Simultaneous pharmacokinetics/pharmacodynamics modeling of recombinant human erythropoietin upon multiple intravenous dosing in rats

Early erythroferrone levels can predict the long-term haemoglobin responses to erythropoiesis-stimulating agents

BACKGROUND AND PURPOSE

Our previous study reported that erythroferrone (ERFE), a newly identified hormone produced by erythroblasts, responded to recombinant human erythropoietin (rHuEPO) sensitively but its dynamics was complicated by double peaks and circadian rhythm. This study intends to elucidate the underlying mechanisms for the double peaks of ERFE dynamics and further determine whether early ERFE measurements can predict haemoglobin responses to rHuEPO.

EXPERIMENTAL APPROACH

By using the purified recombinant rat ERFE protein and investigating its deposition in rats, the production of ERFE was deconvoluted. To explore the role of iron in ERFE production, we monitored short-term changes of iron status after injection of rHuEPO or deferiprone. Pharmacokinetic/pharmacodynamic (PK/PD) modelling was used to confirm the mechanisms and examine the predictive ability of ERFE for long-term haemoglobin responses.

KEY RESULTS

The rRatERFE protein was successfully purified. The production of ERFE was deconvoluted and showed two independent peaks (2 and 8 h). Transient iron decrease was observed at 4 h after rHuEPO injection and deferiprone induced significant increases of ERFE. Based on this mechanism, the PK/PD model could characterize the complex dynamics of ERFE. In addition, the model predictions further revealed a stronger correlation between ERFE and haemoglobin peak values than that for observed values.

CONCLUSIONS AND IMPLICATIONS

The complex dynamics of ERFE should be composited by an immediate release and transient iron deficiency-mediated secondary production of ERFE. The early peak values of ERFE, which occur within a few hours, can predict haemoglobin responses several weeks after ESA treatment.

Scaling Pharmacodynamics from Rats to Humans to Support Erythropoietin and Romiplostim Combination Therapy to Treat Erythropoietin-Resistant Anemia

Recombinant human erythropoietin (rHuEPO) is one of the most effective drugs for the treatment of anemia in patients with chronic kidney disease. However, EPO-resistance is an important contributor to the increased risk of adverse effects. We previously showed that EPO treatment could induce precursor cell depletion, resulting in EPO-resistance. We further found that the combination of EPO with romiplostim, a thrombopoietin receptor agonist that can stimulate the expansion of hematopoietic stem cells, can treat EPO-resistance. In this study, we performed interspecies pharmacodynamic (PD) scaling of this combination therapy for human dose prediction. The pharmacokinetic parameters of both rHuEPO and romiplostim in humans were obtained from previous studies. The PD parameters obtained in rats were scaled to humans using allometric equations. The relationship between PD parameters of the megakaryocyte lineage from rats, monkeys, and humans was in agreement with those from the literature on allometric scaling. The PD response was translated to humans based on allometric scaling and agreed with the observed data. These parameters were used to simulate hemoglobin and platelet response in humans. RHuEPO 50 IU/kg thrice weekly and romiplostim 1 μg/kg once every 4 weeks from the second week is the recommended combination dosing regimen according to the model prediction. Our work successfully scaled the PD of rHuEPO and romiplostim monotherapy from rats to humans. The predicted dosing regimen of each drug in the combination therapy is less intensive than the approved starting dose of each drug, which supports additional evaluations of the combination therapy in humans.

A Novel Combination Therapy of Erythropoietin and Thrombopoietin to Treat Erythropoietin-Resistance anemia

PURPOSE

Treatment with recombinant human erythropoietin (rHuEPO) may correct anemia in patients with chronic kidney disease. However, up to 10% of these patients exhibit EPO resistance or hyporesponsiveness, which may be caused by the depletion of erythroid progenitor cells. Thrombopoietin (TPO) stimulates the self-renewal of stem cells and promotes the growth of early erythroid progenitor cells. The objective of this study was to determine whether the combination of recombinant human TPO (rHuTPO) and rHuEPO could correct the depletion of erythroid precursor cells to treat EPO-resistant anemia.

METHODS

To test our hypothesis, pharmacokinetic (PK) and pharmacodynamic (PD) studies of rHuEPO and rHuTPO were performed in healthy rats. Rats received rHuEPO or rHuTPO alone or in combination. Plasma concentrations of rHuTPO and rHuEPO were measured. PD responses, including erythropoietic and thrombopoietic responses, were assessed in peripheral blood.

RESULTS

On one hand, the results demonstrated the synergistic effect of the combination of rHuEPO and rHuTPO on erythropoiesis. Compared with rHuEPO monotherapy, the combination therapies further stimulated the production of red blood cells and hemoglobin. On the other hand, rHuEPO inhibited the platelet production induced by rHuTPO and mitigate the risk of blood clots. Furthermore, we successfully developed a mechanism-based PD model to simultaneously characterize the responses of the two molecules.

CONCLUSIONS

Overall, our study indicated that a combination therapy of rHuTPO and rHuEPO could be used to treat EPO-resistant anemia and provided a quantitative basis for further optimizing the combination therapy for clinical use.

Fate determination role of erythropoietin and romiplostim in the lineage commitment of hematopoietic progenitors

Erythropoietin (EPO) and thrombopoietin (TPO) have long been known to promote erythropoiesis and megakaryopoiesis, respectively. However, the fate changing role of EPO and TPO on megakaryocyte-erythroid progenitors (MEPs) to develop along the erythroid versus megakaryocyte (MK) lineage remains unclear. We have previously shown that EPO may have fate changing role because EPO treatment could induce progenitor cells depletion and resulted in EPO resistance. Therefore, we hypothesize that a combination of romiplostim, a TPO receptor agonist that could stimulate the expansion of progenitors, with EPO can treat EPO resistance. Using rats with anemia due to chronic kidney disease, we demonstrated that romiplostim synergized with EPO to promote red blood cells production while EPO inhibited platelet production in a dose-dependent manner to reduce the risk of thrombosis. Corroborating findings from in vivo, in vitro experiments demonstrated that romiplostim expanded hematopoietic stem cells and stimulated megakaryopoiesis, while EPO drove the progenitors toward an erythroid fate. We further developed a novel pharmacokinetic-pharmacodynamic model to quantify the effects of EPO and romiplostim on megakaryopoiesis and erythropoiesis simultaneously. The modeling results demonstrated that EPO increased the differentiation rate of MEPs into burst-forming unit-erythroid up to 22-fold, indicating that the slight increase of MEPs induced by romiplostim could be further amplified and recruited by EPO to promote erythropoiesis. The data herein support that romiplostim in combination with EPO can treat EPO resistance. Significance Statement This study clarified that erythropoietin (EPO) drives the fate of megakaryocyte-erythroid progenitors (MEP) toward the erythroid lineage, thus reducing their megakaryocyte (MK) lineage commitment, whereas romiplostim, a thrombopoietin (TPO) receptor agonist (RA), stimulates megakaryopoiesis through the MK-committed progenitor and MEP bifurcation pathways simultaneously. These findings support an innovative combination of romiplostim and EPO to treat EPO-resistant anemia, because the combination therapy further promotes erythropoiesis compared to EPO monotherapy and inhibit platelet production compared to romiplostim monotherapy.

A quantitative systems pharmacology model of hyporesponsiveness to erythropoietin in rats

Recombinant human erythropoietin (rHuEPO) is effective in managing chronic kidney disease and chemotherapy-induced anemia. However, hyporesponsiveness to rHuEPO treatment was reported in about 10% of the patients. A decreased response in rats receiving a single or multiple doses of rHuEPO was also observed. In this study, we aimed to develop a quantitative systems pharmacology (QSP) model to examine hyporesponsiveness to rHuEPO in rats. Pharmacokinetic (PK) and pharmacodynamic (PD) data after a single intravenous dose of rHuEPO (100 IU/kg) was obtained from a previous study (Yan et al. in Pharm Res, 30:1026-1036, 2013) including rHuEPO plasma concentrations, erythroid precursors counts in femur bone marrow and spleen, reticulocytes (RETs), red blood cells (RBCs), and hemoglobin (HGB) in circulation. Parameter values were obtained from literature or calibrated with experimental data. Global sensitivity analysis and model-based simulations were performed to assess parameter sensitivity and hyporesponsiveness. The final QSP model adequately characterizes time courses of rHuEPO PK and nine PD endpoints in both control and treatment groups simultaneously. The model indicates that negative feedback regulation, neocytolysis, and depletion of erythroid precursors are major factors leading to hyporesponsiveness to rHuEPO treatment in rats.

Simultaneous Target-Mediated Drug Disposition Model for Two Small-Molecule Compounds Competing for Their Pharmacological Target: Soluble Epoxide Hydrolase

1-(1-propanoylpiperidin-4-yl)-3-[4-(trifluoromethoxy)phenyl]urea (TPPU) and 1-(4-trifluoro-methoxy-phenyl)-3-(1-cyclopropanecarbonyl-piperidin-4-yl)-urea (TCPU) are potent inhibitors of soluble epoxide hydrolase (sEH) that have much better efficacy in relieving nociceptive response than the Food and Drug Administration-approved drug gabapentin in a rodent model of diabetic neuropathy. Experiments conducted in sEH knockout mice or with coadministration of a potent sEH displacer demonstrated that the pharmacokinetics of TPPU and TCPU were influenced by the specific binding to their pharmacologic target sEH, a phenomenon known as target-mediated drug disposition (TMDD). To quantitatively characterize the complex pharmacokinetics of TPPU and TCPU and gain better understanding on their target occupancy, population pharmacokinetics analysis using a nonlinear mixed-effect modeling approach was performed in the current study. The final model was a novel simultaneous TMDD interaction model, in which TPPU and TCPU compete for sEH, with TCPU binding to an additional unknown target pool with larger capacity that we refer to as a refractory pool. The total amount of sEH enzyme in mice was predicted to be 16.2 nmol, which is consistent with the experimental value of 10 nmol. The dissociate rate constants of TPPU and TCPU were predicted to be 2.24 and 2.67 hours^-1, respectively, which is close to the values obtained from in vitro experiments. Our simulation result predicted that 90% of the sEH will be occupied shortly after a low dose of 0.3 mg/kg TPPU administration, with ≥40% of sEH remaining to be bound with TPPU for at least 7 days. Further efficacy experiments are warranted to confirm the predicted target occupancy. SIGNIFICANCE STATEMENT: Although target-mediated drug disposition (TMDD) models have been well documented, most of them were established in a single compound scenario. Our novel model represents the first TMDD interaction model for two small-molecule compounds competing for the same pharmacological target.

Semi-mechanistic Pharmacokinetic/Pharmacodynamic model of three pegylated rHuEPO and ior®EPOCIM in New Zealand rabbits

Marketed formulations of erythropoietin (EPO) ior®EPOCIM, MIRCERA® and two newly developed pegylated-EPO analogues (PEG-EPO 32 and 40 kDa) formulations were intravenously administered to New Zealand rabbits. A semi-mechanistic Pharmacokinetic/Pharmacodynamic (PK/PD) model describing in a simultaneous and integrated form the time course of reticulocytes, red blood cells and hemoglobin was built to account for the time course of hematopoiesis stimulation after erythropoietin administration. Data analysis was performed based on the population approach with the software NONMEM version 7.3. Erythropoietin disposition of each of the administered formulations was best described with a two compartment model and linear elimination. Different formulations show different clearance and apparent volume of distribution of the central compartment but share estimates of inter-compartmental clearance and apparent peripheral volume of distribution. A semi-mechanistic model including cell proliferation, maturation, and homeostatic regulation provided a good description of the data regardless the type of erythropoietin formulation administered. The system-, and drug-related parameters showed consistency and differed across formulations, respectively. A single IV administration of PEG-EPO 32 and 40 kDa formulations in New Zealand rabbits achieves a median change of 27% and 22% on RET levels, and of 47% and 63% on RBC and HGB levels, respectively compared to MIRCERA®. The administration of new branched PEG-chains formulations improves PK and PD properties of EPO, in terms of increasing elimination half-lives and pharmacological activity on RET, RBC and HGB compared to commercially available formulations (ior®EPOCIM and MIRCERA®).

Population Pharmacokinetic-Pharmacodynamic Modeling of 5-Fluorouracil for Toxicities in Rats

BACKGROUND AND OBJECTIVES

Myelosuppression is a dose-limiting toxicity of 5-fluorouracil (5-FU). Predicting the inter- and intra-patient variability in pharmacokinetics and toxicities of 5-FU may contribute to the individualized medicine. This study aimed to establish a population pharmacokinetic-pharmacodynamic model that could evaluate the inter- and intra-individual variability in the plasma 5-FU concentration, 5-FU-induced body weight loss and myelosuppression in rats.

METHOD

Plasma 5-FU concentrations, body weight loss, and blood cell counts in rats following the intravenous administration of various doses of 5-FU for 4 days were used to develop the population pharmacokinetic-pharmacodynamic model.

RESULTS

The population pharmacokinetic model consisting of a two-compartment model with Michaelis-Menten elimination kinetics successfully characterized the individual and population predictions of the plasma concentration of 5-FU and provided credible parameter estimates. The estimates of inter-individual variability in maximal rate of saturable metabolism and residual variability were 8.1 and 22.0%, respectively. The population pharmacokinetic-pharmacodynamic model adequately described the individual complete time-course of alterations in body weight loss, erythrocyte, leukocyte, and lymphocyte counts in rats treated with various doses of 5-FU. The inter-individual variability of the drug effects in the pharmacodynamic model for body weight loss was 82.6%, which was relatively high. The results of the present study suggest that not only individual fluctuations in the 5-FU concentration but also the cell sensitivity would affect the onset and degree of 5-FU-induced toxicity.

CONCLUSION

This population pharmacokinetic-pharmacodynamic model could evaluate the inter- and intra-individual variability in drug-induced toxicity and guide the assessments of novel anticancer agents in drug development.

Dynamics of Erythropoietic Biomarkers in Response to Treatment With Erythropoietin in Belgrade Rats

Recombinant human erythropoietin (rHuEPO) is used effectively in the treatment of various anemic disorders. Belgrade rat is a useful animal model of anemia caused by defect in iron utilization. The objective of the present study was to investigate the dynamics of erythropoietic biomarkers in Belgrade rats receiving rHuEPO. Pharmacokinetics of rHuEPO was evaluated in Belgrade rats and normal rats after intravenous administration of single doses of the drug (100 and 1350 IU/kg). Pharmacodynamic biomarkers included levels of red blood cells, hemoglobin, and reticulocytes following administration of a single intravenous dose of rHuEPO (100 IU/kg). Red blood cell survival was assessed after treatment with rHuEPO (450 IU/kg), three times a week for 2 weeks. It was found that rHuEPO exhibited non-linear pharmacokinetics in both Belgrade and control rats. At the low dose, plasma concentrations and AUC (area under the curve) were significantly lower while clearance and volume of distribution were higher in Belgrade rats (p < 0.05). At the higher dose, there was no difference in pharmacokinetics between the two groups. Erythropoietic effect of rHuEPO was negligible in Belgrade rats at the dose of 100 IU/kg whereas all studied erythropoietic biomarkers were increased in normal rats. The levels of red blood cells, hemoglobin were significantly lower whereas the percentage of reticulocytes was higher in Belgrade rats compared to that in normal rats (p < 0.05). RHuEPO increased red blood cell survival in both animal groups. In conclusion, rHuEPO effect on erythropoietic biomarkers was stronger in normal rats than Belgrade rats at the studied doses. The findings from this study may provide further insights into understanding of anemic disorders resulting from mutations in the divalent metal transporter.

A Tutorial on Target-Mediated Drug Disposition (TMDD) Models

Target-mediated drug disposition (TMDD) is the phenomenon in which a drug binds with high affinity to its pharmacological target site (such as a receptor) to such an extent that this affects its pharmacokinetic characteristics.1 The aim of this Tutorial is to provide an introductory guide to the mathematical aspects of TMDD models for pharmaceutical researchers. Examples of Berkeley Madonna2 code for some models discussed in this Tutorial are provided in the Supplementary Materials.

Onco-nephrology: an appraisal of the cancer and chronic kidney disease links

A bidirectional relationship has been observed for kidney disease and cancer. On the one hand, cancer is an important complication noted in kidney disease as well as a major cause of morbidity and mortality in this group. On the other hand, improved cancer treatment has prolonged survival, but also increased the development of acute and chronic kidney disease. The combination of cancer and kidney disease makes it challenging for clinicians to provide comprehensive and safe therapies for this group of patients. As such, clinicians caring for this group must develop expertise and become competent in the practice of a newly evolving subspecialty of nephrology known as 'onco-nephrology'. This brief narrative review will focus on the cancer risk in patients with underlying kidney disease, the therapies such as erythropoiesis-stimulating agents on cancer progression and other outcomes, and the appropriate dosing of anti-cancer agents in patients with underlying kidney disease.

Pharmacokinetic-pharmacodynamic (PK-PD) modeling and simulation of 5-fluorouracil for erythropenia in rats

INTRODUCTION

The aim of the present study was to develop a simple pharmacokinetic-pharmacodynamic (PK-PD) model in rats that could predict the onset and degree of erythropenia, a severely toxic side effect that severely limits the use of the anticancer agent 5-fluorouracil (5-FU).

METHODS

Total erythrocyte counts, hemoglobin (Hb) concentrations, and hematocrit (Hct) levels were measured in rats following the intravenous bolus administration of 5-FU for 4 days in order to obtain data for an analysis of the PK-PD model. Our PK-PD model consisted of a two-compartment PK model, with two compartments for the PD model and nine structural PK-PD model parameters.

RESULTS

After the intravenous bolus administration of 5, 10, or 20 mg/kg of 5-FU to rats, absolute erythrocyte counts, Hb concentrations, and Hct levels transiently decreased, reached minimum levels on Days 7-14, and then returned to baseline levels. The nadir values (Cnadir) for rats treated with 5, 10, or 20 mg/kg of 5-FU were significantly decreased to approximately 79.4, 76.3, or 46.5% of the baseline value (Cbaseline) in erythrocyte counts, 86.3, 83.3, or 45.7% of Cbaseline in Hb concentrations, 88.6, 85.5, or 47.1% of Cbaseline in Hct levels, respectively. The PK-PD model effectively captured the features of erythropenia and Cnadir after 5-FU chemotherapy. This PK-PD model was successfully used to characterize the learner relationship between the area under the plasma 5-FU concentration-time curve (AUC0-∞) following the intravenous bolus administration of 5-FU and the Cnadir in erythrocyte counts, Hb concentrations, and Hct levels after the 5-FU treatment.

DISCUSSION

The results of the present study suggest that the administration of a pharmacokinetically modified dose of 5-FU could minimize the Cnadir in erythrocyte counts, Hb concentrations, and Hct levels following the administration of 5-FU. The PK-PD model and simulation represent valuable approaches for quantifying and predicting erythropenia as well as determining individual doses and the time at which the subsequent course of the treatment should start.

The quantification of reticulocyte maturation and neocytolysis in normal and erythropoietin stimulated rats

A technique has recently been proposed for obtaining the reticulocyte (RET) age distribution from the flow cytometric reticulocyte count. It allows for a quantitative characterization of reticulocyte dynamics. In this work this technique was applied to characterize the blood, bone marrow and spleen reticulocytes in homeostatic and erythropoietically stimulated rats in order to determine the reticulocyte maturation times in the bone marrow and blood; and to confirm the presence of ineffective erythropoiesis (neocytolysis). The latter was done by comparing the reticulocyte removal rate from blood with bilirubin formation after erythropoiesis stimulation. A single subcutaneous dose (4050 IU/kg) of recombinant human erythropoietin (rHuEPO) was administered to rats, then their reticulocytes were stained with thiazole orange and the distribution of the fluorescent signal measured using flow cytometry. The obtained signal distribution of the reticulocytes was transformed to the age distribution and a set of basic parameters reflecting reticulocyte dynamics was determined. Bilirubin concentrations were measured to directly assess the presence of reticulocyte irreversible removal. The bilirubin formation was found to be considerably modulated by rHuEPO and corresponded well to the determined reticulocyte removal rate. The initial increase and subsequent decrease of the reticulocyte maturation time in blood was quantitated and directly linked with RET mobilization from the bone marrow. A substantial number (60%) of reticulocytes is sequestrated during homeostasis in rats. This number increases and then decreases after rHuEPO administration, as also reflected by bilirubin formation. Flow cytometry seems to be an excellent method for studying RET dynamics and the presence of young RBC neocytolysis.

Solution and implementation of distributed lifespan models

We consider a population where every individual has a unique lifespan. After expiring of its lifespan the individual has to leave the population. A realistic approach to describe these lifespans is by a continuous distribution. Such distributed lifespan models (DLSMs) were introduced earlier in the indirect response context and consist of the mathematical convolution operator to describe the rate of change. Therefore, DLSMs could not directly be implemented in standard PKPD software. In this work we present the solution representation of DLSMs with and without a precursor population and an implementation strategy for DLSMs in ADAPT , NONMEM and MATLAB . We fit hemoglobin measurements from literature and investigate computational properties.

A biomathematical model of human erythropoiesis under erythropoietin and chemotherapy administration

Anaemia is a common haematologic side effect of dose-dense multi-cycle cytotoxic polychemotherapy requiring erythrocyte transfusions or erythropoietin (EPO) administration. To simulate the effectiveness of different EPO application schedules, we performed both modelling of erythropoiesis under chemotherapy and pharmacokinetic and dynamic modelling of EPO applications in the framework of a single comprehensive biomathematical model. For this purpose, a cell kinetic model of bone marrow erythropoiesis was developed that is based on a set of differential compartment equations describing proliferation and maturation of erythropoietic cell stages. The system is regulated by several feedback loops comprising those mediated by EPO. We added a model of EPO absorption after injection at different sites and a pharmacokinetic model of EPO derivatives to account for the effects of external EPO applications. Chemotherapy is modelled by a transient depletion of bone marrow cell stages. Unknown model parameters were determined by fitting the predictions of the model to data sets of circulating erythrocytes, haemoglobin, haematocrit, percentage of reticulocytes or EPO serum concentrations derived from the literature or cooperating clinical study groups. Parameter fittings resulted in a good agreement of model and data. Depending on site of injection and derivative (Alfa, Beta, Delta, Darbepoetin), nine groups of EPO applications were distinguished differing in either absorption kinetics or pharmacokinetics. Finally, eight different chemotherapy protocols were modelled. The model was validated on the basis of scenarios not used for parameter fitting. Simulations were performed to analyze the impact of EPO applications on the risk of anaemia during chemotherapy. We conclude that we established a model of erythropoiesis under chemotherapy that explains a large set of time series data under EPO and chemotherapy applications. It allows predictions regarding yet untested EPO schedules. Prospective clinical studies are needed to validate model predictions and to explore the feasibility and effectiveness of the proposed schedules.

Effects of erythropoietin receptors and erythropoiesis-stimulating agents on disease progression in cancer

Erythropoiesis-stimulating agents (ESAs) increase red blood cell (RBC) production in bone marrow by activating the erythropoietin receptor (EpoR) on erythrocytic-progenitor cells. Erythropoiesis-stimulating agents are approved in the United States and Europe for treating anaemia in cancer patients receiving chemotherapy based on randomised, placebo-controlled trials showing that ESAs reduce RBC transfusions. Erythropoiesis-stimulating agent-safety issues include thromboembolic events and concerns regarding whether ESAs increase disease progression and/or mortality in cancer patients. Several trials have reported an association between ESA use and increased disease progression and/or mortality, whereas other trials in the same tumour types have not provided similar findings. This review thoroughly examines available evidence regarding whether ESAs affect disease progression. Both clinical-trial data on ESAs and disease progression, and preclinical data on how ESAs could affect tumour growth are summarised. Preclinical topics include (i) whether tumour cells express EpoR and could be directly stimulated to grow by ESA exposure and (ii) whether endothelial cells express EpoR and could be stimulated by ESA exposure to undergo angiogenesis and indirectly promote tumour growth. Although assessment and definition of disease progression vary across studies, the current clinical data suggest that ESAs may have little effect on disease progression in chemotherapy patients, and preclinical data indicate a direct or indirect effect of ESAs on tumour growth is not strongly supported.

Performance and robustness of the Monte Carlo importance sampling algorithm using parallelized S-ADAPT for basic and complex mechanistic models

The Monte Carlo Parametric Expectation Maximization (MC-PEM) algorithm can approximate the true log-likelihood as precisely as needed and is efficiently parallelizable. Our objectives were to evaluate an importance sampling version of the MC-PEM algorithm for mechanistic models and to qualify the default estimation settings in SADAPT-TRAN. We assessed bias, imprecision and robustness of this algorithm in S-ADAPT for mechanistic models with up to 45 simultaneously estimated structural parameters, 14 differential equations, and 10 dependent variables (one drug concentration and nine pharmacodynamic effects). Simpler models comprising 15 parameters were estimated using three of the ten dependent variables. We set initial estimates to 0.1 or 10 times the true value and evaluated 30 bootstrap replicates with frequent or sparse sampling. Datasets comprised three dose levels with 16 subjects each. For simultaneous estimation of the full model, the ratio of estimated to true values for structural model parameters (median [5-95% percentile] over 45 parameters) was 1.01 [0.94-1.13] for means and 0.99 [0.68-1.39] for between-subject variances for frequent sampling and 1.02 [0.81-1.47] for means and 1.02 [0.47-2.56] for variances for sparse sampling. Imprecision was ≤25% for 43 of 45 means for frequent sampling. Bias and imprecision was well comparable for the full and simpler models. Parallelized estimation was 23-fold (6.9-fold) faster using 48 threads (eight threads) relative to one thread. The MC-PEM algorithm was robust and provided unbiased and adequately precise means and variances during simultaneous estimation of complex, mechanistic models in a 45 dimensional parameter space with rich or sparse data using poor initial estimates.

Development of a new pre- and post-processing tool (SADAPT-TRAN) for nonlinear mixed-effects modeling in S-ADAPT

Mechanistic modeling greatly benefits from automated pre- and post-processing of model code and modeling results. While S-ADAPT provides many state-of-the-art parametric population estimation methods, its pre- and post-processing capabilities are limited. Our objective was to develop a fully automated, open-source pre- and post-processor for nonlinear mixed-effects modeling in S-ADAPT. We developed a new translator tool (SADAPT-TRAN) based on Perl scripts. These scripts (a) automatically translate the core model components into robust Fortran code, (b) perform extensive mutual error checks across all input files and the raw dataset, (c) extend the options of the Monte Carlo Parametric Expectation Maximization (MC-PEM) algorithm, and (d) improve the numerical robustness of the model code. The post-processing scripts automatically summarize the results of one or multiple models as tables and, by generating problem specific R scripts, provide an extended series of standard and covariate-stratified diagnostic plots. The SADAPT-TRAN package substantially improved the efficiency to specify, debug, and evaluate models and enhanced the flexibility of using the MC-PEM algorithm for parallelized estimation in S-ADAPT. The parameter variability model can take any combination of normally, log-normally, or logistically distributed parameters and the SADAPT-TRAN package can automatically generate the Fortran code required to specify between occasion variability. Extended estimation features are available to avoid local minima, estimate means with negligible variances, and estimate variances for fixed means. The SADAPT-TRAN package significantly facilitated model development in S-ADAPT, reduced model specification errors, and provided useful error messages for beginner and advanced users. This benefit was greatest for complex mechanistic models.