An Algorithm for Nonparametric Estimation of a Multivariate Mixing Distribution with Applications to Population Pharmacokinetics

Multiple Model Optimal Sampling Promotes Accurate Vancomycin Area-Under-the-Curve Estimation Using a Single Sample in Critically Ill Children

BACKGROUND

Area-under-the-curve (AUC)-directed vancomycin therapy is recommended; however, AUC estimation in critically ill children is difficult owing to the need for multiple samples and lack of informative models.

METHODS

The authors prospectively enrolled critically ill children receiving intravenous (IV) vancomycin for suspected infection and evaluated the accuracy of Bayesian estimation of AUC from a single, optimally timed sample. During the dosing interval, when clinical therapeutic drug monitoring was performed, an optimally timed sample was collected, which was determined for each subject using an established population pharmacokinetic model and the multiple model optimal function of Pmetrics, a nonparametric population pharmacokinetic modeling software. The model was embedded in InsightRx NOVA (InsightRx, Inc.) for individual Bayesian estimation of AUC using the optimal sample versus all available samples (optimally timed sample + clinical samples).

RESULTS

Eighteen children were included. The optimal sampling time to inform Bayesian estimation of vancomycin AUC was highly variable, with trough samples being optimally informative in 32% of children. Optimal samples were collected by clinical nurses within 15 minutes of the goal time in 14 of 18 participants (78%). Compared with all samples, Bayesian AUC estimation with optimal samples had a mean bias of 0.4% (±5.9%) and mean imprecision of 4.6% (±3.6%). Bias of optimal sampling was <10% for 17 of the 18 participants (94%). When estimating AUC using only a peak sample (≤2 hours after dose) or only a trough (≤30 minutes before next dose), bias was <10% for 78% and 86% of participants, respectively.

CONCLUSIONS

Optimal sampling supports accurate Bayesian estimation of vancomycin AUC from a single plasma sample in critically ill children.

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.

Individual meropenem epithelial lining fluid and plasma PK/PD target attainment

It is unclear whether plasma is a reliable surrogate for target attainment in the epithelial lining fluid (ELF). The objective of this study was to characterize meropenem target attainment in plasma and ELF using prospective samples. The first 24-hour T>MIC was evaluated vs 1xMIC and 4xMIC targets at the patient (i.e., fixed MIC of 2 mg/L) and population [i.e., cumulative fraction of response (CFR) according to EUCAST MIC distributions] levels for both plasma and ELF. Among 65 patients receiving ≥24 hours of treatment, 40% of patients failed to achieve >50% T>4xMIC in plasma and ELF, and 30% of patients who achieved >50% T>4xMIC in plasma had <50% T>4xMIC in ELF. At 1xMIC and 4xMIC targets, 3% and 25% of patients with >95% T>MIC in plasma had <50% T>MIC in ELF, respectively. Those with a CRCL >115 mL/min were less likely to achieve >50%T>4xMIC in ELF (P < 0.025). In the population, CFR for Escherichia coli at 1xMIC and 4xMIC was >97%. For Pseudomonas aeruginosa, CFR was ≥90% in plasma and ranged 80%-85% in ELF at 1xMIC when a loading dose was applied. CFR was reduced in plasma (range: 75%-81%) and ELF (range: 44%-60%) in the absence of a loading dose at 1xMIC. At 4xMIC, CFR for P. aeruginosa was 60%-86% with a loading dose and 18%-62% without a loading dose. We found that plasma overestimated ELF target attainment inup to 30% of meropenem-treated patients, CRCL >115 mL/min decreased target attainment in ELF, and loading doses increased CFR in the population.

Optimizing Vancomycin Therapy in Critically Ill Children: A Population Pharmacokinetics Study to Inform Vancomycin Area under the Curve Estimation Using Novel Biomarkers

Area under the curve (AUC)-directed vancomycin therapy is recommended, but Bayesian AUC estimation in critically ill children is difficult due to inadequate methods for estimating kidney function. We prospectively enrolled 50 critically ill children receiving IV vancomycin for suspected infection and divided them into model training (n = 30) and testing (n = 20) groups. We performed nonparametric population PK modeling in the training group using Pmetrics, evaluating novel urinary and plasma kidney biomarkers as covariates on vancomycin clearance. In this group, a two-compartment model best described the data. During covariate testing, cystatin C-based estimated glomerular filtration rate (eGFR) and urinary neutrophil gelatinase-associated lipocalin (NGAL; full model) improved model likelihood when included as covariates on clearance. We then used multiple-model optimization to define the optimal sampling times to estimate AUC24 for each subject in the model testing group and compared the Bayesian posterior AUC24 to AUC24 calculated using noncompartmental analysis from all measured concentrations for each subject. Our full model provided accurate and precise estimates of vancomycin AUC (bias 2.3%, imprecision 6.2%). However, AUC prediction was similar when using reduced models with only cystatin C-based eGFR (bias 1.8%, imprecision 7.0%) or creatinine-based eGFR (bias -2.4%, imprecision 6.2%) as covariates on clearance. All three model(s) facilitated accurate and precise estimation of vancomycin AUC in critically ill children.

A Method for Evaluating Robustness of Limited Sampling Strategies—Exemplified by Serum Iohexol Clearance for Determination of Measured Glomerular Filtration Rate

In combination with Bayesian estimates based on a population pharmacokinetic model, limited sampling strategies (LSS) may reduce the number of samples required for individual pharmacokinetic parameter estimations. Such strategies reduce the burden when assessing the area under the concentration versus time curves (AUC) in therapeutic drug monitoring. However, it is not uncommon for the actual sample time to deviate from the optimal one. In this work, we evaluate the robustness of parameter estimations to such deviations in an LSS. A previously developed 4-point LSS for estimation of serum iohexol clearance (i.e., dose/AUC) was used to exemplify the effect of sample time deviations. Two parallel strategies were used: (a) shifting the exact sampling time by an empirical amount of time for each of the four individual sample points, and (b) introducing a random error across all sample points. The investigated iohexol LSS appeared robust to deviations from optimal sample times, both across individual and multiple sample points. The proportion of individuals with a relative error greater than 15% (P15) was 5.3% in the reference run with optimally timed sampling, which increased to a maximum of 8.3% following the introduction of random error in sample time across all four time points. We propose to apply the present method for the validation of LSS developed for clinical use.

A proof of concept reinforcement learning based tool for non parametric population pharmacokinetics workflow optimization

The building of population pharmacokinetic models can be described as an iterative process in which given a model and a dataset, the pharmacometrician introduces some changes to the model specification, then perform an evaluation and based on the predictions obtained performs further optimization. This process (perform an action, witness a result, optimize your knowledge) is a perfect scenario for the implementation of Reinforcement Learning algorithms. In this paper we present the conceptual background and a implementation of one of those algorithms aiming to show pharmacometricians how to automate (to a certain point) the iterative model building process.We present the selected discretization for the action and the state space. SARSA (State-Action-Reward-State-Action) was selected as the RL algorithm to use, configured with a window of 1000 episodes with and a limit of 30 actions per episode. SARSA was configured to control an interface to the Non-Parametric Optimal Design algorithm, that was actually performing the parameter optimization.The Reinforcement Learning (RL) based agent managed to obtain the same likelihood and number of support points, with a distribution similar to the reported in the original paper. The total amount of time used by the train the agent was 5.5 h although we think this time can be further improved. It is possible to automatically find the structural model that maximizes the final likelihood for an specific pharmacokinetic dataset by using RL algorithm. The framework provided could allow the integration of even more actions i.e: add/remove covariates, non-linear compartments or the execution of secondary analysis. Many limitations were found while performing this study but we hope to address them all in future studies.

Isavuconazole Pharmacokinetics and Pharmacodynamics in Children

Isavuconazole is a broad-spectrum azole anti-fungal not yet approved in children. We conducted a retrospective, single-center review of isavuconazole use and routine therapeutic drug monitoring in pediatric patients, extracting demographic, dosing, concentration, mortality and hepatoxicity data. We constructed a nonparametric population model using Pmetrics. Of 26 patients, 19 (73%) were male. The mean (SD) age and weight were 12.7 (5.5) years and 50.9 (26.8) kg. Eighty percent received between 9.7 and 10.6 mg/kg per dose. Ten (38%) subjects had proven fungal disease and eight (31%) had probable disease, mostly with Candida and Aspergillus spp. The predicted steady-state isavuconazole concentrations in our patients were similar to previous reports in children and adults, and simulations with the proposed dosing of 10 mg/kg/dose every 8 h for 2 days followed by once daily maintenance matched effective adult exposures. Attributable mortality (5 of 11 deaths) was associated with steady-state daily AUC < 60 mg∗h/L and higher AST/ALT with trough concentrations > 5 mg/L. Neither dose nor trough alone correlated well with AUC, but AUC can be estimated with one sample 10 h after the first maintenance dose or a trough concentration, if combined with a Bayesian approach or a peak and trough without a Bayesian approach.

Individualized Patient Care Through Model-Informed Precision Dosing: Reflections on Training Future Practitioners

Prior to his passing, Dr. Roger Jelliffe, expressed the need for educating future physicians and clinical pharmacists on the availability of computer-based tools to support dose optimization in patients in stable or unstable physiological states. His perspectives were to be captured in a commentary for the AAPS J with a focus on incorporating population pharmacokinetic (PK)/pharmacodynamic (PD) models that are designed to hit the therapeutic target with maximal precision. Unfortunately, knowing that he would be unable to complete this project, Dr. Jelliffe requested that a manuscript conveying his concerns be completed upon his passing. With this in mind, this final installment of the AAPS J theme issue titled "Alternative Perspectives for Evaluating Drug Exposure Characteristics in a Population - Avoiding Analysis Pitfalls and Pigeonholes" is an effort to honor Dr. Jelliffe's request, conveying his concerns and the need to incorporate modeling and simulation into the training of physicians and clinical pharmacists. Accordingly, Dr. Jelliffe's perspectives have been integrated with those of the other three co-authors on the following topics: the clinical utility of population PK models; the role of multiple model (MM) dosage regimens to identify an optimal dose for an individual; tools for determining dosing regimens in renal dialysis patients (or undergoing other therapies that modulate renal clearance); methods to analyze and track drug PK in acutely ill patients presenting with high inter-occasion variability; implementation of a 2-cycle approach to minimize the duration between blood samples taken to estimate the changing PK in an acutely ill patient and for the generation of therapeutic decisions in advance for each dosing cycle based on an analysis of the previous cycle; and the importance of expressing therapeutic drug monitoring results as 1/variance rather than as the coefficient of variation. Examples showcase why, irrespective of the overall approach, the combination of therapeutic drug monitoring and computer-informed precision dosing is indispensable for maximizing the likelihood of achieving the target drug concentrations in the individual patient.

Combination Therapy to Kill Mycobacterium tuberculosis in Its Nonreplicating Persister Phenotype

Mycobacterium tuberculosis (Mtb) exists in various metabolic states, including a nonreplicating persister (NRP) phenotype which may affect response to therapy. We have adopted a model-informed strategy to accelerate discovery of effective Mtb treatment regimens and previously found pretomanid (PMD), moxifloxacin (MXF), and bedaquiline (BDQ) to readily kill logarithmic- and acid-phase Mtb. Here, we studied multiple concentrations of each drug in flask-based, time-kill studies against NRP Mtb in single-, two- and three-drug combinations, including the active M2 metabolite of BDQ. We used nonparametric population algorithms in the Pmetrics package for R to model the data and to simulate the 95% confidence interval of bacterial population decline due to the two-drug combination regimen of PMD + MXF and compared this to observed declines with three-drug regimens. PMD + MXF at concentrations equivalent to average or peak human concentrations effectively eradicated Mtb. Unlike other states for Mtb, we observed no sustained emergence of less susceptible isolates for any regimen. The addition of BDQ as a third drug significantly (P < 0.05) shortened time to total bacterial suppression by 3 days compared to the two-drug regimen, similar to our findings for Mtb in logarithmic or acid growth phases.

Population PBPK modeling using parametric and nonparametric methods of the Simcyp Simulator, and Bayesian samplers

Physiologically‐based pharmacokinetic (PBPK) models usually include a large number of parameters whose values are obtained using in vitro to in vivo extrapolation. However, such extrapolations can be uncertain and may benefit from inclusion of evidence from clinical observations via parametric inference. When clinical interindividual variability is high, or the data sparse, it is essential to use a population pharmacokinetics inferential framework to estimate unknown or uncertain parameters. Several approaches are available for that purpose, but their relative advantages for PBPK modeling are unclear. We compare the results obtained using a minimal PBPK model of a canonical theophylline dataset with quasi‐random parametric expectation maximization (QRPEM), nonparametric adaptive grid estimation (NPAG), Bayesian Metropolis‐Hastings (MH), and Hamiltonian Markov Chain Monte Carlo sampling. QRPEM and NPAG gave consistent population and individual parameter estimates, mostly agreeing with Bayesian estimates. MH simulations ran faster than the others methods, which together had similar performance.

Parametric and Nonparametric Methods in Population Pharmacokinetics: Experts' Discussion on Use, Strengths, and Limitations

Population pharmacokinetics consists of analyzing pharmacokinetic (PK) data collected in groups of individuals. Population PK is widely used to guide drug development and to inform dose adjustment via therapeutic drug monitoring and model-informed precision dosing. There are 2 main types of population PK methods: parametric (P) and nonparametric (NP). The characteristics of P and NP population methods have been previously reviewed. The aim of this article is to answer some frequently asked questions that are often raised by scholars, clinicians, and researchers about P and NP population PK methods. The strengths and limitations of both approaches are explained, and the characteristics of the main software programs are presented. We also review the results of studies that compared the results of both approaches in the analysis of real data. This opinion article may be informative for potential users of population methods in PK and guide them in the selection and use of those tools. It also provides insights on future research in this area.

A pharmacokinetics-based approach to the monitoring of patient adherence to atorvastatin therapy

The inadequate adherence of patients whose hyperlipidemia is treated with atorvastatin (ATR) to medical instructions presents a serious health risk. Our aim was to develop a flexible approach based on therapeutic drug monitoring (TDM), nonparametric population pharmacokinetic modeling, and Monte Carlo simulation to differentiate adherent patients from partially and nonadherent individuals in a nonrandomized, unicentric, observational study. Sixty-five subjects were enrolled. Nonparametric, mixed-effect population pharmacokinetic models of the sums of atorvastatin and atorvastatin lactone concentrations (ATR+ATRL) and of the concentrations of the acid and lactone forms of ATR and its 2- and 4-hydroxylated pharmacologically active metabolites (ATR+MET) were elaborated by including the TDM results obtained in 128 samples collected from thirty-nine subjects. Monte Carlo simulation was performed based on the elaborated models to establish the probabilities of attaining a specific ATR+ATRL or ATR+MET concentration in the range of 0.002-10 nmol (mg dose)-1 L-1 at 1-24 h postdose by adherent, partially adherent, and nonadherent patients. The results of the simulations were processed to allow the estimation of the adherence of further 26 subjects who were phlebotomized at sampling times of 2-20 h postdose by calculating the probabilities of attaining the ATR+ATRL and ATR+MET concentrations measured in these subjects in adherent, partially adherent, and nonadherent individuals. The best predictive values of the estimates of adherence could be obtained with sampling at early sampling times. 61.54% and 38.46% of subjects in the adherence testing set were estimated to be fully and partially adherent, respectively, while in all cases the probability of nonadherence was extremely low. The evaluation of patient adherence to ATR therapy based on pharmacokinetic modeling and Monte Carlo simulation has important advantages over the collection of trough samples and the use of therapeutic ranges.

Building optimal 3-drug combination chemotherapy regimens to eradicate Mycobacterium tuberculosis in its slow growth acid phase

Mycobacterium tuberculosis (Mtb) metabolic state affects the response to therapy. Quantifying the effect of antimicrobials in the acid- and nonreplicating-metabolic phases of Mtb growth will help to optimize therapy for tuberculosis. As a brute-force approach to all possible drug combinations against Mtb in all different metabolic states is impossible, we have adopted a model-informed strategy to accelerate the discovery. Using multiple concentrations of each drug in time kill studies, we examined single-, two- and three-drug combinations of pretomanid, moxifloxacin, and bedaquiline plus its active metabolite against Mtb in its acid-phase metabolic state. We used a nonparametric modeling approach to generate full distributions of interaction terms between pretomanid and moxifloxacin for susceptible and less-susceptible populations. From the model, we could predict the 95% confidence interval of the simulated total bacterial population decline due to the 2-drug combination regimen of pretomanid and moxifloxacin and compare this to observed declines with 3 drug regimens. We found that the combination of pretomanid and moxifloxacin at concentrations equivalent to average or peak human concentrations effectively eradicated Mtb in its acid growth phase and prevented emergence of less susceptible isolates. The addition of bedaquiline as a third drug shortened time to total and less susceptible bacterial suppression by 8 days compared to the 2-drug regimen, which was significantly faster than the 2-drug kill.