Likelihood comparisons in bounded outcome score analysis must be internally consistent.

Clinical trial endpoints are often bounded outcome scores (BOS), which are variables having restricted values within finite intervals. Common analysis approaches may treat the data as continuous, categorical, or a mixture of both. The appearance of BOS data being simultaneously continuous and categorical easily leads to confusions in pharmacometrics regarding the appropriate domain for model evaluation and the circumstances under which data likelihoods can be compared. This commentary aims to clarify these fundamental issues and facilitate appropriate pharmacometric analyses.

Latent variable indirect response modeling of clinical efficacy endpoints with combination therapy: application to guselkumab and golimumab in patients with ulcerative colitis.

Accurate characterization of longitudinal exposure-response of clinical trial endpoints is important in optimizing dose and dosing regimens in drug development. Clinical endpoints are often categorical, for which much progress has been made recently in latent variable indirect response (IDR) modeling with single drugs. However, such applications have not yet been used for trials employing multiple drugs administered concurrently. This study aims to demonstrate that the latent variable IDR approach provides a convenient longitudinal exposure-response modeling framework to assess potential interaction effects of combination therapies. This is illustrated by an application to the exposure-response modeling of guselkumab, a monoclonal antibody in clinical development that blocks the interleukin-23p19 subunit, and golimumab, a monoclonal antibody that binds with high affinity to tumor necrosis factor-alpha. A Phase 2a study was conducted in 214 patients with moderate-to severe active ulcerative colitis for which longitudinal assessments of disease severity based on patient-reported measures of rectal bleeding, stool frequency, and symptomatic remission were evaluated as categorical endpoints, and fecal calprotectin as a continuous endpoint. The modeling results suggested independent pharmacodynamic guselkumab and golimumab effects on fecal calprotectin as a continuous endpoint, as well as interaction effects on the categorical endpoints that may be explained by an additional pathway of competitive interaction.

Variability and uncertainty: interpretation and usage of pharmacometric simulations and intervals.

Variability and estimation uncertainty are important sources of variation in pharmacometric simulations. Different combinations of uncertainty and the variability components lead to a variety types of simulation intervals, and many realized and unrealized confusions exist among pharmacometricians on their interpretation and usage. This commentary aims to clarify some of the important underlying concepts and provide a convenient guideline on pharmacometric simulation conduct and interpretation.

Population Pharmacokinetic and Exposure-Response Model Simulations: Predicted Exposure and Efficacy for Maintenance Doses of Intravenous Golimumab Every 6 or 8 Weeks in Patients With Moderately to Severely Active Rheumatoid Arthritis.

PURPOSE: Golimumab is approved to treat moderate-to-severe active rheumatoid arthritis when given intravenously at weeks 0 and 4, then every 8 weeks (Q8W) with concomitant methotrexate. These analyses assessed whether a shorter dosing interval could ameliorate diminished efficacy experienced by a small proportion of patients toward the end of the dosing interval. METHODS: Population pharmacokinetic and exposure-response modeling simulations were performed for intravenous golimumab 2 mg/kg at weeks 0 and 4, then Q8W or every 6 weeks (Q6W) through 1 year. A 2-compartment pharmacokinetic model with linear clearance developed based on GO-FURTHER (A Multicenter, Randomized, Double-blind, Placebo-controlled Trial of Golimumab, an Anti-TNFα Monoclonal Antibody, Administered Intravenously, in Patients With Active Rheumatoid Arthritis Despite Methotrexate Therapy) study data was used for pharmacokinetic simulations. A latent-variable indirect exposure-response model developed based on GO-FURTHER American College of Rheumatology (ACR) 20%/50%/70% improvement (ACR20, ACR50, and ACR70, respectively) data was used to predict clinical endpoints of ACR20/ACR50/ACR70 response rates. FINDINGS: For Q6W and Q8W dosing, respectively, predicted median golimumab steady-state trough (Ctrough,ss) concentrations were 0.57 and 0.24 µg/mL, and Cmax at steady state values were 33.1 and 32.9 µg/mL. Predicted peak median ACR20 steady-state response rates were 76.7% (Q6W) and 75.6% (Q8W). Predicted median ACR20 response rates at Ctrough,ss increased by 4.7 percentage points with Q6W (73.7%) versus Q8W (69.0%) dosing. Greater improvement in ACR20 response rates at trough time points was predicted in patients with lower golimumab trough serum concentrations. Consistent findings were observed for ACR50/ACR70 response rates. IMPLICATIONS: These simulations suggest that intravenous golimumab Q6W dosing increases golimumab Ctrough,ss, which may improve clinical response in the small proportion of patients with rheumatoid arthritis with waning efficacy at the end of the standard dosing interval. CLINICALTRIALS: gov identifier: NCT00973479. Clinicaltrialsregister.eu: EudraCT 2008-006064-11.

Pharmacokinetic/Pharmacodynamic Analysis of Guselkumab for Treatment of Palmoplantar Pustulosis: Clinical Implications of Guselkumab Dose, Disease Severity, and Smoking in Japanese Patients.

Guselkumab is a human IgG1λ monoclonal antibody that has been approved for treatment of multiple immunologic diseases including palmoplantar pustulosis in Japan. The efficacy of guselkumab in reducing disease severity as compared with placebo has been demonstrated in phase 2 and 3 clinical studies. In some patients assigned to the placebo treatment, worsening of Palmoplantar Pustulosis Area and Severity Index (PPPASI) score was noted. Most of these patients were smokers, raising a possibility of an association of smoking with the disease progression. To understand the clinical implications of guselkumab dose, baseline disease severity, and smoking on the treatment effect and describe the longitudinal relationship between guselkumab exposure and the PPPASI score, a pharmacokinetic/pharmacodynamic modeling analysis was conducted using the pooled data from 1 phase 2 and 1 phase 3 study. Data from 207 Japanese patients (77% women and 60% smokers) with a median PPPASI score of 24.6 were included in the analysis. The observed treatment efficacy (the PPPASI score reduction) appeared to be similar at the current approved dose (100 mg) and the higher dose (200 mg). A greater PPPASI score reduction (in absolute points) is expected in patients with higher baseline PPPASI score (severe disease). However, the higher baseline did not translate to larger magnitude of the change from baseline (in percentage) in the PPPASI score. Incorporating a linear disease progression effect in the model significantly decreased the Nonlinear Mixed Effects Modeling objective function value (P < .001). Smoking status appeared to be related to disease worsening in some patients, but the covariate did not reach statistical significance in the model.

Improving categorical endpoint longitudinal exposure-response modeling through the joint modeling with a related endpoint.

Exposure-response modeling is important to optimize dose and dosing regimens in clinical drug development. While primary clinical trial endpoints often have few categories and thus provide only limited information, sometimes there may be additional, more informative endpoints. Benefits of fully incorporating relevant information in longitudinal exposure-response modeling through joint modeling have recently been shown. This manuscript aims to further investigate the benefit of joint modeling of an ordered categorical primary endpoint with a related near-continuous endpoint, through the sharing of model parameters in the latent variable indirect response (IDR) modeling framework. This is illustrated by analyzing the data collected through up to 116 weeks from a phase 3b response-adaptive trial of ustekinumab in patients with psoriasis. The primary endpoint was based on the 6-point physician's global assessment (PGA) score. The Psoriasis area and severity Index (PASI) data, ranging from 0 to 72 with 0.1 increments, were also available. Separate and joint latent variable Type I IDR models of PGA and PASI scores were developed and compared. The results showed that the separate PGA model had a substantial structural bias, which was corrected by the joint modeling of PGA and PASI scores.

Pharmacokinetic Modeling and Predictive Performance: Practical Considerations for Therapeutic Monoclonal Antibodies.

Population pharmacokinetic (PopPK) model parameter estimation and predictive performance depend on the data adequacy for model building. PopPK models of therapeutic monoclonal antibodies (mAbs) may not be well supported by commonly used sparse sampling in late-stage development because of the slow absorption (days) and long half-life (weeks) of mAbs, affecting accuracy of predicted exposure metrics which are often used to support drug development. A case study was presented for a representative mAb to compare the predictive performance of two established PopPK models from their respective data. Differences in datasets for model building (including sample size, sampling schedule and route of administration), model structure and parameters, and key derived exposure metrics were compared, and the resulting differences in model prediction were elaborated. With the majority of the data used for developing models being trough concentration (Ctrough) data, both models projected similar Ctrough and area under the concentration-time curve (AUC) but different peak concentrations (Cmax) at steady state following the same subcutaneous dose regimen. Our case study supports the importance of appropriate sampling schemes for PopPK model development and exposure metric estimation. We recommend collecting proper random pharmacokinetic samples, in addition to troughs, to allow adequate characterization of PopPK models for mAbs. Selecting the informative model and relevant pharmacokinetic metrics could be critical in driving drug development decision-making, especially in simulation-based exposure matching to inform doses in special populations such as pediatrics.

Extrapolating Pharmacodynamic Effects From Adults to Pediatrics: A Case Study of Ustekinumab in Pediatric Patients With Moderate to Severe Plaque Psoriasis.

Ustekinumab (STELARA) is a human monoclonal antibody against interleukins-12 and -23 for the treatment of adult and adolescent (≥ 12 to < 18 years of age) patients with moderate-to-severe plaque psoriasis. A phase III study was recently completed in pediatric patients (≥ 6 to < 12 years of age) with psoriasis. The objectives of the current analysis were to develop a population pharmacokinetic (PK) model and a joint longitudinal exposure-response model using ordered categorial end points derived from Psoriasis Area and Severity Index (PASI) and Physician's Global Assessment (PGA) scores (namely a joint PASI response criteria (PRC) and PGA model) to characterize the PK and exposure-response relationship of ustekinumab in pediatric patients with psoriasis. The developed pediatric models reasonably predicted the PK of ustekinumab, as well as the PRC and PGA clinical response in pediatric patients with psoriasis. In addition, the joint PRC and PGA modeling framework was able to adequately extrapolate clinical response in pediatric patients using data collected from clinical studies in adult patients with psoriasis.

Application of Trial Simulation in the Design of a Prospective Study for Concentration-QTc Analysis in Support of a Thorough QT Study Waiver.

The concentration-QTc (C-QTc) analysis is often applied in the first-in-human (FIH) study to demonstrate the absence of a QTc effect in support of a TQT waiver. However, a C-QTc analysis without properly designed sensitivity could fail to conclude the absence of a QTc effect at high concentrations, even though the compound is QTc negative. This is because the 90% confidence interval (CI) of the model-derived ∆∆QTc grows wider with increasing concentration, and the upper-bound could cross the 10-ms threshold, even though the slope is close to 0. So far, there is no simple math formula to calculate the sensitivity/specificity of a C-QTc analysis. A PK/QTc trial simulation scheme was applied to optimize the design features of a C-QTc trial in FIH studies by evaluating the study's sensitivity over a wide concentration range, circumventing the problem of not knowing the target concentration during FIH studies. It was also used to ensure that the specificity of the trial was well-controlled. Simulation showed that the study sensitivity can be quantitatively gauged by optimizing the dose range, the number of samples per subjects or subject number, and by sampling around Tmax, and at steady-state. The specificity of the trial can also be evaluated with this approach, and it is important to combine model-derived ∆∆QTc and slope estimate in the evaluation. The trial simulation approach helps maximize the probability of success of C-QTc analyses in FIH studies intended to support a TQT waiver.

Application of Beta-Distribution and Combined Uniform and Binomial Methods in Longitudinal Modeling of Bounded Outcome Score Data.

Disease status is often measured with bounded outcome scores (BOS) which takes a discrete set of values on a finite range. The distribution of such data is often skewed, rendering the standard analysis methods assuming normal distribution inappropriate. Among the methods used for BOS analyses, two of them have the ability to predict the data within its natural range and accommodate data skewness: (1) a recently proposed beta-distribution based approach and (2) a mixture model known as CUB (combined uniform and binomial). This manuscript compares the two approaches, using an established mechanism-based longitudinal exposure-response model to analyze data from a phase 2 clinical trial in psoriatic patients. The beta-distribution-based approach was confirmed to perform well, and CUB also showed potential. A separate issue of modeling clinical trial data is that the collected baseline disease score range may be more limited than that of post-treatment disease score due to clinical trial inclusion criteria, a fact that is typically ignored in longitudinal modeling. The effect of baseline disease status restriction should in principle be adjusted for in longitudinal modeling.

Facilitating Longitudinal Exposure-Response Modeling of a Composite Endpoint Using the Joint Modeling of Sparsely and Frequently Collected Subcomponents.

Longitudinal exposure-response modeling plays an important role in optimizing dose and dosing regimens in clinical drug development. Certain clinical trials contain induction and maintenance phases where the maintenance treatment depends on the subjects' achieving the main endpoint outcome in the induction phase. Due to logistic difficulties and cost considerations, the main endpoint is usually collected more sparsely than a subcomponent (or other related endpoints). The sparse collection of the main endpoint hampers its longitudinal modeling. In principle, the frequent collection of a subcomponent allows its longitudinal modeling. However, the model evaluation via the visual predictive check (VPC) in the maintenance phase is difficult due to the requirement of the main-endpoint model to identify the treatment subgroups. This manuscript proposes a solution to this dilemma via the joint modeling of the main endpoint and the subcomponent. The challenges are illustrated by analyzing the data collected up to 60 weeks from a phase III trial of ustekinumab in patients with moderate-to-severe ulcerative colitis (UC). The main endpoint Mayo score, a commonly used composite endpoint to measure the severity of UC, was collected only at baseline, the end of the induction phase, and the end of the maintenance phase. The partial Mayo score, which is a major subset of the Mayo score, was collected at nearly every 4 weeks. A longitudinal joint exposure-response model, developed under a latent-variable Indirect Response modeling framework, described the Mayo score time course and facilitated the VPC model evaluation under a response-adaptive trial design.

Applying Beta Distribution in Analyzing Bounded Outcome Score Data.

Disease status is often measured with bounded outcome scores (BOS) which report a discrete set of values on a finite range. The distribution of such data is often non-standard, such as J- or U-shaped, for which standard analysis methods assuming normal distribution become inappropriate. Most BOS analysis methods aim to either predict the data within its natural range or accommodate data skewness, but not both. In addition, a frequent modeling objective is to predict clinical response of treatment using derived disease endpoints, defined as meeting certain criteria of improvement from baseline in disease status. This objective has not yet been addressed in existing BOS data analyses. This manuscript compares a recently proposed beta distribution-based approach with the standard continuous analysis approach, using an established mechanism-based longitudinal exposure-response model to analyze data from two phase 3 clinical studies in psoriatic patients. The beta distribution-based approach is shown to be superior in describing the BOS data and in predicting the derived endpoints, along with predicting the response time course of a highly sensitive subpopulation.

Population Pharmacokinetics and Exposure-Response Modeling Analyses of Ustekinumab in Adults With Moderately to Severely Active Ulcerative Colitis.

To characterize the pharmacokinetics (PK) and exposure-response (E-R) relationship of ustekinumab, an anti-interleukin-12/interleukin-23 (IL-12/IL-23) human monoclonal antibody, in the treatment of moderately to severely active ulcerative colitis (UC), population PK and E-R modeling analyses were conducted based on the data from the pivotal phase 3 induction and maintenance studies in UC patients. The observed serum concentration-time data of ustekinumab were adequately described by a 2-compartment linear PK model with first-order absorption and first-order elimination. Body weight, baseline serum albumin, sex, and antibodies to ustekinumab were the covariates to influence ustekinumab PK, but the magnitudes of the effects of these covariates were not considered clinically relevant, and dose adjustment was not warranted. Positive E-R relationships were demonstrated between ustekinumab exposure metrics and clinical endpoints (including clinical response, clinical remission, and endoscopic healing based on Mayo score) at induction week 8 and maintenance week 44, consistent with the effectiveness of ustekinumab in the induction and maintenance treatment of patients with UC. E-R modeling results suggest that ustekinumab ∼6 mg/kg intravenous induction and 90-mg subcutaneous every-8-week maintenance dose would produce greater efficacy than the 130 mg intravenous induction and the 90-mg subcutaneous every-12-week maintenance regimen, respectively. Our work provides a comprehensive evaluation of ustekinumab PK and E-R in a modeling framework to support ustekinumab dose recommendations in patients with UC.

On the Comparison of Methods in Analyzing Bounded Outcome Score Data.

Clinical trial endpoints often take the form of bounded outcome scores (BOS) which report a discrete set of values on a finite range. Conceptually such endpoints are ordered categorical in nature, but in practice they are often analyzed as continuous variables, which may result in data range violations and difficulties to handle data skewness. Analysis methods dedicated for BOS data have been proposed; however, much confusion exists among pharmacometricians on how to compare the possible methods. This commentary reviews the main methods used in pharmacometrics applications and discusses their theoretical and practical comparisons. The expected performance of some conceptually appealing methods in different situations is discussed, and a guideline is provided on selecting analysis methods in practice.

Population Pharmacokinetics and Exposure-Response Modeling Analyses of Golimumab in Children With Moderately to Severely Active Ulcerative Colitis.

Population pharmacokinetics (PK) and exposure-response (E-R) analyses were conducted to compare the PK and E-R relationships of golimumab between children and adults with ulcerative colitis. PK data following subcutaneous golimumab administration to children with ulcerative colitis (6-17 years) in the PURSUIT-PEDS-PK study, adults with ulcerative colitis in the PURSUIT study, and children with pediatric polyarticular juvenile idiopathic arthritis (2-17 years) in the GO-KIDS study, were included in the population PK analysis. E-R analysis was conducted using logistic regression to link serum golimumab concentration and Mayo score-based efficacy outcomes in pediatric and adult ulcerative colitis. Golimumab PK was adequately described by a 1-compartment model with first-order absorption and elimination. Golimumab apparent clearance and volume of distribution increased with body weight. Golimumab apparent clearance was higher in patients with lower serum albumin, no methotrexate use, and positive antibodies to golimumab; age was not an influential factor after accounting for body weight. Model-estimated terminal half-life (9.2 days in children; 9.5 days in adults) and other PK parameters suggest that golimumab PK properties are generally comparable between children and adults with ulcerative colitis. Simulations suggest that a higher induction dose than that tested in PURSUIT-PEDS-PK may be needed for children ≤45 kg to achieve exposures comparable to adults. Comparable E-R relationships between children and adults with ulcerative colitis were observed, although children appeared to be more responsive for the more stringent remission end point. The overall comparable PK and E-R relationships between children and adults support the extrapolation of golimumab efficacy from the adult to the pediatric ulcerative colitis population.

Modeling near-continuous clinical endpoint as categorical: application to longitudinal exposure-response modeling of Mayo scores for golimumab in patients with ulcerative colitis.

Accurate characterization of exposure-response relationship of clinical endpoints is important in drug development to identify optimal dose regimens. Endpoints with ≥ 10 ordered categories are typically analyzed as continuous. This manuscript aims to show circumstances where it is advantageous to analyze such data as ordered categorical. The results of continuous and categorical analyses are compared in a latent-variable based Indirect Response modeling framework for the longitudinal modeling of Mayo scores, ranging from 0 to 12, which is commonly used as a composite endpoint to measure the severity of ulcerative colitis (UC). Exposure response modeling of Mayo scores is complicated by the fact that studies typically include induction and maintenance phases with re-randomizations and other response-driven dose adjustments. The challenges are illustrated in this work by analyzing data collected from 3 phase II/III trials of golimumab in patients with moderate-to-severe UC. Visual predictive check was used for model evaluations. The ordered categorical approach is shown to be accurate and robust compared to the continuous approach. In addition, a disease progression model with an empirical bi-phasic rate of onset was found to be superior to the commonly used placebo model with one onset rate. An application of this modeling approach in guiding potential dose-adjustment was illustrated.

Joint longitudinal model development: application to exposure-response modeling of ACR and DAS scores in rheumatoid arthritis patients treated with sirukumab.

Exposure-response modeling is important to optimize dose and dosing regimen in clinical drug development. The joint modeling of multiple endpoints is made possible in part by recent progress in latent variable indirect response (IDR) modeling for ordered categorical endpoints. This manuscript presents the results of joint modeling of continuous and ordered categorical endpoints in the latent variable IDR modeling framework through the sharing of model parameters, with an application to the exposure-response modeling of sirukumab. Sirukumab is a human anti- interleukin-6 (IL-6) monoclonal antibody that binds soluble human IL-6 thus blocking IL-6 signaling, which plays a major role in the pathophysiology of rheumatoid arthritis (RA). A phase 2 clinical trial was conducted in patients with active RA despite methotrexate therapy, who received subcutaneous (SC) administration of either placebo or sirukumab of 25, 50 or 100 mg every 4 weeks (q4w) or 100 mg every 2 weeks (q2w). Major efficacy endpoints were the 20, 50, and 70% improvement in the American College of Rheumatology (ACR20, ACR50, and ACR70) disease severity criteria, and the 28-joint disease activity score using C-reactive protein (DAS28). The ACR endpoints were treated as ordered categorical and DAS28 as continuous. The results showed that, compared with the common approach of separately modeling the endpoints, the joint model could describe the observed data better with fewer parameters through the sharing of random effects, and thus more precisely characterize the dose-response relationship. The implications on future dose and dosing regimen optimization are discussed in contrast with those from landmark analysis.

Exposure-Response Modeling Analyses for Sirukumab, a Human Monoclonal Antibody Targeting Interleukin 6, in Patients With Moderately to Severely Active Rheumatoid Arthritis.

To characterize the dose-exposure-response relationship of sirukumab, an anti-interleukin 6 human monoclonal antibody, in the treatment of moderately to severely active rheumatoid arthritis (RA), we conducted exposure-response (E-R) modeling analyses based on data from two pivotal phase 3 placebo-controlled trials of sirukumab in patients with RA who were inadequate responders to nonbiologic disease-modifying antirheumatic drugs or anti-tumor necrosis factor α agents. A total of 2176 patients were included for the analyses and received subcutaneous administration of either placebo or sirukumab 50 mg every 4 weeks or 100 mg every 2 weeks. The clinical endpoints were 20%, 50%, and 70% improvement in the American College of Rheumatology response criteria (ie, ACR20, ACR50, and ACR70), and 28-joint Disease Activity Index Score (DAS28) using C-reactive protein. To provide a thorough assessment of the sirukumab E-R relationship, 2 pharmacokinetic/pharmacodynamic modeling approaches were implemented, including joint longitudinal modeling (ie, indirect response modeling of the time course of the 2 clinical endpoints) and landmark analyses (ie, direct linking of selected pharmacokinetic parameters to response at week 16 or 24). Results from both modeling analyses were generally consistent, and collectively suggested that the sirukumab subcutaneous dose of 50 mg every 4 weeks would produce near-maximal efficacy. No covariates identified in the E-R modeling analyses would have a significant impact on dose-response. Despite body weight and comorbid diabetes having significant effect on sirukumab exposure, simulations suggested that their effect on efficacy was small. Our work provides a comprehensive evaluation of sirukumab E-R to support dose recommendations in patients with RA.

A comprehensive evaluation of exposure-response relationships in clinical trials: application to support guselkumab dose selection for patients with psoriasis.

Guselkumab, a human IgG1 monoclonal antibody that blocks interleukin-23, has been evaluated in one Phase 2 and two Phase 3 trials in patients with moderate-to-severe psoriasis, in which disease severity was assessed using Psoriasis Area and Severity Index (PASI) and Investigator's Global Assessment (IGA) scores. Through the application of landmark and longitudinal exposure-response (E-R) modeling analyses, we sought to predict the guselkumab dose-response (D-R) relationship using data from 1459 patients who participated in these trials. A recently developed novel latent-variable Type I Indirect Response joint model was applied to PASI75/90/100 and IGA response thresholds, with placebo effect empirically modeled. An effect of body weight on E-R, independent of pharmacokinetics, was identified. Thorough landmark analyses also were implemented using the same dataset. The E-R models were combined with a population pharmacokinetic model to generate D-R predictions. The relative merits of longitudinal and landmark analysis also are discussed. The results provide a comprehensive and robust evaluation of the D-R relationship.