showed that milk concentrations of the marker residue of tulathromycin were below the limit of detection (LOD = 1.8 ng/ml) 39 days after the second injection. A 2-compartment model with milk as an excretory compartment best described tulathromycin plasma and CP-60,300 milk pharmacokinetic data. The model-predicted data correlated with the measured data very well. The NLME-PK model estimated that tulathromycin plasma concentrations were below LOD (1.2 ng/ml) 43 days after a single injection, and 62 days after the second injection with a 95% confidence. These estimated times are much longer than the current meat withdrawal time recommendation of 18 days for tulathromycin in non-lactating cattle. Conclusions: The results suggest that twice subcutaneous injections of 2.5 mg/kg tulathromycin are a clinically safe extra-label alternative approach for treating pulmonary infections in lactating goats, but a prolonged withdrawal time of at least 39 days after the second injection should be considered to prevent violative residues in milk and any dairy goat being used for meat should have an extended meat withdrawal time

The use of the SAEM algorithm in MONOLIX software for estimation of population pharmacokinetic-pharmacodynamic-viral dynamics parameters of maraviroc in asymptomatic HIV subjects

Using simulated viral load data for a given maraviroc monotherapy study design, the feasibility of different algorithms to perform parameter estimation for a pharmacokinetic-pharmacodynamic-viral dynamics (PKPD-VD) model was assessed. The assessed algorithms are the first-order conditional estimation method with interaction (FOCEI) implemented in NONMEM VI and the SAEM algorithm implemented in MONOLIX version 2.4. Simulated data were also used to test if an effect compartment and/or a lag time could be distinguished to describe an observed delay in onset of viral inhibition using SAEM. The preferred model was then used to describe the observed maraviroc monotherapy plasma concentration and viral load data using SAEM. In this last step, three modelling approaches were compared; (i) sequential PKPD-VD with fixed individual Empirical Bayesian Estimates (EBE) for PK, (ii) sequential PKPD-VD with fixed population PK parameters and including concentrations, and (iii) simultaneous PKPD-VD. Using FOCEI, many convergence problems (56%) were experienced with fitting the sequential PKPD-VD model to the simulated data. For the sequential modelling approach, SAEM (with default settings) took less time to generate population and individual estimates including diagnostics than with FOCEI without diagnostics. For the given maraviroc monotherapy sampling design, it was difficult to separate the viral dynamics system delay from a pharmacokinetic distributional delay or delay due to receptor binding and subsequent cellular signalling. The preferred model included a viral load lag time without inter-individual variability. Parameter estimates from the SAEM analysis of observed data were comparable among the three modelling approaches. For the sequential methods, computation time is approximately 25% less when fixing individual EBE of PK parameters with omission of the concentration data compared with fixed population PK parameters and retention of concentration data in the PD-VD estimation step. Computation times were similar for the sequential method with fixed population PK parameters and the simultaneous PKPD-VD modelling approach. The current analysis demonstrated that the SAEM algorithm in MONOLIX is useful for fitting complex mechanistic models requiring multiple differential equations. The SAEM algorithm allowed simultaneous estimation of PKPD and viral dynamics parameters, as well as investigation of different model sub-components during the model building process. This was not possible with the FOCEI method (NONMEM version VI or below). SAEM provides a more feasible alternative to FOCEI when facing lengthy computation times and convergence problems with complex models