Impact of pharmacokinetic-pharmacodynamic model linearization on the accuracy of population information matrix and optimal design

Developments of CRBN-based PROTACs as potential therapeutic agents

Protease-targeted chimeras (PROTACs) are a new technology that is receiving much attention in the treatment of diseases. The mechanism is to inhibit protein function by hijacking the ubiquitin E3 ligase for protein degradation. Heterogeneous bifunctional PROTACs contain a ligand for recruiting E3 ligase, a linker, and another ligand to bind to the target protein for degradation. A variety of small-molecule PROTACs (CRBN, VHL, IAPs, MDM2, DCAF15, DCAF16, and RNF114-based PROTACs) have been identified so far. In particular, CRBN-based PROTACs (e.g., ARV-110 and ARV-471) have received more attention for their promising therapeutic intervention. To date, CRBN-based PRTOACs have been extensively explored worldwide and have excelled not only in cancer diseases but also in cardiovascular diseases, immune diseases, neurodegenerative diseases, and viral infections. In this review, we will provide a comprehensive update on the latest research progress in CRBN-based PRTOACs area. Following the criteria, such as disease area and drug target class, we will present the degradants in alphabetical order by target. We also provide our own perspective on the future prospects and potential challenges facing PROTACs.

Fisher information matrix for nonlinear mixed effects multiple response models: evaluation of the appropriateness of the first order linearization using a pharmacokinetic/pharmacodynamic model

We focus on the Fisher information matrix used for design evaluation and optimization in nonlinear mixed effects multiple response models. We evaluate the appropriateness of its expression computed by linearization as proposed for a single response model. Using a pharmacokinetic-pharmacodynamic (PKPD) example, we first compare the computation of the Fisher information matrix with approximation to one derived from the observed matrix on a large simulation using the stochastic approximation expectation-maximization algorithm (SAEM). The expression of the Fisher information matrix for multiple responses is also evaluated by comparison with the empirical information obtained through a replicated simulation study using the first-order linearization estimation methods implemented in the NONMEM software (first-order (FO), first-order conditional estimate (FOCE)) and the SAEM algorithm in the MONOLIX software. The predicted errors given by the approximated information matrix are close to those given by the information matrix obtained without linearization using SAEM and to the empirical ones obtained with FOCE and SAEM. The simulation study also illustrates the accuracy of both FOCE and SAEM estimation algorithms when jointly modelling multiple responses and the major limitations of the FO method. This study highlights the appropriateness of the approximated Fisher information matrix for multiple responses, which is implemented in PFIM 3.0, an extension of the R function PFIM dedicated to design evaluation and optimization. It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite.

ANALYSIS OF POPULATION PHARMACOKINETIC DATA USING NONMEM AND WinBUGS

The aim of this report is to describe the use of WinBUGS for two datasets that arise from typical population pharmacokinetic studies. The first dataset relates to gentamicin concentration-time data that arose as part of routine clinical care of 55 neonates. The second dataset incorporated data from 96 patients receiving enoxaparin. Both datasets were originally analyzed by using NONMEM. In the first instance, although NONMEM provided reasonable estimates of the fixed effects parameters it was unable to provide satisfactory estimates of the between-subject variance. In the second instance, the use of NONMEM resulted in the development of a successful model, albeit with limited available information on the between-subject variability of the pharmacokinetic parameters. WinBUGS was used to develop a model for both of these datasets. Model comparison for the enoxaparin dataset was performed by using the posterior distribution of the log-likelihood and a posterior predictive check. The use of WinBUGS supported the same structural models tried in NONMEM. For the gentamicin dataset a one-compartment model with intravenous infusion was developed, and the population parameters including the full between-subject variance-covariance matrix were available. Analysis of the enoxaparin dataset supported a two compartment model as superior to the one-compartment model, based on the posterior predictive check. Again, the full between-subject variance-covariance matrix parameters were available. Fully Bayesian approaches using MCMC methods, via WinBUGS, can offer added value for analysis of population pharmacokinetic data.

Pharmacokinetic and pharmacodynamic population modeling of orally administered rabeprazole in healthy Chinese volunteers by the NONMEM method

The pharmacokinetic-pharmacodynamic (PK-PD) relationship of the proton pump inhibitor rabeprazole in healthy Chinese volunteers was characterized via a population approach. Healthy Chinese male volunteers were enrolled in the clinical trial. Subjects were divided into three groups by their CYP2C19 genotype. Serum concentrations of rabeprazole were determined using high performance liquid chromatography (HPLC). The intragastric pH values were monitored simultaneously. Data analysis was performed using nonlinear mixed-effects modeling as implemented in the NONMEM software package. The final PK-PD model incorporated a one-compartment PK model with one-order absorption from the gastroenteric trace, first-order elimination pathway with one fixed-effect genotype modeling, and a full sigmoidal Emax PD model (X +/- SE: E0 = 2.30 +/- 0.189; Emax = 7.32 +/- 0.662; EC50 = 51.3 +/- 2.142 ng/ml; Hill coefficient = 5.00 +/- 0.556). The time profiles for concentration and pH value, as well as the concentration-pH value relationship of rabeprazole in healthy Chinese volunteers were well described by the developed population PK-PD model.

Robust population pharmacokinetic experiment design

The population approach to estimating mixed effects model parameters of interest in pharmacokinetic (PK) studies has been demonstrated to be an effective method in quantifying relevant population drug properties. The information available for each individual is usually sparse. As such, care should be taken to ensure that the information gained from each population experiment is as efficient as possible by designing the experiment optimally, according to some criterion. The classic approach to this problem is to design "good" sampling schedules, usually addressed by the D-optimality criterion. This method has the drawback of requiring exact advanced knowledge (expected values) of the parameters of interest. Often, this information is not available. Additionally, if such prior knowledge about the parameters is misspecified, this approach yields designs that may not be robust for parameter estimation. In order to incorporate uncertainty in the prior parameter specification, a number of criteria have been suggested. We focus on ED-optimality. This criterion leads to a difficult numerical problem, which is made tractable here by a novel approximation of the expectation integral usually solved by stochastic integration techniques. We present two case studies as evidence of the robustness of ED-optimal designs in the face of misspecified prior information. Estimates from replicate simulated population data show that such misspecified ED-optimal designs recover parameter estimates that are better than similarly misspecified D-optimal designs, and approach estimates gained from D-optimal designs where the parameters are correctly specified.

Simultaneous population optimal design for pharmacokinetic-pharmacodynamic experiments

Multiple outputs or measurement types are commonly gathered in biological experiments. Often, these experiments are expensive (such as clinical drug trials) or require careful design to achieve the desired information content. Optimal experimental design protocols could help alleviate the cost and increase the accuracy of these experiments. In general, optimal design techniques ignore between-individual variability, but even work that incorporates it (population optimal design) has treated simultaneous multiple output experiments separately by computing the optimal design sequentially, first finding the optimal design for one output (eg, a pharmacokinetic [PK] measurement) and then determining the design for the second output (eg, a pharmacodynamic [PD] measurement). Theoretically, this procedure can lead to biased and imprecise results when the second model parameters are also included in the first model (as in PK-PD models). We present methods and tools for simultaneous population D-optimal experimental designs, which simultaneously compute the design of multiple output experiments, allowing for correlation between model parameters. We then apply these methods to simulated PK-PD experiments. We compare the new simultaneous designs to sequential designs that first compute the PK design, fix the PK parameters, and then compute the PD design in an experiment. We find that both population designs yield similar results in designs for low sample number experiments, with simultaneous designs being possibly superior in situations in which the number of samples is unevenly distributed between outputs. Simultaneous population D-optimality is a potentially useful tool in the emerging field of experimental design.

Comparison of two design optimality criteria applied to a nonlinear model

In chemical kinetic or pharmacokinetic studies, many mathematical models are nonlinear with respect to the model parameters. This may cause serious problems for parameter estimation. A D-optimum design, which is very popular and effective for linear models, is not so good for nonlinear models with strong parameter curvature. In this article, we compare two optimality criteria applied to a nonlinear model. Both of them minimize the volume of the confidence ellipsoid of the parameters: D-optimality uses a linear approximation of the volume, and Q-optimality uses a quadratic approximation. We compute the relative design efficiencies and use a parameter-effect curvature measure to compute the number of observations that reduces the "curvature effect" to a specified level and improves the parameter estimation. The calculated designs differ significantly, and the Q-optimum design shows increasingly better statistical properties as the curvature increases. We present our results both graphically and as tables of numerical values.

Optimization of individual and population designs using Splus

We address the problem of design optimization for individual and population pharmacokinetic studies. We develop Splus generic functions for pharmacokinetic design optimization: IFIM, a function for individual design optimization similar to the ADAPT II software, and PFIM_OPT, a function for population design optimization which is an extension of the Splus function PFIM for population design evaluation. Both evaluate and optimise designs using the Simplex algorithm. IFIM optimizes the sampling times in continuous intervals of times; PFIM_OPT optimizes either, for a given group structure of the population design, only the sampling times taken in some given continuous intervals or, both the sampling times and the group structure, performing then statistical optimization. A combined variance error model can be supplied with the possibility to include parameters of the error model as parameters to be estimated. The performance of the optimization with the Simplex algorithm is demonstrated with two pharmacokinetic examples: by comparison of the optimized designs to those of the ADAPT II software for IFIM, and to those obtained using a grid search or the Fedorov-Wynn algorithm for PFIM_OPT. The influence of the variance error model on design optimization was investigated. For a given total number of samples, different group structures of a population design are compared, showing their influence on the population design efficiency. The functions IFIM and PFIM_OPT offer new efficient solutions for the increasingly important task of optimization of individual or population pharmacokinetic designs.

Further developments of the Fisher information matrix in nonlinear mixed effects models with evaluation in population pharmacokinetics

We extend the development of the expression of the Fisher information matrix in nonlinear mixed effects models for designs evaluation. We consider the dependence of the marginal variance of the observations with the mean parameters and assume an heteroscedastic variance error model. Complex models with interoccasions variability and parameters quantifying the influence of covariates are introduced. Two methods using a Taylor expansion of the model around the expectation of the random effects or a simulated value, using then Monte Carlo integration, are proposed and compared. Relevance of the resulting standard errors is investigated in a simulation study with NONMEM.