dOFV distributions: a new diagnostic for the adequacy of parameter uncertainty in nonlinear mixed-effects models applied to the bootstrap

Bayesian estimation in NONMEM

Bayesian estimation is a powerful but underutilized tool for answering drug development questions. In this tutorial, the principles of Bayesian model development, assessment, and prior selection will be outlined. An example pharmacokinetic (PK) model will be used to demonstrate the implementation of Bayesian modeling using the nonlinear mixed-effects modeling software NONMEM.

A quantitative approach to the choice of number of samples for percentile estimation in bootstrap and visual predictive check analyses

Understanding the uncertainty in parameter estimates or in derived secondary variables is important in all data analysis activities. In pharmacometrics, this is often done based on the standard errors from the variance–covariance matrix of the estimates. Confidence intervals derived in this way are by definition symmetrical, which may lead to implausible outcomes, and will require translation to generate uncertainties in derived variables. An often‐used alternative is numerical percentile estimation by, for example, nonparametric bootstraps to circumvent these issues. Visual predictive checks (VPCs), which is a commonly used model diagnostic tool in pharmacometric analyses, also rely on the estimation of percentiles through numerical approaches. Given the cost in terms of run times and processing times for these methods, it is important to consider the trade‐off between the number of bootstrap samples or simulated data sets in the VPCs, to the increase in precision related to a large number of bootstrap samples or simulated data sets. The objective with this tutorial is to provide a quantitative framework for assessing the precision in estimated percentile limits in bootstrap and visual predictive checks analyses to facilitate an informed choice of confidence interval width, number of bootstrap samples/simulated data sets, and required level of precision.

Conditional Non-parametric Bootstrap for Non-linear Mixed Effect Models

PURPOSE

Non-linear mixed effect models are widely used and increasingly integrated into decision-making processes. Propagating uncertainty is an important element of this process, and while standard errors (SE) on pa- rameters are most often computed using asymptotic approaches, alternative methods such as the bootstrap are also available. In this article, we propose a modified residual parametric bootstrap taking into account the different levels of variability involved in these models.

METHODS

The proposed approach uses samples from the individual conditional distribution, and was implemented in R using the saemix algorithm. We performed a simulation study to assess its performance in different scenarios, comparing it to the asymptotic approximation and to standard bootstraps in terms of coverage, also looking at bias in the parameters and their SE.

RESULTS

Simulations with an Emax model with different designs and sigmoidicity factors showed a similar coverage rate to the parametric bootstrap, while requiring less hypotheses. Bootstrap improved coverage in several scenarios compared to the asymptotic method especially for the variance param-eters. However, all bootstraps were sensitive to estimation bias in the original datasets.

CONCLUSIONS

The conditional bootstrap provided better coverage rate than the traditional residual bootstrap, while preserving the structure of the data generating process.

Assessing parameter uncertainty in small-n pharmacometric analyses: value of the log-likelihood profiling-based sampling importance resampling (LLP-SIR) technique

Assessing parameter uncertainty is a crucial step in pharmacometric workflows. Small datasets with ten or fewer subjects appear regularly in drug development and therapeutic use, but it is unclear which method to assess parameter uncertainty is preferable in such situations. The aim of this study was to (i) systematically evaluate the performance of standard error (SE), bootstrap (BS), log-likelihood profiling (LLP), Bayesian approaches (BAY) and sampling importance resampling (SIR) to assess parameter uncertainty in small datasets and (ii) to evaluate methods to provide proposal distributions for the SIR. A simulation study was conducted and the 0-95% confidence interval (CI) and coverage for each parameter was evaluated and compared to reference CIs derived by stochastic simulation and estimation (SSE). A newly proposed LLP-SIR, combining the proposal distribution provided by LLP with SIR, was included in addition to conventional SE-SIR and BS-SIR. Additionally, the methods were applied to a clinical dataset. The determined CIs differed substantially across the methods. The CIs of SE, BS, LLP and BAY were not in line with the reference in datasets with ≤ 10 subjects. The best alignment was found for the LLP-SIR, which also provided the best coverage results among the SIR methods. The best overall results regarding the coverage were provided by LLP and BAY across all parameters and dataset sizes. To conclude, the popular SE and BS methods are not suitable to derive parameter uncertainty in small datasets containing ≤ 10 subjects, while best performances were observed with LLP, BAY and LLP-SIR.

Differences in the Pharmacokinetics of Gentamicin between Oncology and Nononcology Pediatric Patients

Dosing gentamicin in pediatric patients can be difficult due to its narrow therapeutic index. A significantly higher percentage of fat mass has been observed in children receiving oncology treatment than in those who are not. Differences in the pharmacokinetics of gentamicin between oncology and nononcology pediatric patients and individual dosage requirements were evaluated in this study, using normal fat mass (NFM) as a body size descriptor. Data from 423 oncology and 115 nononcology patients were analyzed. Differences in drug disposition were observed between the oncology and nononcology patients, with oncology patients having a 15% lower central volume of distribution and 32% lower intercompartmental clearance. Simulations based on the population pharmacokinetic model demonstrated low exposure target attainment in all individuals at the current clinical recommended starting dose of 7.5 mg/kg of body weight once daily, with 57.4% of oncology and 35.7% of nononcology subjects achieving a peak concentration (C _max) of ≥25 mg/liter and 64.3% of oncology and 65.6% of nononcology subjects achieving an area under the concentration-time curve at 24 h postdose (AUC₂₄) of ≥70 mg · h/liter after the first dose. Based on simulations, the extent of the impact of differences in drug disposition between the two cohorts appeared to be dependent on the exposure target under examination. Greater differences in achieving a C _max target of >25 mg/liter than an AUC₂₄ target of ≥70 mg · h/liter between the cohorts was observed. Further investigation into whether differences in the pharmacokinetics of gentamicin between oncology and nononcology patients are a consequence of changes in body composition is required.

Population pharmacokinetic modeling of sustained release lithium in the serum, erythrocytes and urine of patients with bipolar disorder

PURPOSE

Lithium (Li), the first-line treatment of bipolar disorder, was first developed as an immediate-release form with a routine therapeutic drug monitoring 12 h after the last dose. In Europe, the most commonly prescribed form is a sustained release (srLi). Yet no pharmacokinetics (PK) study has been published of srLi, administered once a day, in adults. The present study describes srLi PK in the serum and erythrocytes of bipolar patients.

METHODS

To assess srLi PK, we studied prospectively 17 French bipolar patients on a median dose of 1000 mg (600-1600) for at least 2 years. Serum (S), erythrocyte (E) concentrations, and urinary (U) amount were collected over 8 h after 15 days of morning intake using monitoring electronic medical system (MEMs). Population PK parameters were estimated using the SAEM algorithm (MONOLIX 4.3.3 software).

RESULTS

Using a population approach, we built a PK population model of srLi including one S compartment (V_S = 23.0 L, Cl_S = 1.21 L h^-1), one E compartment (V_E = 64.7 L, Cl_SE = 3.63 L h^-1, Cl_ES = 9.46 L h^-1), and one U compartment (F = 0.62) and estimate the ratio of concentrations to Li in E over S at 0.38 with 27% between-subject variability.

CONCLUSION

This is a PK model of srLi once a day in bipolar patients using a population approach simultaneously describing Li concentrations in serum, erythrocytes, and urine which provide an estimate of the ratio of concentration in erythrocyte over serum and its between-subject variability (BSV).

Semimechanistic Population Pharmacokinetic Model to Predict the Drug-Drug Interaction Between S-ketamine and Ticlopidine in Healthy Human Volunteers

Low‐dose oral S‐ketamine is increasingly used in chronic pain therapy, but extensive cytochrome P450 (CYP) mediated metabolism makes it prone to pharmacokinetic drug‐drug interactions (DDIs). In our study, concentration‐time data from five studies were used to develop a semimechanistic model that describes the ticlopidine‐mediated inhibition of S‐ketamine biotransformation. A mechanistic model was implemented to account for reversible and time‐dependent hepatic CYP2B6 inactivation by ticlopidine, which causes elevated S‐ketamine exposure in vivo. A pharmacokinetic model was developed with gut wall and hepatic clearances for S‐ketamine, its primary metabolite norketamine, and ticlopidine. Nonlinear mixed effects modeling approach was used (NONMEM version 7.3.0), and the final model was evaluated with visual predictive checks and the sampling‐importance‐resampling procedure. Our final model produces biologically plausible output and demonstrates that ticlopidine is a strong inhibitor of CYP2B6 mediated S‐ketamine metabolism. Simulations from our model may be used to evaluate chronic pain therapy with S‐ketamine.

Lessons learned from IDeAl - 33 recommendations from the IDeAl-net about design and analysis of small population clinical trials

BACKGROUND

IDeAl (Integrated designs and analysis of small population clinical trials) is an EU funded project developing new statistical design and analysis methodologies for clinical trials in small population groups. Here we provide an overview of IDeAl findings and give recommendations to applied researchers.

METHOD

The description of the findings is broken down by the nine scientific IDeAl work packages and summarizes results from the project's more than 60 publications to date in peer reviewed journals. In addition, we applied text mining to evaluate the publications and the IDeAl work packages' output in relation to the design and analysis terms derived from in the IRDiRC task force report on small population clinical trials.

RESULTS

The results are summarized, describing the developments from an applied viewpoint. The main result presented here are 33 practical recommendations drawn from the work, giving researchers a comprehensive guidance to the improved methodology. In particular, the findings will help design and analyse efficient clinical trials in rare diseases with limited number of patients available. We developed a network representation relating the hot topics developed by the IRDiRC task force on small population clinical trials to IDeAl's work as well as relating important methodologies by IDeAl's definition necessary to consider in design and analysis of small-population clinical trials. These network representation establish a new perspective on design and analysis of small-population clinical trials.

CONCLUSION

IDeAl has provided a huge number of options to refine the statistical methodology for small-population clinical trials from various perspectives. A total of 33 recommendations developed and related to the work packages help the researcher to design small population clinical trial. The route to improvements is displayed in IDeAl-network representing important statistical methodological skills necessary to design and analysis of small-population clinical trials. The methods are ready for use.

An automated sampling importance resampling procedure for estimating parameter uncertainty

Quantifying the uncertainty around endpoints used for decision-making in drug development is essential. In nonlinear mixed-effects models (NLMEM) analysis, this uncertainty is derived from the uncertainty around model parameters. Different methods to assess parameter uncertainty exist, but scrutiny towards their adequacy is low. In a previous publication, sampling importance resampling (SIR) was proposed as a fast and assumption-light method for the estimation of parameter uncertainty. A non-iterative implementation of SIR proved adequate for a set of simple NLMEM, but the choice of SIR settings remained an issue. This issue was alleviated in the present work through the development of an automated, iterative SIR procedure. The new procedure was tested on 25 real data examples covering a wide range of pharmacokinetic and pharmacodynamic NLMEM featuring continuous and categorical endpoints, with up to 39 estimated parameters and varying data richness. SIR led to appropriate results after 3 iterations on average. SIR was also compared with the covariance matrix, bootstrap and stochastic simulations and estimations (SSE). SIR was about 10 times faster than the bootstrap. SIR led to relative standard errors similar to the covariance matrix and SSE. SIR parameter 95% confidence intervals also displayed similar asymmetry to SSE. In conclusion, the automated SIR procedure was successfully applied over a large variety of cases, and its user-friendly implementation in the PsN program enables an efficient estimation of parameter uncertainty in NLMEM.