Powers of the likelihood ratio test and the correlation test using empirical bayes estimates for various shrinkages in population pharmacokinetics

"De-Shrinking" EBEs: The Solution for Bayesian Therapeutic Drug Monitoring

BACKGROUND

Therapeutic drug monitoring (TDM) aims at individualising a dosage regimen and is increasingly being performed by estimating individual pharmacokinetic parameters via empirical Bayes estimates (EBEs). However, EBEs suffer from shrinkage that makes them biased. This bias is a weakness for TDM and probably a barrier to the acceptance of drug dosage adjustments by prescribers.

OBJECTIVE

The aim of this article is to propose a methodology that allows a correction of EBE shrinkage and an improvement in their precision.

METHODS

As EBEs are defined, they can be seen as a special case of ridge estimators depending on a parameter usually denoted λ. After a bias correction depending on λ, we chose λ so that the individual pharmacokinetic estimations have minimal imprecision. Our estimate is by construction always better than EBE with respect to bias (i.e. shrinkage) and precision.

RESULTS

We illustrate the performance of this approach with two different drugs: iohexol and isavuconazole. Depending on the patient's actual pharmacokinetic parameter values, the improvement given by our approach ranged from 0 to 100%.

CONCLUSION

This innovative methodology is promising since, to the best of our knowledge, no other individual shrinkage correction has been proposed.

Population Pharmacokinetic-B Cell Modeling for Ofatumumab in Patients with Relapsing Multiple Sclerosis

BACKGROUND

Ofatumumab, a fully human anti-CD20 monoclonal antibody indicated for the treatment of relapsing forms of multiple sclerosis (RMS), binds to a unique conformational epitope, thereby depleting B cells very efficiently and allowing subcutaneous administration at lower doses.

OBJECTIVES

The aims were to characterize the relationship between ofatumumab concentration and B cell levels, including the effect of covariates such as body weight, age, or baseline B cell count, and use simulations to confirm the chosen therapeutic dose.

METHODS

Graphical and regression analyses previously performed based on data from a dose-range finding study provided the B cell depletion target used in the present work. All available adult phase 2/3 data for ofatumumab in RMS patients were pooled to develop a population pharmacokinetics (PK)-B cell count model, using nonlinear mixed-effects modeling. The population PK-B cell model was used to simulate B cell depletion and repletion times and the effect of covariates on PK and B cell metrics, as well as the dose response across a range of subcutaneous ofatumumab monthly doses.

RESULTS

The final PK-B cell model was developed using data from 1486 patients. The predetermined B cell target was best achieved and sustained with the 20-mg dose regimen, with median B cell count reaching 8 cells/µL in 11 days and negligible repletion between doses. Only weight had a significant effect on PK, which did not translate into any clinically relevant effect on B cell levels.

CONCLUSION

The PK-B cell modeling confirms the dose chosen for the licensed ofatumumab regimen and demonstrates no requirement for dose adjustment based on adult patient characteristics.

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.

Efficient algorithms for covariate analysis with dynamic data using nonlinear mixed-effects model

Nonlinear mixed-effects modeling is one of the most popular tools for analyzing repeated measurement data, particularly for applications in the biomedical fields. Multiple integration and nonlinear optimization are the two major challenges for likelihood-based methods in nonlinear mixed-effects modeling. To solve these problems, approaches based on empirical Bayesian estimates have been proposed by breaking the problem into a nonlinear mixed-effects model with no covariates and a linear regression model without random effect. This approach is time-efficient as it involves no covariates in the nonlinear optimization. However, covariate effects based on empirical Bayesian estimates are underestimated and the bias depends on the extent of shrinkage. Marginal correction method has been proposed to correct the bias caused by shrinkage to some extent. However, the marginal approach appears to be suboptimal when testing covariate effects on multiple model parameters, a situation that is often encountered in real-world data analysis. In addition, the marginal approach cannot correct the inaccuracy in the associated p-values. In this paper, we proposed a simultaneous correction method (nSCEBE), which can handle the situation where covariate analysis is performed on multiple model parameters. Simulation studies and real data analysis showed that nSCEBE is accurate and efficient for both effect-size estimation and p-value calculation compared with the existing methods. Importantly, nSCEBE can be >2000 times faster than the standard mixed-effects models, potentially allowing utilization for high-dimension covariate analysis for longitudinal or repeated measured outcomes.

SCEBE: an efficient and scalable algorithm for genome-wide association studies on longitudinal outcomes with mixed-effects modeling

Genome-wide association studies (GWAS) using longitudinal phenotypes collected over time is appealing due to the improvement of power. However, computation burden has been a challenge because of the complex algorithms for modeling the longitudinal data. Approximation methods based on empirical Bayesian estimates (EBEs) from mixed-effects modeling have been developed to expedite the analysis. However, our analysis demonstrated that bias in both association test and estimation for the existing EBE-based methods remains an issue. We propose an incredibly fast and unbiased method (simultaneous correction for EBE, SCEBE) that can correct the bias in the naive EBE approach and provide unbiased P-values and estimates of effect size. Through application to Alzheimer's Disease Neuroimaging Initiative data with 6 414 695 single nucleotide polymorphisms, we demonstrated that SCEBE can efficiently perform large-scale GWAS with longitudinal outcomes, providing nearly 10 000 times improvement of computational efficiency and shortening the computation time from months to minutes. The SCEBE package and the example datasets are available at https://github.com/Myuan2019/SCEBE.

High-throughput and efficient multilocus genome-wide association study on longitudinal outcomes

MOTIVATION

With the emerging of high-dimensional genomic data, genetic analysis such as genome-wide association studies (GWAS) have played an important role in identifying disease-related genetic variants and novel treatments. Complex longitudinal phenotypes are commonly collected in medical studies. However, since limited analytical approaches are available for longitudinal traits, these data are often underutilized. In this article, we develop a high-throughput machine learning approach for multilocus GWAS using longitudinal traits by coupling Empirical Bayesian Estimates from mixed-effects modeling with a novel ℓ0-norm algorithm.

RESULTS

Extensive simulations demonstrated that the proposed approach not only provided accurate selection of single nucleotide polymorphisms (SNPs) with comparable or higher power but also robust control of false positives. More importantly, this novel approach is highly scalable and could be approximately >1000 times faster than recently published approaches, making genome-wide multilocus analysis of longitudinal traits possible. In addition, our proposed approach can simultaneously analyze millions of SNPs if the computer memory allows, thereby potentially allowing a true multilocus analysis for high-dimensional genomic data. With application to the data from Alzheimer's Disease Neuroimaging Initiative, we confirmed that our approach can identify well-known SNPs associated with AD and were much faster than recently published approaches (≥6000 times).

AVAILABILITY AND IMPLEMENTATION

The source code and the testing datasets are available at https://github.com/Myuan2019/EBE_APML0.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

A novel quantification of information for longitudinal data analyzed by mixed-effects modeling

Nonlinear mixed-effects (NLME) modeling is one of the most powerful tools for analyzing longitudinal data especially under the sparse sampling design. The determinant of the Fisher information matrix is a commonly used global metric of the information that can be provided by the data under a given model. However, in clinical studies, it is also important to measure how much information the data provide for a certain parameter of interest under the assumed model, for example, the clearance in population pharmacokinetic models. This paper proposes a new, easy-to-interpret information metric, the "relative information" (RI), which is designed for specific parameters of a model and takes a value between 0% and 100%. We establish the relationship between interindividual variability for a specific parameter and the variance of the associated parameter estimator, demonstrating that, under a "perfect" experiment (eg, infinite samples or/and minimum experimental error), the RI and the variance of the model parameter estimator converge, respectively, to 100% and the ratio of the interindividual variability for that parameter and the number of subjects. Extensive simulation experiments and analyses of three real datasets show that our proposed RI metric can accurately characterize the information for parameters of interest for NLME models. The new information metric can be readily used to facilitate study designs and model diagnosis.

Population Pharmacokinetic Analysis of Phenytoin After Intravenous Administration of Fosphenytoin in Adult and Elderly Epileptic Patients

BACKGROUND

Fosphenytoin, the diphosphate ester salt of phenytoin, is widely used to treat status epilepticus. The aim of this study was to develop a population pharmacokinetic (PPK) model to describe serum phenytoin concentrations after the intravenous administration of fosphenytoin in adult and elderly epileptic patients.

METHODS

Patient backgrounds, laboratory tests, and prescribed drugs were retrospectively collected from electronic medical records. Patients who received fosphenytoin were enrolled. The PPK analysis was performed using NONMEM 7.3.0 with the first-order conditional estimation method with interaction. Age, sex, laboratory tests, and coadministered drugs were selected as candidates for covariates. Significance levels for forward inclusion and backward elimination were set at 0.05 and 0.01, respectively. The study protocol was approved by the Fukuoka Tokushukai Ethics Committee.

RESULTS

A total of 340 serum phenytoin concentrations from 200 patients treated with fosphenytoin were available. The median age and body weight of the population were 71 years and 53.4 kg, respectively. A linear 1-compartment model with the conversion rate of fosphenytoin to phenytoin clearly described the pharmacokinetics of phenytoin after the intravenous administration of fosphenytoin. Age was detected as a covariate of clearance (CL): CL (L/h) = 1.99 × (body weight/53.4) × (age/71). Goodness-of-fit plots revealed the high-predictive performance of the final PPK model, and systematic deviations were not observed. The final model was validated by a prediction-corrected visual predictive check and bootstrap analysis.

CONCLUSIONS

We herein developed a PPK model to describe phenytoin concentrations after the intravenous administration of fosphenytoin. Age was identified as a significant covariate for CL.

A quick and accurate method for the estimation of covariate effects based on empirical Bayes estimates in mixed-effects modeling: Correction of bias due to shrinkage

Nonlinear mixed-effects modeling is a popular approach to describe the temporal trajectory of repeated measurements of clinical endpoints collected over time in clinical trials, to distinguish the within-subject and the between-subject variabilities, and to investigate clinically important risk factors (covariates) that may partly explain the between-subject variability. Due to the complex computing algorithms involved in nonlinear mixed-effects modeling, estimation of covariate effects is often time-consuming and error-prone owing to local convergence. We develop a fast and accurate estimation method based on empirical Bayes estimates from the base mixed-effects model without covariates, and simple regressions outside of the nonlinear mixed-effect modeling framework. Application of the method is illustrated using a pharmacokinetic dataset from an anticoagulation drug for the prevention of major cardiovascular events in patients with acute coronary syndrome. Both the application and extensive simulations demonstrated that the performance of this high-throughput method is comparable to the commonly used maximum likelihood estimation in nonlinear mixed-effects modeling.

Adjusted adaptive Lasso for covariate model-building in nonlinear mixed-effect pharmacokinetic models

One important aim in population pharmacokinetics (PK) and pharmacodynamics is identification and quantification of the relationships between the parameters and covariates. Lasso has been suggested as a technique for simultaneous estimation and covariate selection. In linear regression, it has been shown that Lasso possesses no oracle properties, which means it asymptotically performs as though the true underlying model was given in advance. Adaptive Lasso (ALasso) with appropriate initial weights is claimed to possess oracle properties; however, it can lead to poor predictive performance when there is multicollinearity between covariates. This simulation study implemented a new version of ALasso, called adjusted ALasso (AALasso), to take into account the ratio of the standard error of the maximum likelihood (ML) estimator to the ML coefficient as the initial weight in ALasso to deal with multicollinearity in non-linear mixed-effect models. The performance of AALasso was compared with that of ALasso and Lasso. PK data was simulated in four set-ups from a one-compartment bolus input model. Covariates were created by sampling from a multivariate standard normal distribution with no, low (0.2), moderate (0.5) or high (0.7) correlation. The true covariates influenced only clearance at different magnitudes. AALasso, ALasso and Lasso were compared in terms of mean absolute prediction error and error of the estimated covariate coefficient. The results show that AALasso performed better in small data sets, even in those in which a high correlation existed between covariates. This makes AALasso a promising method for covariate selection in nonlinear mixed-effect models.

Combined Analysis of Phase I and Phase II Data to Enhance the Power of Pharmacogenetic Tests

We show through a simulation study how the joint analysis of data from phase I and phase II studies enhances the power of pharmacogenetic tests in pharmacokinetic (PK) studies. PK profiles were simulated under different designs along with 176 genetic markers. The null scenarios assumed no genetic effect, while under the alternative scenarios, drug clearance was associated with six genetic markers randomly sampled in each simulated dataset. We compared penalized regression Lasso and stepwise procedures to detect the associations between empirical Bayes estimates of clearance, estimated by nonlinear mixed effects models, and genetic variants. Combining data from phase I and phase II studies, even if sparse, increases the power to identify the associations between genetics and PK due to the larger sample size. Design optimization brings a further improvement, and we highlight a direct relationship between η‐shrinkage and loss of genetic signal.