Application of pharmacometric methods to understand warfarin dose response

Existing warfarin dosing methods do not accurately predict warfarin maintenance doses for patients in the lower or upper quartile of dose requirements. It was argued that this is related to the use of the international normalised ratio (INR) as a sole marker of anticoagulation for warfarin dose individualisation. The overarching premise of this thesis was that the coagulation proteins are on the causal path from warfarin dose to INR response and that a measure of coagulation protein response in addition to the INR will be helpful in the prediction of future anticoagulant response. The aim of this thesis was to apply pharmacometric methods to understand the coagulation kinetics underpinning the warfarin dose response and to introduce a new perspective to the prediction of anticoagulant response to warfarin. A joint model was developed to quantify the influence of warfarin on all six vitamin K-dependent coagulation proteins (factors II, VII, IX, X, and proteins C and S) simultaneously. The full correlation structures that exist between parameters at the individual level and between residual errors of different coagulation proteins were accounted for. Of all the coagulation proteins considered, factor VII was found to have the shortest degradation half-life and will therefore be the first to reach a new steady-state following a perturbation introduced by warfarin. Subsequently, the influence of coagulation proteins and their interactions on the INR was explored based on simulations from a mechanistic coagulation network model. A sensitivity analysis revealed that INR is most sensitive to factor VII and an isobologram analysis demonstrated that the presence of more than one coagulation protein deficiencies is redundant for INR effect. It was proposed that factor VII is the most influential on the INR and that the use of factor VII as a marker of anticoagulation (in addition to the INR) may improve the prediction of the anticoagulant response. A factor VII-based method for the prediction of anticoagulant response to warfarin was developed based on a heuristic model-order reduction of the coagulation network model. The prediction method was shown to be associated with minimal bias and its use was illustrated using data from one typical simulated patient and two real patients supporting a proof-of-principle. Finally, a framework for systematic evaluation of model assumptions was developed. In particular, a flowchart was proposed to evaluate assumptions based on the impact and the probability of assumption violation. The assumptions underpinning the pharmacometric analyses presented in this thesis were evaluated and used to illustrate the utility of the proposed framework. In this thesis, both the top-down and bottom-up pharmacometric analyses were applied to explore the coagulation kinetics underpinning warfarin dose response. Standard methods such as population analysis, model simulations, isobologram analysis, and sensitivity analysis were employed. A heuristic model-order reduction method was experimented and seemed to work well although generalisation of the method to other settings requires prospective testing. The work conducted in this thesis offered a new perspective on the prediction of anticoagulant response. The next step would be to extend the current method to the prediction of warfarin maintenance dose. This would require setting up and evaluating a dose individualisation algorithm (perhaps Bayesian) that incorporates a factor VII-INR bivariate response variable. Last but not least, a framework for systematic evaluation of assumptions was proposed. An important future step would be to apply the framework to a series of other settings to fully explore the utility and robustness of the framework to different model-building processes and model use settings

Application of pharmacometric methods to understand warfarin dose response

Existing warfarin dosing methods do not accurately predict warfarin maintenance doses for patients in the lower or upper quartile of dose requirements. It was argued that this is related to the use of the international normalised ratio (INR) as a sole marker of anticoagulation for warfarin dose individualisation. The overarching premise of this thesis was that the coagulation proteins are on the causal path from warfarin dose to INR response and that a measure of coagulation protein response in addition to the INR will be helpful in the prediction of future anticoagulant response. The aim of this thesis was to apply pharmacometric methods to understand the coagulation kinetics underpinning the warfarin dose response and to introduce a new perspective to the prediction of anticoagulant response to warfarin. A joint model was developed to quantify the influence of warfarin on all six vitamin K-dependent coagulation proteins (factors II, VII, IX, X, and proteins C and S) simultaneously. The full correlation structures that exist between parameters at the individual level and between residual errors of different coagulation proteins were accounted for. Of all the coagulation proteins considered, factor VII was found to have the shortest degradation half-life and will therefore be the first to reach a new steady-state following a perturbation introduced by warfarin. Subsequently, the influence of coagulation proteins and their interactions on the INR was explored based on simulations from a mechanistic coagulation network model. A sensitivity analysis revealed that INR is most sensitive to factor VII and an isobologram analysis demonstrated that the presence of more than one coagulation protein deficiencies is redundant for INR effect. It was proposed that factor VII is the most influential on the INR and that the use of factor VII as a marker of anticoagulation (in addition to the INR) may improve the prediction of the anticoagulant response. A factor VII-based method for the prediction of anticoagulant response to warfarin was developed based on a heuristic model-order reduction of the coagulation network model. The prediction method was shown to be associated with minimal bias and its use was illustrated using data from one typical simulated patient and two real patients supporting a proof-of-principle. Finally, a framework for systematic evaluation of model assumptions was developed. In particular, a flowchart was proposed to evaluate assumptions based on the impact and the probability of assumption violation. The assumptions underpinning the pharmacometric analyses presented in this thesis were evaluated and used to illustrate the utility of the proposed framework. In this thesis, both the top-down and bottom-up pharmacometric analyses were applied to explore the coagulation kinetics underpinning warfarin dose response. Standard methods such as population analysis, model simulations, isobologram analysis, and sensitivity analysis were employed. A heuristic model-order reduction method was experimented and seemed to work well although generalisation of the method to other settings requires prospective testing. The work conducted in this thesis offered a new perspective on the prediction of anticoagulant response. The next step would be to extend the current method to the prediction of warfarin maintenance dose. This would require setting up and evaluating a dose individualisation algorithm (perhaps Bayesian) that incorporates a factor VII-INR bivariate response variable. Last but not least, a framework for systematic evaluation of assumptions was proposed. An important future step would be to apply the framework to a series of other settings to fully explore the utility and robustness of the framework to different model-building processes and model use settings

Bounded integer model‐based analysis of psoriasis area and severity index in patients with moderate‐to‐severe plaque psoriasis receiving BI 730357

Abstract BI 730357 is investigated as an oral treatment of plaque psoriasis. We analyzed the impact of three dosage regimens on the Psoriasis Area and Severity Index (PASI) response with modeling based on phase I and II data from 109 healthy subjects and 274 patients with moderate‐to‐severe plaque psoriasis. The pharmacokinetics (PK) was characterized by a two‐compartment model with dual absorption paths and a first‐order elimination. Higher baseline C‐reactive protein was associated with lower clearance and patients generally had lower clearance compared with healthy subjects. A bounded integer PK/pharmacodynamic model characterized the effect on the observed PASI. The maximum drug effect was largest for patients with no prior biologic use, smaller for patients with prior use of non‐interleukin‐17 inhibitors, and smallest for patients with prior interleukin‐17 inhibitor use. The models allowed robust simulation of large patient populations, predicting a plateau in PASI outcomes for BI 730357 exposure above 2000 nmol/L

A joint model for vitamin K-dependent clotting factors and anticoagulation proteins

Background Warfarin acts by inhibiting the reduction of vitamin K (VK) to its active form, thereby decreasing the production of VK-dependent coagulation proteins. The aim of this research is to develop a joint model for the VK-dependent clotting factors II, VII, IX and X, and the anticoagulation proteins, proteins C and S, during warfarin initiation. Methods Data from 18 patients with atrial fibrillation who had warfarin therapy initiated were available for analysis. Nine blood samples were collected from each subject at baseline, and at 1–5, 8, 15 and 29 days after warfarin initiation and assayed for factors II, VII, IX and X, and proteins C and S. Warfarin concentration–time data were not available. The coagulation proteins data were modelled in a stepwise manner using NONMEM® Version 7.2. In the first stage, each of the coagulation proteins was modelled independently using a kinetic-pharmacodynamic model. In the subsequent step, the six kinetic-pharmacodynamic models were combined into a single joint model. Results One patient was administered VK and was excluded from the analysis. Each kinetic-pharmacodynamic model consisted of two parts: (1) a common one-compartment pharmacokinetic model with first-order absorption and elimination for warfarin; and (2) an inhibitory E max model linked to a turnover model for coagulation proteins. In the joint model, an unexpected pharmacodynamic lag was identified and the estimated degradation half-life of VK-dependent coagulation proteins were in agreement with previously published values. The model provided an adequate fit to the observed data. Conclusion The joint model represents the first work to quantify the influence of warfarin on all six VK-dependent coagulation proteins simultaneously. Future work will expand the model to predict the influence of exogenously administered VK on the time course of clotting factor concentrations after warfarin overdose and during perioperative warfarin reversal procedures

Assessment of the nlmixr R package for population pharmacokinetic modeling: A metformin case study

AIM: nlmixr offers first-order conditional estimation with or without interaction (FOCE or FOCEi) and stochastic approximation estimation-maximisation (SAEM) to fit nonlinear mixed-effect models (NLMEM). We modelled metformin's pharmacokinetic data using nlmixr and investigated SAEM and FOCEi's performance with respect to bias and precision of parameter estimates, and robustness to initial estimates. METHOD: Compartmental models were fitted. The final model was determined based on the objective function value and inspection of goodness-of-fit plots. The bias and precision of parameter estimates were compared between SAEM and FOCEi using stochastic simulations and estimations. For robustness, parameters were re-estimated as the initial estimates were perturbed 100-times and resultant changes evaluated. RESULTS: Absorption kinetics of metformin depends significantly on food status. Under the fasted state, the first-order absorption into the central compartment was preceded by zero-order infusion into the depot compartment, whereas for the fed state, the absorption into the depot was instantaneous followed by first-order absorption from depot into the central compartment. The mean of relative mean estimation error (rMEE) ( ME E SAEM ME E FOCEi ) and rRMSE ( RMS E SAEM RMS E FOCEi ) was 0.48 and 0.35 respectively. All parameter estimates given by SAEM appeared to be narrowly distributed and were close to the true value used for simulation. In contrast, the distribution of estimates from FOCEi were skewed and more biased . When initial estimates were perturbed, FOCEi estimates were more biased and imprecise. DISCUSSION: nlmixr is reliable for NLMEM. SAEM was superior to FOCEi in terms of bias and precision, and more robust against initial estimate perturbations

Assessment of the nlmixr R package for population pharmacokinetic modeling: a metformin case study

Aimnlmixr offers first-order conditional estimation (FOCE), FOCE with interaction (FOCEi) and stochastic approximation estimation-maximisation (SAEM) to fit nonlinear mixed-effect models (NLMEM). We modelled metformin's pharmacokinetic data using nlmixr and investigated SAEM and FOCEi's performance with respect to bias and precision of parameter estimates, and robustness to initial estimates. MethodCompartmental models were fitted. The final model was determined based on the objective function value and inspection of goodness-of-fit plots. The bias and precision of parameter estimates were compared between SAEM and FOCEi using stochastic simulations and estimations. For robustness, parameters were re-estimated as the initial estimates were perturbed 100 times and resultant changes evaluated. ResultsThe absorption kinetics of metformin depend significantly on food status. Under the fasted state, the first-order absorption into the central compartment was preceded by zero-order infusion into the depot compartment, whereas for the fed state, the absorption into the depot was instantaneous followed by first-order absorption from depot into the central compartment. The means of relative mean estimation error (rMEE) ( MEESAEMMEEFOCEi$$\frac{\mathrm{ME}{\mathrm{E}}_{\mathrm{SAEM}}}{\mathrm{ME}{\mathrm{E}}_{\mathrm{FOCEi}}}$$ ) and rRMSE ( RMSESAEMRMSEFOCEi$$\frac{\mathrm{RMS}{\mathrm{E}}_{\mathrm{SAEM}}}{\mathrm{RMS}{\mathrm{E}}_{\mathrm{FOCEi}}}$$ ) were 0.48 and 0.35, respectively. All parameter estimates given by SAEM appeared to be narrowly distributed and were close to the true value used for simulation. In contrast, the distribution of estimates from FOCEi were skewed and more biased. When initial estimates were perturbed, FOCEi estimates were more biased and imprecise. Discussionnlmixr is reliable for NLMEM. SAEM was superior to FOCEi in terms of bias and precision, and more robust against initial estimate perturbations

Rituximab pharmacokinetic and pharmacokinetic-pharmacodynamic evaluation based on a study in diffuse large B-cell lymphoma : Influence of tumor size on pharmacokinetic and assessment of pharmacokinetic similarity

Dr. Reddy's Laboratories rituximab (DRL_RI; Dr. Reddy's Laboratories SA, Basel, Switzerland) is under development as a rituximab biosimilar. Study RI-01-002 (Clinical Trials Registry - India/2012/11/003129), comparing DRL_RI to the reference medicinal product (RMP) MabThera® (Roche, Grenzach-Wyhlen, Germany), demonstrated pharmacokinetic (PK) equivalence and showed comparable pharmacodynamic, efficacy, safety, and immunogenicity profiles. We used data from the same study to perform population PK and PK–pharmacodynamic analyses: first exploring possible factors influencing the PK similarity assessment between products and then performing simulations to investigate the impact of tumor size on rituximab PK. Nonlinear mixed-effects models for PK, tumor size, tumor size–PK, and tumor response were developed independently. The final PK model included drug product as a dose-scaling parameter and predicted a 6.75% higher dose reaching the system in RMP-treated patients. However, when tumor size was included in the tumor size–PK model, the drug product effect was no longer observed. The model rather indicated that patients with larger tumor size have higher clearance. Further simulations confirmed that higher baseline tumor size is associated to slightly lower rituximab exposure. Tumor response, described by a continuous-time Markov model, did not differ between drug products. Both had higher effects during the first 20 weeks of treatment. Also, the model described a subpopulation of nonresponders to treatment (42%) with faster transitions to a worse state. The different rituximab exposure initially detected between drug products (6.75%) was shown using PK/PK–pharmacodynamic analysis to be attributed to a tumor size imbalance between treatment groups. PK/PK–pharmacodynamic analyses may contribute to PK similarity assessments