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.

Visual predictive check of longitudinal models and dropout.

Visual predictive checks (VPC) are commonly used to evaluate pharmacometrics models. However their performance may be hampered if patients with worse outcomes drop out earlier, as often occurs in clinical trials, especially in oncology. While methods accounting for dropouts have appeared in literature, they vary in assumptions, flexibility, and performance, and the differences between them are not widely understood. This manuscript aims to elucidate which methods can be used to handle VPC with dropout and when, along with a more informative VPC approach using confidence intervals. Additionally, we propose constructing the confidence interval based on the observed data instead of the simulated data. The theoretical framework for incorporating dropout in VPCs is developed and applied to propose two approaches: full and conditional. The full approach is implemented using a parametric time-to-event model, while the conditional approach is implemented using both parametric and Cox proportional-hazard (CPH) models. The practical performances of these approaches are illustrated with an application to the tumor growth dynamics (TGD) modeling of data from two cancer clinical trials of nivolumab and docetaxel, where patients were followed until disease progression. The dataset consisted of 3504 tumor size measurements from 855 subjects, which were described by a TGD model. The dropout of subjects was described by a Weibull or CPH model. Simulated datasets were also used to further illustrate the properties of the VPC methods. The results showed that the more familiar full approach might not provide meaningful improvement for TGD model evaluation over the naive approach of not adjusting for dropout, and could be outperformed by the conditional approach using either the Weibull model or the Cox proportional hazard model. Overall, including confidence intervals in VPC should improve interpretation, the conditional approach was shown to be more generally applicable when dropout occurs, and the nonparametric approach could provide additional robustness.

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.

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.

Integrated pharmacokinetic/viral dynamic model for daclatasvir/asunaprevir in treatment of patients with genotype 1 chronic hepatitis C.

In order to develop an integrated pharmacokinetic/viral dynamic (PK/VD) model to predict long-term virological response rates to daclatasvir (DCV) and asunaprevir (ASV) combination therapy in patients infected with genotype 1 (GT1) chronic hepatitis C virus (HCV), a systematic publication search was conducted for DCV and ASV administered alone and/or in combination in healthy subjects or patients with GT1 HCV infection. On the basis of a constructed meta-database, an integrated PK/VD model was developed, which adequately described both DCV and ASV PK profiles and viral load time curves. The IC50 values of DCV and ASV were estimated to be 0.041 and 2.45 µg/L, respectively, in GT1A patients. A sigmoid Emax function was applied to describe the antiviral effects of DCV and ASV, depending on the drug concentrations in the effect compartment. An empirical exponential function revealed that IC50 changing over time described drug resistance in HCV GT1A patients during DCV or ASV monotherapy. Finally, the PK/VD model was evaluated externally by comparing the expected and observed virological response rates during and post-treatment with DCV and ASV combination therapy in HCV GT1B patients. Both the rates were in general agreement. Our PK/VD model provides a useful platform for the characterization of pharmacokinetic/pharmacodynamic relationships and the prediction of long-term virological response rates to aid future development of direct acting antiviral drugs.

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.

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.

Improvement in latent variable indirect response modeling of multiple categorical clinical endpoints: application to modeling of guselkumab treatment effects in psoriatic patients.

Exposure-response modeling plays an important role in optimizing dose and dosing regimens during clinical drug development. The 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 aims to investigate the level of improvement achievable by jointly modeling two such endpoints in the latent variable IDR modeling framework through the sharing of model parameters. This is illustrated with an application to the exposure-response of guselkumab, a human IgG1 monoclonal antibody in clinical development that blocks IL-23. A Phase 2b study was conducted in 238 patients with psoriasis for which disease severity was assessed using Psoriasis Area and Severity Index (PASI) and Physician's Global Assessment (PGA) scores. A latent variable Type I IDR model was developed to evaluate the therapeutic effect of guselkumab dosing on 75, 90 and 100% improvement of PASI scores from baseline and PGA scores, with placebo effect empirically modeled. The results showed that the joint model is able to describe the observed data better with fewer parameters compared with the common approach of separately modeling the endpoints.

Challenges in longitudinal exposure-response modeling of data from complex study designs: a case study of modeling CDAI score for ustekinumab in patients with Crohn's disease.

Informative exposure-response modeling of clinical endpoints is important in drug development to identify optimum dose and dosing regimens. Despite much recent progress in mechanism-based longitudinal modeling of clinical data, challenges remain in clinical trials of diseases such as Crohn's disease, where a commonly used composite endpoint Crohn's Disease Activity Index (CDAI) has considerable variation in its administration and scoring between different assessors and complex study designs typically include maintenance phases with randomized withdrawal re-randomizations and other response driven dose adjustments. This manuscript illustrates the complexities of exposure-response modeling of such composite endpoint data through a latent-variable based Indirect Response model framework for CDAI scores using data from three phase III trials of ustekinumab in patients with moderate-to-severe Crohn's Disease. Visual predictive check was used to evaluate model performance. Potential impacts of the study design on model development and evaluation of the E-R relationship in the induction and maintenance phases of treatment are discussed. Certain biases appeared difficult to overcome, and an autocorrelated residual error model was found to provide improvement.

Improvement in latent variable indirect response joint modeling of a continuous and a categorical clinical endpoint in rheumatoid arthritis.

Improving the quality of exposure-response modeling is important in clinical drug development. The general joint modeling of multiple endpoints is made possible in part by recent progress on the latent variable indirect response (IDR) modeling for ordered categorical endpoints. This manuscript aims to investigate, when modeling a continuous and a categorical clinical endpoint, the level of improvement achievable by joint modeling in the latent variable IDR modeling framework through the sharing of model parameters for the individual endpoints, guided by the appropriate representation of drug and placebo mechanism. This was illustrated with data from two phase III clinical trials of intravenously administered mAb X for the treatment of rheumatoid arthritis, with the 28-joint disease activity score (DAS28) and 20, 50, and 70% improvement in the American College of Rheumatology (ACR20, ACR50, and ACR70) disease severity criteria were used as efficacy endpoints. The joint modeling framework led to a parsimonious final model with reasonable performance, evaluated by visual predictive check. The results showed that, compared with the more common approach of separately modeling the endpoints, it is possible for the joint model to be more parsimonious and yet better describe the individual endpoints. In particular, the joint model may better describe one endpoint through subject-specific random effects that would not have been estimable from data of this endpoint alone.

Information contributed by meta-analysis in exposure-response modeling: application to phase 2 dose selection of guselkumab in patients with moderate-to-severe psoriasis.

Ustekinumab, a human immunoglobulin G1 kappa (IgG1κ) monoclonal antibody that binds with high affinity to human interleukin (IL)-12 and IL-23, has been approved to treat patients with psoriasis. Guselkumab is a related human IgG1 monoclonal antibody in clinical development which specifically blocks IL-23. The objective of this study was to study the exposure-response relationship of guselkumab to guide dose selection for a Phase 2 study in patients with moderate-to-severe psoriasis. Data were available from a Phase 1 study of 47 healthy subjects and 24 patients with psoriasis who received various doses of guselkumab. Disease severity was assessed using Psoriasis Area and Severity Index (PASI) scores in all studies. Individual pharmacokinetic parameters were derived from population pharmacokinetics modeling for the purpose of exposure-response modeling to guide dosing regimen selection. A population mechanism-based exposure-response model of guselkumab was developed to evaluate the association of guselkumab dosing with PASI scores using a Type I indirect response model, with placebo effect empirically modeled. The model was subsequently updated, first by incorporating data from psoriasis patients who received placebo (n = 765) and from patients actively treated with ustekinumab 45 or 90 mg (n = 1,230) in two ustekinumab Phase 3 trials. Inclusion of this additional ustekinumab data and the consequent contributions to specific model components substantially reduced uncertainties in all model components except for one parameter. Additional sensitivity analyses showed that the dose selection decision was robust to this remaining uncertainty. The described approach underscores the importance of utilizing all available sources of information in dose selection decisions, along with the importance of effective development team interaction.

Latent variable indirect response joint modeling of a continuous and a categorical clinical endpoint.

Informative exposure-response modeling of clinical endpoints is important in drug development. There has been much recent progress in latent variable modeling of ordered categorical endpoints, including the application of indirect response (IDR) models and accounting for residual correlations between multiple categorical endpoints. This manuscript describes a framework of latent-variable-based IDR models that facilitate easy simultaneous modeling of a continuous and a categorical clinical endpoint. The model was applied to data from two phase III clinical trials of subcutaneously administered ustekinumab for the treatment of psoriatic arthritis, where Psoriasis Area and Severity Index scores and 20, 50, and 70 % improvement in the American College of Rheumatology response criteria were used as efficacy endpoints. Visual predictive check and external validation showed reasonable parameter estimation precision and model performance.

Latent variable indirect response modeling of categorical endpoints representing change from baseline.

Accurate exposure-response modeling is important in drug development. Methods are still evolving in the use of mechanistic, e.g., indirect response (IDR) models to relate discrete endpoints, mostly of the ordered categorical form, to placebo/co-medication effect and drug exposure. When the discrete endpoint is derived using change-from-baseline measurements, a mechanistic exposure-response modeling approach requires adjustment to maintain appropriate interpretation. This manuscript describes a new modeling method that integrates a latent-variable representation of IDR models with standard logistic regression. The new method also extends to general link functions that cover probit regression or continuous clinical endpoint modeling. Compared to an earlier latent variable approach that constrained the baseline probability of response to be 0, placebo effect parameters in the new model formulation are more readily interpretable and can be separately estimated from placebo data, thus allowing convenient and robust model estimation. A general inherent connection of some latent variable representations with baseline-normalized standard IDR models is derived. For describing clinical response endpoints, Type I and Type III IDR models are shown to be equivalent, therefore there are only three identifiable IDR models. This approach was applied to data from two phase III clinical trials of intravenously administered golimumab for the treatment of rheumatoid arthritis, where 20, 50, and 70% improvement in the American College of Rheumatology disease severity criteria were used as efficacy endpoints. Likelihood profiling and visual predictive checks showed reasonable parameter estimation precision and model performance.

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.

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.

Informative dropout modeling of longitudinal ordered categorical data and model validation: application to exposure-response modeling of physician's global assessment score for ustekinumab in patients with psoriasis.

The physician's global assessment (PGA) score is a 6-point measure of psoriasis severity that is widely used in clinical trials to assess response to psoriasis treatment. The objective of this study was to perform exposure-response modeling using the PGA score as a pharmacodynamic endpoint following treatment with ustekinumab in patients with moderate-to-severe psoriasis who participated in two Phase 3 studies (PHOENIX 1 and PHOENIX 2). Patients were randomly assigned to receive ustekinumab 45 or 90 mg or placebo, followed by active treatment or placebo crossover to ustekinumab, dose intensification or randomized withdrawal and long-term extension periods. A novel joint longitudinal-dropout model was developed from serum ustekinumab concentrations, PGA scores, and patient dropout information. The exposure-response component employed a semi-mechanistic drug model, integrated with disease progression and placebo effect under the mixed-effect logistic regression framework. This allowed potential tolerance to be investigated with a mechanistic approach. The dropout component of the joint model allowed the examination of its potential influence on the exposure-response relationship. The flexible Weibull dropout hazard function was used. Visual predictive check of the joint longitudinal-dropout model required special handling, and a conditional approach was proposed. The conditional approach was extended to external model validation. Finally, appropriate interpretation of model validation is discussed. This longitudinal-dropout model can serve as a basis to support future alternative dosing regimens for ustekinumab in patients with moderate-to-severe plaque psoriasis.