Monte Carlo Parametric Expectation Maximization Research Articles

RPEM: Randomized Monte Carlo parametric expectation maximization algorithm.

Inspired from quantum Monte Carlo, by sampling discrete and continuous variables at the same time using the Metropolis-Hastings algorithm, we present a novel, fast, and accurate high performance Monte Carlo Parametric Expectation Maximization (MCPEM) algorithm. We named it Randomized Parametric Expectation Maximization (RPEM). We compared RPEM with NONMEM's Importance Sampling Method (IMP), Monolix's Stochastic Approximation Expectation Maximization (SAEM), and Certara's Quasi-Random Parametric Expectation Maximization (QRPEM) for a realistic two-compartment voriconazole model with ordinary differential equations using simulated data. We show that RPEM is as fast and as accurate as the algorithms IMP, QRPEM, and SAEM for the voriconazole model in reconstructing the population parameters, for the normal and log-normal cases.

Using medical claims database to develop a population disease progression model for leuprorelin-treated subjects with hormone-sensitive prostate cancer.

Androgen deprivation therapy (ADT) is a widely used treatment for patients with hormone-sensitive prostate cancer (PCa). However, duration of treatment response varies, and most patients eventually experience disease progression despite treatment. Leuprorelin is a luteinizing hormone-releasing hormone (LHRH) agonist, a commonly used form of ADT. Prostate-specific antigen (PSA) is a biomarker for monitoring disease progression and predicting treatment response and survival in PCa. However, time-dependent profile of tumor regression and growth in patients with hormone-sensitive PCa on ADT has never been fully characterized. In this analysis, nationwide medical claims database provided by Humana from 2007 to 2011 was used to construct a population-based disease progression model for patients with hormone-sensitive PCa on leuprorelin. Data were analyzed by nonlinear mixed effects modeling utilizing Monte Carlo Parametric Expectation Maximization (MCPEM) method in NONMEM. Covariate selection was performed using a modified Wald's approximation method with backward elimination (WAM-BE) proposed by our group. 1113 PSA observations from 264 subjects with malignant PCa were used for model development. PSA kinetics were well described by the final covariate model. Model parameters were well estimated, but large between-patient variability was observed. Hemoglobin significantly affected proportion of drug-resistant cells in the original tumor, while baseline PSA and antiandrogen use significantly affected treatment effect on drug-sensitive PCa cells (Ds). Population estimate of Ds was 3.78 x 10-2 day-1. Population estimates of growth rates for drug-sensitive (Gs) and drug-resistant PCa cells (GR) were 1.96 x 10-3 and 6.54 x 10-4 day-1, corresponding to a PSA doubling time of 354 and 1060 days, respectively. Proportion of the original PCa cells inherently resistant to treatment was estimated to be 1.94%. Application of population-based disease progression model to clinical data allowed characterization of tumor resistant patterns and growth/regression rates that enhances our understanding of how PCa responds to ADT.

Novel Hybrid GPU–CPU Implementation of Parallelized Monte Carlo Parametric Expectation Maximization Estimation Method for Population Pharmacokinetic Data Analysis

The development of a population PK/PD model, an essential component for model-based drug development, is both time- and labor-intensive. A graphical-processing unit (GPU) computing technology has been proposed and used to accelerate many scientific computations. The objective of this study was to develop a hybrid GPU-CPU implementation of parallelized Monte Carlo parametric expectation maximization (MCPEM) estimation algorithm for population PK data analysis. A hybrid GPU-CPU implementation of the MCPEM algorithm (MCPEMGPU) and identical algorithm that is designed for the single CPU (MCPEMCPU) were developed using MATLAB in a single computer equipped with dual Xeon 6-Core E5690 CPU and a NVIDIA Tesla C2070 GPU parallel computing card that contained 448 stream processors. Two different PK models with rich/sparse sampling design schemes were used to simulate population data in assessing the performance of MCPEMCPU and MCPEMGPU. Results were analyzed by comparing the parameter estimation and model computation times. Speedup factor was used to assess the relative benefit of parallelized MCPEMGPU over MCPEMCPU in shortening model computation time. The MCPEMGPU consistently achieved shorter computation time than the MCPEMCPU and can offer more than 48-fold speedup using a single GPU card. The novel hybrid GPU-CPU implementation of parallelized MCPEM algorithm developed in this study holds a great promise in serving as the core for the next-generation of modeling software for population PK/PD analysis.

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.

Pharmacodynamic Modeling of Anti-Cancer Activity of Tetraiodothyroacetic Acid in a Perfused Cell Culture System

Unmodified or as a poly[lactide-co-glycolide] nanoparticle, tetraiodothyroacetic acid (tetrac) acts at the integrin αvβ3 receptor on human cancer cells to inhibit tumor cell proliferation and xenograft growth. To study in vitro the pharmacodynamics of tetrac formulations in the absence of and in conjunction with other chemotherapeutic agents, we developed a perfusion bellows cell culture system. Cells were grown on polymer flakes and exposed to various concentrations of tetrac, nano-tetrac, resveratrol, cetuximab, or a combination for up to 18 days. Cells were harvested and counted every one or two days. Both NONMEM VI and the exact Monte Carlo parametric expectation maximization algorithm in S-ADAPT were utilized for mathematical modeling. Unmodified tetrac inhibited the proliferation of cancer cells and did so with differing potency in different cell lines. The developed mechanism-based model included two effects of tetrac on different parts of the cell cycle which could be distinguished. For human breast cancer cells, modeling suggested a higher sensitivity (lower IC50) to the effect on success rate of replication than the effect on rate of growth, whereas the capacity (Imax) was larger for the effect on growth rate. Nanoparticulate tetrac (nano-tetrac), which does not enter into cells, had a higher potency and a larger anti-proliferative effect than unmodified tetrac. Fluorescence-activated cell sorting analysis of harvested cells revealed tetrac and nano-tetrac induced concentration-dependent apoptosis that was correlated with expression of pro-apoptotic proteins, such as p53, p21, PIG3 and BAD for nano-tetrac, while unmodified tetrac showed a different profile. Approximately additive anti-proliferative effects were found for the combinations of tetrac and resveratrol, tetrac and cetuximab (Erbitux), and nano-tetrac and cetuximab. Our in vitro perfusion cancer cell system together with mathematical modeling successfully described the anti-proliferative effects over time of tetrac and nano-tetrac and may be useful for dose-finding and studying the pharmacodynamics of other chemotherapeutic agents or their combinations.

Use of pharmacodynamic endpoints for the evaluation of levofloxacin for the treatment of acute maxillary sinusitis

Sinusitis remains 1 of the most common reasons for antimicrobial prescriptions in the United States, with health care costs approaching $4 billion annually. We utilized the serial sinus aspirate sampling (SSAS) technique to obtain daily specimens to evaluate the time course of drug effect in patients with acute maxillary sinusitis. Eighteen patients with a radiologically confirmed acute maxillary sinusitis were enrolled into a study evaluating the relationship between levofloxacin exposure and the time course of antimicrobial effect using SSAS. SSAS was performed daily during therapy for bacteriologic evaluation. Six steady-state levofloxacin concentrations were obtained. Levofloxacin plasma and sinus aspirate concentrations were modeled using Monte Carlo Parametric Expectation Maximization algorithm implemented in S-ADAPT 1.53. Endpoints evaluated included time to resolution of signs and symptoms and time to sinus sterilization. Among the 18 enrolled patients, 15 were clinically evaluable. From these, 1 Streptococcus pneumoniae, 3 Haemophilus influenzae, 1 Moraxella catarrhalis, 1 Corynebacterium spp., and 1 coagulase-negative Staphylococcus organisms were isolated, with the latter 2 organisms being likely contaminants. For the pathogens, levofloxacin MIC values ranged from 0.03 to 2 mg/L. All pathogens were eradicated by the 4th day of therapy. The median and mean time to sinus sterilization (pathogens only) was 1 and 1.4 days, respectively. The median time to resolution of each sign and symptom ranged from 1.5 to 12–19 days, with the 83% of total signs and symptoms resolved by the end of therapy (day 5). The mean plasma area under the concentration-time curve (AUC) (mg ∙ h/L) was 100.1 ( n = 14, %CV = 27). Plasma AUC/MIC ratios ranged from 33.9 to 1696 for isolated pathogens. In this pilot SSAS study, levofloxacin rapidly eradicated isolated pathogens from the maxillary sinus.

Semi-physiological pharmacokinetic-pharmacodynamic (PK/PD) models for troxacitabine-induced neutropenia and thrombocytopenia

13002 Background: Neutropenia and thrombocytopenia are the dose-limiting toxicities of troxacitabine in Phase 1 studies. The present study’s aim was to develop a novel semi-physiological PK/PD model that can simultaneously describe the time course of the absolute neutrophil and platelet count changes in cancer patients receiving troxacitabine. Methods: The mixed-effect modeling was performed using the Monte-Carlo Parametric Expectation Maximization algorithm implemented in SADAPT program. The analysis was based on PK/PD data from 31 subjects who received troxacitabine/cisplatin combination every 28 days at five different dose levels (4.8/50, 4.8/75, 6.4/50, 6.4/75, 8.0/75 mg/m2). The PD model consisted of 1) a troxicatabine-sensitive uncommitted progenitor cell compartment, which differentiates into committed neutrophil and platelet progenitor cells that are also sensitive to the troxacitabine, and 2) transit compartments for neutrophils and platelets that represent maturation stages in bone marrow. To capture the rebound phenomena and maintain the hemostasis, the model included a feedback mechanism for both neutrophils and platelets. The troxacitabine concentrationtion-time profiles affected the proliferation of sensitive progenitor cells through an inhibitory sigmoidal Emax model. A three-compartment linear pharmacokinetic model was developed to describe the troxaicibatine concentration-time profile. Results: The PD model described the time-course of troxacitabine- induced neutrophil and platelet cytopenias and accounted for the large observed inter-patient variability. The model predicted that neutrophil progenitor cells were more sensitive to troxacitabine therapy compared to platelet progenitor cells. Furthermore, the model suggested that the troxacitabine-induced neutropenia and thrombocytopenia are reversible and non-cumulative events. Conclusions: This novel model can describe both the intensity and duration of troxacitabine-induced thrombocytopenia and neutropenia rather than simply considering the nadir values. It may be valuable for selecting treatment regimens that minimize troxacitabine’s dose-limiting hematological toxicities. No significant financial relationships to disclose.

Population pharmacokinetic/pharmacodynamic modeling of systemic corticosteroid inhibition of whole blood lymphocytes: modeling interoccasion pharmacodynamic variability.

To develop a population pharmacokinetic/pharmacodynamic (PK/PD) model that characterizes the effects of major systemic corticosteroids on lymphocyte trafficking and responsiveness. Single, presumably equivalent, doses of intravenous hydrocortisone (HC), dexamethasone (DEX), methylprednisolone (MPL), and oral prednisolone (PNL) were administered to five healthy male subjects in a five--way crossover, placebo--controlled study. Measurements included plasma drug and cortisol concentrations, total lymphocyte counts, and whole blood lymphocyte proliferation (WBLP). Population data analysis was performed using a Monte Carlo-Parametric Expectation Maximization algorithm. The final indirect, multi-component, mechanism-based model well captured the circadian rhythm exhibited in cortisol production and suppression, lymphocyte trafficking, and WBLP temporal profiles. In contrast to PK parameters, variability of drug concentrations producing 50% maximal immunosuppression (IC(50)) were larger between subjects (73-118%). The individual log-transformed reciprocal posterior Bayesian estimates of IC(50) for ex vivo WBLP were highly correlated with those determined in vitro for the four drugs (r ( 2 ) = 0.928). The immunosuppressive dynamics of the four corticosteroids was well described by the population PK/PD model with the incorporation of inter-occasion variability for several model components. This study provides improvements in modeling systemic corticosteroid effects and demonstrates greater variability of system and dynamic parameters compared to pharmacokinetics.

Pharmacokinetic–Pharmacodynamic–Efficacy Analysis of Efalizumab in Patients with Moderate to Severe Psoriasis

Efalizumab is a humanized anti-CD11a monoclonal antibody that demonstrated efficacy in the treatment of patients with psoriasis. The objective of this study was to perform a pharmacokinetic (PK)-pharmacodynamic (PD)-efficacy (E) modeling analysis with intersubject variability assessment to increase our understanding of the interaction of efalizumab with CD11a on T cells and consequent reduction in severity of disease in psoriasis patients. A total of 6,329 samples from 240 patients in five Phase I and II clinical studies were used in the analysis. For the analysis, plasma efalizumab concentration was used as the PK measurement, the percent of predose CD11a was used as the PD measurement, and the psoriasis area and severity index was used as the measure of efficacy. A receptor-mediated PK/PD model was developed that describes the dynamic interaction of efalizumab binding with CD11a. In the efficacy model, the rate of psoriasis skin production is directly proportional to the amount of free surface CD11a on T cells, which is offset by the rate of skin healing. An additional CD11a-independent component to psoriasis skin production accounted for incomplete response to efalizumab therapy. A Monte Carlo parametric expectation maximization method implemented in the ADAPT II program was used to obtain the estimate of population parameters and inter- and intrasubject variability. The final model described the PK/PD/E data in psoriasis patients reasonably well. In addition, simulations using the final model suggested that efalizumab administered less frequently could possibly be more convenient with similar efficacy.