Experiment design for nonparametric models based on minimizing Bayes Risk: application to voriconazole¹

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.

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

Population pharmacokinetic (PK) modeling has become a cornerstone of drug development and optimal patient dosing. This approach offers great benefits for datasets with sparse sampling, such as in pediatric patients, and can describe between-patient variability. While most current algorithms assume normal or log-normal distributions for PK parameters, we present a mathematically consistent nonparametric maximum likelihood (NPML) method for estimating multivariate mixing distributions without any assumption about the shape of the distribution. This approach can handle distributions with any shape for all PK parameters. It is shown in convexity theory that the NPML estimator is discrete, meaning that it has finite number of points with nonzero probability. In fact, there are at most N points where N is the number of observed subjects. The original infinite NPML problem then becomes the finite dimensional problem of finding the location and probability of the support points. In the simplest case, each point essentially represents the set of PK parameters for one patient. The probability of the points is found by a primal-dual interior-point method; the location of the support points is found by an adaptive grid method. Our method is able to handle high-dimensional and complex multivariate mixture models. An important application is discussed for the problem of population pharmacokinetics and a nontrivial example is treated. Our algorithm has been successfully applied in hundreds of published pharmacometric studies. In addition to population pharmacokinetics, this research also applies to empirical Bayes estimation and many other areas of applied mathematics. Thereby, this approach presents an important addition to the pharmacometric toolbox for drug development and optimal patient dosing.

Fasting Status and Circadian Variation Must be Considered When Performing AUC-based Therapeutic Drug Monitoring of Tacrolimus in Renal Transplant Recipients

Therapeutic drug monitoring (TDM) is mandatory for the immunosuppressive drug tacrolimus (Tac). For clinical applicability, TDM is performed using morning trough concentrations. With recent developments making tacrolimus concentration determination possible in capillary microsamples and Bayesian estimator predicted area under the concentration curve (AUC), AUC‐guided TDM may now be clinically applicable. Tac circadian variation has, however, been reported, with lower systemic exposure following the evening dose. The aim of the present study was to investigate tacrolimus pharmacokinetic (PK) after morning and evening administrations of twice‐daily tacrolimus in a real‐life setting without restrictions regarding food and concomitant drug timing. Two 12 hour tacrolimus investigations were performed; after the morning dose and the following evening dose, respectively, in 31 renal transplant recipients early after transplantation both in a fasting‐state and under real‐life nonfasting conditions (14 patients repeated the investigation). We observed circadian variation under fasting‐conditions: 45% higher peak‐concentration and 20% higher AUC following the morning dose. In the real‐life nonfasting setting, the PK‐profiles were flat but comparable after the morning and evening doses, showing slower absorption rate and lower AUC compared with the fasting‐state. Limited sampling strategies using concentrations at 0, 1, and 3 hours predicted AUC after fasting morning administration, and samples obtained at 1, 3, and 6 hours predicted AUC for the other conditions (evening and real‐life nonfasting). In conclusion, circadian variation of tacrolimus is present when performed in patients who are in the fasting‐state, whereas flatter PK‐profiles and no circadian variation was present in a real‐life, nonfasting setting.

Population pharmacokinetics and Bayesian estimators for intravenous mycophenolate mofetil in haematopoietic stem cell transplant patients

AIMS

Intravenous mycophenolate mofetil (IV MMF), a prodrug of mycophenolic acid (MPA), is used during nonmyeloablative and reduced-intensity conditioning haematopoetic stem cell transplantation (HCT) to improve engraftment and reduce graft-versus-host disease. The aims of this study were to develop population pharmacokinetic models and Bayesian estimators based on limited sampling strategies to allow for individual dose adjustment of intravenous mycophenolate mofetil administered by infusion in haematopoietic stem cell transplant patients.

METHODS

Sixty-three MPA concentration-time profiles (median [min-max] = 6 [4-7] samples) were collected from 34 HCT recipients transplanted for 14 (1-45) days and administered IV MMF every 8 hours, concomitantly with cyclosporine. The database was split into development (75%) and validation (25%) datasets. Pharmacokinetic models characterized by a single compartment with first-order elimination, combined with two gamma distributions to describe the transformation of MMF into mycophenolic acid, were developed using in parallel nonparametric (Pmetrics) and parametric (ITSIM) approaches. The performances of the models and the derived Bayesian estimators were evaluated in the validation set.

RESULTS

The best limited sampling strategy led to a bias (min, max), root mean square error between observed and modeled interdose areas under the curve in the validation dataset of -11.72% (-31.08%, 5.00%), 14.9% for ITSIM and -2.21% (-23.40%, 30.01%), 12.4% for Pmetrics with three samples collected at 0.33, 2 and 3 hours post dosing.

CONCLUSION

Population pharmacokinetic models and Bayesian estimators for IV MMF in HCT have been developed and are now available online (https://pharmaco.chu-limoges.fr) for individual dose adjustment based on the interdose area under the curve.

A Quantitative Comparison Approach for Methylphenidate Drug Regimens in Attention-Deficit/Hyperactivity Disorder Treatment

OBJECTIVE

Different methylphenidate (MPH) formulations, immediate release (IR) or extended release (ER), have been developed to treat Attention-Deficit/Hyperactivity Disorder (ADHD). A better use of these formulations, with a proper choice of their timing, dosage, and combination, can help to attain optimal therapeutic effect while maintaining a good quality of life. In this study, we aim at presenting a quantitative comparison approach to help identify drug regimens that provide best therapeutic performances and respect patients' specific needs.

METHODS

Using pharmacokinetic (PK) models of various MPH formulations constructed with data in hand and a formerly developed performance metric for MPH regimens, we proposed a statistical integral strategy for regimen comparison, which comprises a sequential, a relative, and a probability-over-threshold method. The first is hierarchical in nature and sequentially compares the regimen performance, the total daily dose, and the administration frequency. The second compares two regimens by quantifying their similarity. The third computes the probability of an incremental regimen performance over a specified threshold. The first two comparison approaches are used for naive patients, whereas the third one is for patients under treatment.

RESULTS

PK models of one compartment effectively describe both the IR and ER data. Applied to three frequent MPH clinical situations, the three-methods strategy is able to distinguish the regimens proposed for each. A combined regimen of IR and ER taken at the same time performs better than a single ER dose.

CONCLUSION

The proposed statistical strategy is able to differentiate ADHD regimens in various clinically relevant situations, and adapt the use of MPH drugs to a patient's daily routine. Since it does not compare fixed doses and formulations but rather any MPH regimen, our approach generalizes the current context of bioequivalence study and provides an accessible computational tool for objectively selecting MPH regimens.

Prospective Trial on the Use of Trough Concentration versus Area under the Curve To Determine Therapeutic Vancomycin Dosing

We hypothesized that dosing vancomycin to achieve trough concentrations of >15 mg/liter overdoses many adults compared to area under the concentration-time curve (AUC)-guided dosing. We conducted a 3-year, prospective study of vancomycin dosing, plasma concentrations, and outcomes. In year 1, nonstudy clinicians targeted trough concentrations of 10 to 20 mg/liter (infection dependent) and controlled dosing. In years 2 and 3, the study team controlled vancomycin dosing with BestDose Bayesian software to achieve a daily, steady-state AUC/MIC ratio of ≥400, with a maximum AUC value of 800 mg · h/liter, regardless of trough concentration. For Bayesian estimation of AUCs, we used trough samples in years 1 and 2 and optimally timed samples in year 3. We enrolled 252 adults who were ≥18 years old with ≥1 available vancomycin concentration. Only 19% of all trough concentrations were therapeutic versus 70% of AUCs (P < 0.0001). After enrollment, median trough concentrations by year were 14.4, 9.7, and 10.9 mg/liter (P = 0.005), with 36%, 7%, and 6% over 15 mg/liter (P < 0.0001). Bayesian AUC-guided dosing in years 2 and 3 was associated with fewer additional blood samples per subject (3.6, 2.0, and 2.4; P = 0.003), shorter therapy durations (8.2, 5.4, and 4.7 days; P = 0.03), and reduced nephrotoxicity (8%, 0%, and 2%; P = 0.01). The median inpatient stay was 20 days among nephrotoxic patients versus 6 days (P = 0.002). There was no difference in efficacy by year, with 42% of patients having microbiologically proven infections. Compared to trough concentration targets, AUC-guided, Bayesian estimation-assisted vancomycin dosing was associated with decreased nephrotoxicity, reduced per-patient blood sampling, and shorter length of therapy, without compromising efficacy. These benefits have the potential for substantial cost savings. (This study has been registered at ClinicalTrials.gov under registration no. NCT01932034.).