Covariate modeling in pharmacometrics: General points for consideration.

Modeling the relationships between covariates and pharmacometric model parameters is a central feature of pharmacometric analyses. The information obtained from covariate modeling may be used for dose selection, dose individualization, or the planning of clinical studies in different population subgroups. The pharmacometric literature has amassed a diverse, complex, and evolving collection of methodologies and interpretive guidance related to covariate modeling. With the number and complexity of technologies increasing, a need for an overview of the state of the art has emerged. In this article the International Society of Pharmacometrics (ISoP) Standards and Best Practices Committee presents perspectives on best practices for planning, executing, reporting, and interpreting covariate analyses to guide pharmacometrics decision making in academic, industry, and regulatory settings.

Characterization of exposure-Clinical Dementia Rating-Sum of Boxes relationship in subjects with early Alzheimer's disease from the aducanumab Phase 3 trials.

Clinical Dementia Rating-Sum of Boxes (CDR-SB) assessments from two Phase 3 studies (ENGAGE and EMERGE) of aducanumab in subjects with early Alzheimer's disease (AD) were pooled to develop an exposure-response (ER) model. A linear model in the logit-transformed scaled CDR-SB best characterized the time profile for placebo- and aducanumab-treated subjects, with concentration as the exposure metric. The model allowed delineation of slow (4%), typical (86%), and fast (10%) progressing subpopulations in the data. The estimated drug effect on the disease progression rate was significant, 2.05 L/(g·year), with a 95% confidence interval (1.60, 2.50) that did not include zero. Following an evaluation of a series of ER model forms including differential drug and null effects either between the studies or among the three progression classes, the final ER model with a common (pooled) estimate of the drug effect between the studies and among the three progression classes was considered parsimonious. The final model provides supportive evidence that the two studies demonstrate a common intrinsic pharmacology. None of the identified covariates (Mini-Mental State Examination-BL score and Asian race) were clinically meaningful. Finally, simulations demonstrated that the intrinsic pharmacology remained consistent between the two Phase 3 studies.

A Time-to-Event Exposure-Response Model for Amyloid-Related Imaging Abnormalities Following Administration of Aducanumab to Subjects With Early Alzheimer Disease.

Amyloid-related imaging abnormalities with edema (ARIA-E) have been reported in patients with early Alzheimer disease treated with aducanumab. ARIA-E incidence has been observed to be dependent on both dose and apolipoprotein E4 carrier status. A time-to-event (TTE) approach applying data from 2 phase 3 studies (studies 301 and 302) was used to describe the effect of aducanumab serum exposure on the instantaneous risk of 2 end points: the first incidence of ARIA-E and time to ARIA-E resolution. A total of 3251 subjects with 826 events supported the TTE model to characterize the first ARIA-E event. The TTE resolution model was supported by data from 768 of 826 subjects who had ARIA-E resolved. Relationships between drug concentrations and ARIA-E events were modeled with a hazard function dependent on time, aducanumab serum concentrations, attenuation of aducanumab exposure effects with time (ie, potential for tolerance to aducanumab exposure), study, and apolipoprotein E4 carrier status. The TTE model showed that ARIA-E incidence rates were higher during the first 200 days, followed by a reduction in rates. The change in event rate reflects the attenuation of drug effect, thereby providing support for the current proposed titration regimen. Time to ARIA-E resolution was characterized by a constant baseline hazard with a probability to resolution affected by baseline ARIA-E severity and aducanumab concentration. ARIA-E resolution was found to be driven primarily by baseline hazard and time and suggested that aducanumab concentration effect is a minor contributor to the time to resolution of ARIA-E.

Population pharmacokinetics and standard uptake value ratio of aducanumab, an amyloid plaque-removing agent, in patients with Alzheimer's disease.

Aducanumab is a human immunoglobulin G1 anti-amyloid beta (Aß) antibody currently being evaluated for potential treatment of patients with early Alzheimer's disease. This paper describes the relationship between the population pharmacokinetics (PopPKs) and pharmacokinetics-pharmacodynamics (PKs-PDs) of aducanumab using data from phase I to III clinical studies, with standard uptake value ratio (SUVR) used as a PD marker. Across clinical studies, aducanumab was administered intravenously either as a single dose ranging from 0.3 to 60 mg/kg or as multiple doses of 1, 3, 6, or 10 mg/kg every 4 weeks. A titration regimen with maintenance doses of 3, 6, or 10 mg/kg was also evaluated. Aducanumab PK was characterized with a two-compartment model with first-order elimination. No nonlinearities in PKs were observed. The PopPK-PD model was developed using a sequential estimation approach. The time course of amyloid plaques, as expressed by composite SUVR measured using positron emission tomography, was described using an indirect response model with drug effect stimulating the elimination of SUVR. None of the identified covariates on PK and the PopPK-PD model were clinically relevant. The PopPK-PD model showed that magnitude, duration, and consistency of dosing are important factors determining the degree of Aß removal. The intrinsic pharmacology of aducanumab remained consistent across studies.

Population pharmacokinetics of pegaptanib sodium (Macugen(®)) in patients with diabetic macular edema.

OBJECTIVE: Population pharmacokinetic modeling of pegaptanib was undertaken to determine influence of renal function on apparent clearance. METHODS: In a randomized, double-masked multicenter trial, intravitreal pegaptanib (0.3, 1.0, or 3.0 mg/eye) was administered in patients with diabetic macular edema every 6 weeks for 12-30 weeks. A one-compartment model with first-order absorption, distribution volume, and clearance was used to characterize the pegaptanib plasma concentration-time profile. RESULTS: In 58 patients, increases in area under the concentration-time curve (AUC) to end of the dosing interval (AUC0-tau) and maximum concentration with repeat doses were <6%, indicating minimal plasma accumulation. Sex and race did not have clinically significant effects on pegaptanib exposure. In the final model, the AUC extrapolated to infinite time and maximum concentration increased by ≥50% in older patients (aged >68 years) relative to younger patients due to decreases in creatinine clearance (CRCL), a significant predictor of clearance. Pegaptanib clearance was reduced by 29% when CRCL decreased by 50%. The change in exposure with CRCL (range, 0-190 mL/minute) was < 10-fold with 0.3-3.0 mg doses. CONCLUSION: While pegaptanib clearance and AUC were significantly influenced by CRCL, the predicted exposure in patients with renal insufficiency or renal failure shows no evidence that a dose adjustment is warranted, given the tenfold margin of safety observed over the dose range of 0.3-3.0 mg.

Population dose-response analysis of daily seizure count following vigabatrin therapy in adult and pediatric patients with refractory complex partial seizures.

Vigabatrin is an irreversible inhibitor of γ-aminobutyric acid transaminase (GABA-T) and is used as an adjunctive therapy for adult patients with refractory complex partial seizures (rCPS). The purpose of this investigation was to describe the relationship between vigabatrin dosage and daily seizure rate for adults and children with rCPS and identify relevant covariates that might impact seizure frequency. This population dose-response analysis used seizure-count data from three pediatric and two adult randomized controlled studies of rCPS patients. A negative binomial distribution model adequately described daily seizure data. Mean seizure rate decreased with time after first dose and was described using an asymptotic model. Vigabatrin drug effects were best characterized by a quadratic model using normalized dosage as the exposure metric. Normalized dosage was an estimated parameter that allowed for individualized changes in vigabatrin exposure based on body weight. Baseline seizure rate increased with decreasing age, but age had no impact on vigabatrin drug effects after dosage was normalized for body weight differences. Posterior predictive checks indicated the final model was capable of simulating data consistent with observed daily seizure counts. Total normalized vigabatrin dosages of 1, 3, and 6 g/day were predicted to reduce seizure rates 23.2%, 45.6%, and 48.5%, respectively.

Covariate selection in pharmacometric analyses: a review of methods.

Covariate selection is an activity routinely performed during pharmacometric analysis. Many are familiar with the stepwise procedures, but perhaps not as many are familiar with some of the issues associated with such methods. Recently, attention has focused on selection procedures that do not suffer from these issues and maintain good predictive properties. In this review, we endeavour to put the main variable selection procedures into a framework that facilitates comparison. We highlight some issues that are unique to pharmacometric analyses and provide some thoughts and strategies for pharmacometricians to consider when planning future analyses.

Vigabatrin pediatric dosing information for refractory complex partial seizures: results from a population dose-response analysis.

We predicted vigabatrin dosages for adjunctive therapy for pediatric patients with refractory complex partial seizures (rCPS) that would produce efficacy comparable to that observed for approved adult dosages. A dose-response model related seizure-count data to vigabatrin dosage to identify dosages for pediatric rCPS patients. Seizure-count data were obtained from three pediatric and two adult rCPS clinical trials. Dosages were predicted for oral solution and tablet formulations. Predicted oral solution dosages to achieve efficacy comparable to that of a 1 g/day adult dosage were 350 and 450 mg/day for patients with body weight ranges 10-15 and >15-20 kg, respectively. Predicted oral solution dosages for efficacy comparable to a 3 g/day adult dosage were 1,050 and 1,300 mg/day for weight ranges 10-15 and >15-20 kg, respectively. Predicted tablet dosage for efficacy comparable to a 1 g/day adult dosage was 500 mg/day for weight ranges 25-60 kg. Predicted tablet dosage for efficacy comparable to a 3 g/day adult dosage was 2,000 mg for weight ranges 25-60 kg. Vigabatrin dosages were identified for pediatric rCPS patients with body weights ≥10 kg.

Population pharmacokinetics analysis of vigabatrin in adults and children with epilepsy and children with infantile spasms.

BACKGROUND AND OBJECTIVES: Vigabatrin is an inhibitor of γ-aminobutyric acid transaminase. The purpose of these analyses was to develop a population pharmacokinetics model to characterize the vigabatrin concentration-time profile for adults and children with refractory complex partial seizures (rCPS) and for children with infantile spasms (IS); to identify covariates that affect its disposition, and to enable predictions of systemic vigabatrin exposure for patients 1-12 months of age. METHODS: Vigabatrin pharmacokinetic data from six randomized controlled clinical trials and one open-label study were analyzed using nonlinear mixed-effects modeling. Data collected from 349 adults with rCPS and 119 pediatric patients with rCPS or IS were used in the analyses. RESULTS: A two-compartment model with first-order elimination and transit-compartment absorption consisting of five transit compartments adequately described the vigabatrin concentration-time data for these adult and pediatric patient populations. An exponential error model was used to estimate inter-individual variability for the transit-rate constant (k tr) (24.2 %), elimination rate constant (k) (14.7 %) and apparent central volume of distribution (V c/F) (18 %). For the study of children with IS, inter-occasion variability was estimated for k tr (58.1 %) and relative bioavailability (F) (26.9 %). Covariate analysis indicated that age, creatinine clearance (CLCR), and body weight were important predictors of vigabatrin pharmacokinetic parameters. Vigabatrin apparent clearance increased with increasing CLCR, consistent with renal excretion (primary pathway of vigabatrin elimination). Rate of vigabatrin absorption was dependent on age. The rate was slower in younger patients, which resulted in a smaller predicted maximum concentration and longer predicted time to maximum concentrations. Vigabatrin V c/F, apparent inter-compartmental clearance between the central and peripheral compartment, and apparent peripheral volume of distribution were increased with greater patient body weights. Sex did not contribute significantly to vigabatrin pharmacokinetic variability. CONCLUSION: The model adequately described vigabatrin pharmacokinetic and enabled predictions of systemic exposures in pediatric patients 1-12 months of age.

Model-based approach for optimization of atazanavir dose recommendations for HIV-infected pediatric patients.

Atazanavir (Reyataz; ATV) is a well-tolerated protease inhibitor (PI) that is indicated as a once-daily treatment for HIV infections. These features of ATV, combined with its virologic potency, make it particularly desirable for the treatment of HIV-infected pediatric patients. The objective of this study was to use a model-based approach to recommend body weight-based ATV capsule doses for pediatric patients. ATV concentration-time data from three adult studies and one pediatric study were described by a C(0)-delinked one-compartment model to guard against introducing bias in pharmacokinetic (PK) parameter estimates due to the potential nonadherence in outpatient studies. The apparent clearance (CL/F) and apparent volume of distribution (V/F) were determined to increase with body weight, and CL/F was 40.9% lower in patients receiving ATV comedication with ritonavir (RTV). The relative bioavailability (F(rel)) of ATV was 132% higher with RTV comedication and was 35.5% lower for the ATV powder formulation than the capsule formulation. Model-based simulations were used to recommend weight-based ATV capsule doses of 150 to 300 mg boosted with 100 mg RTV for pediatric patients weighing ≥15 kg, such that the exposures in these patients are similar to those obtained in HIV-infected adults treated with the recommended ATV/RTV dose of 300/100 mg.

Exposure-response modeling using latent variables for the efficacy of a JAK3 inhibitor administered to rheumatoid arthritis patients.

Currently, no general methods have been developed to relate pharmacologically based models, such as indirect response models, to discrete or ordered categorical data. We propose the use of an unobservable latent variable (LV), through which indirect response models can be linked with drug exposure. The resulting indirect latent variable response model (ILVRM) is demonstrated using a case study of a JAK3 inhibitor, which was administered to patients in a rheumatoid arthritis (RA) study. The clinical endpoint for signs and symptoms in RA is the American College of Rheumatology response criterion of 20%--a binary response variable. In this case study, four exposure-response models, which have different pharmacological interpretations, were constructed and fitted using the ILVRM method. Specifically, two indirect response models, an effect compartment model, and a model which assumes instantaneous (direct) drug action were assessed and compared for their ability to predict the response data. In general, different model interpretations can influence drug inference, such as time to drug effect onset, as well as affect extrapolations of responses to untested experimental conditions, and the underlying pharmacology that operates to generate key response features does not change because the response was measured discretely. Consideration of these model interpretations can impact future study designs and ultimately provide greater insight into drug development strategies.

Collapsing mechanistic models: an application to dose selection for proof of concept of a selective irreversible antagonist.

When data fail to support fully mechanistic models, alternative modeling strategies must be pursued. Simpler, more empirical models or the fixing of various rate constants are necessary to avoid over-parameterization. Fitting empirical models can dilute information, limit interpretation, and cloud inference. Fixing rate constants requires external, relevant, and reliable information on the mechanism and can introduce subjectivity as well as complicate determining the validity of model extrapolation. Furthermore, both these methods ignore the possibility that failure of the data to support the mechanistic model could contain information about the pharmacodynamic process. If the pathway has processes with "fast" dynamics, these steps could collapse yielding parametrically simpler classes of models. The collapsed models would retain the mechanistic interpretation of the full model, which is crucial for performing substantive inference, while reducing the number of parameters to be estimated. These concepts are illustrated through their manifestations on the dose-effect relationship and ensuing dose selection for a proof of concept study. Specifically, a mechanistic model for a selective irreversible antagonist was posited and candidate classes of models were derived utilizing "fast dynamics" assumptions. Model assessment determined the rate-limiting step facilitating pertinent inference with respect to the mechanism. For comparison, inference using a more empirical modeling strategy is also presented. A general solution for the collapse of the typical PK-PD model differential equations is provided in Appendix A.

How modeling and simulation have enhanced decision making in new drug development.

The idea of model-based drug development championed by Lewis Sheiner, in which pharmacostatistical models of drug efficacy and safety are developed from preclinical and available clinical data, offers a quantitative approach to improving drug development and development decision-making. Examples are presented that support this paradigm. The first example describes a preclinical model of behavioral activity to predict potency and time-course of response in humans and assess the potential for differentiation between compounds. This example illustrates how modeling procedures expounded by Lewis Sheiner provided the means to differentiate potency and the lag time between drug exposure and response and allow for rapid decision making and dose selection. The second example involves planning a Phase 2a dose-ranging and proof of concept trial in Alzheimer's disease (AD). The issue was how to proceed with the study and what criteria to use for a go/no go decision. The combined knowledge of AD disease progression, and preclinical and clinical information about the drug were used to simulate various clinical trial scenarios to identify an efficient and effective Phase 2 study. A design was selected and carried out resulting in a number of important learning experiences as well as extensive financial savings. The motivation for this case in point was the "Learn-Confirm" paradigm described by Lewis Sheiner. The final example describes the use of Pharmacokinetic and Pharmacodynamic (PK/PD) modeling and simulation to confirm efficacy across doses. In the New Drug Application for gabapentin, data from two adequate and well-controlled clinical trials was submitted to the Food and Drug Administration (FDA) in support of the approval of the indication for the treatment of post-herpetic neuralgia. The clinical trial data was not replicated for each of the sought dose levels in the drug application presenting a regulatory dilemma. Exposure response analysis submitted in the New Drug Application was applied to confirm the evidence of efficacy across these dose levels. Modeling and simulation analyses showed that the two studies corroborate each other with respect to the pain relief profiles. The use of PK/PD information confirmed evidence of efficacy across the three studied doses, eliminating the need for additional clinical trials and thus supporting the approval of the product. It can be speculated that the work by Lewis Sheiner reflected in the FDA document titled "Innovation or Stagnation: Challenge and Opportunity on the Critical Path to New Medical Products" made this scientific approach to the drug approval process possible.

A two-part mixture model for longitudinal adverse event severity data.

We fit a mixed effects logistic regression model to longitudinal adverse event (AE) severity data (four-point ordered categorical response) to describe the dose-AE severity response for an investigational drug. The distribution of the predicted interindividual random effects (Bayes predictions) was extremely bimodal. This extreme bimodality indicated that biased parameter estimates and poor predictive performance were likely. The distribution's primary mode was composed of patients that did not experience an AE. Moreover, the Bayes predictions of these non-AE patients were nearly degenerative, i.e., the predictions were nearly identical. To resolve this extreme bimodality we propose using a two-part mixture modeling approach. The first part models the incidence of AE's, and the second part models the severity grade given the patient had an AE. Unconditional probability predictions are calculated by mixing the incidence and severity model probability predictions. We also report results of simulation studies, which assess the predictive and statistical (bias and precision) performance of our approach.