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

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.

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.

Exposure-response modeling of tocilizumab in rheumatoid arthritis using continuous composite measures and their individual components

AIMS

Tocilizumab has a direct effect on inflammatory markers. Therefore, composite measures for disease activity assessment in rheumatoid arthritis (RA) using these inflammatory markers may not be suitable for tocilizumab treatment. We used a modelling approach to describe the tocilizumab exposure-response relationship and to investigate the different dynamics of the individual components of the routinely used continuous composite measures.

METHODS

Pharmacokinetic (PK), clinical and laboratory data were obtained from a prospective, observational, single-centre study involving 35 subjects with RA treated with intravenous tocilizumab. A population PK/pharmacodynamic analysis was performed using nonlinear mixed effects models.

RESULTS

The population for model development comprised 1086, 1083 and 1082 observations calculated with the disease activity score based on 28 joint (DAS28) and the simplified and clinical disease activity scores (SDAI, CDAI). The tocilizumab exposure-response relationship was described with an indirect-response model. Two main groups of individual components were identified based on their different dynamics under tocilizumab treatment: (i) tender and swollen joint counts and patient and evaluator global assessment showed a slower decrease of their baseline value (half-life: 4.6 weeks, RSE: 24%) and the need for higher serum drug concentration (EC₅₀ : 4.60 μg/mL, RSE: 103%, IIV: 359%) than (ii) C-reactive protein and erythrocyte sedimentation rate (half-life: 2.3 weeks, RSE 19%; EC₅₀ : 0.878 μg/mL, RSE: 41%, IIV: 238%).

CONCLUSION

Our study confirms a different dynamics of the individual components of the most frequently used continuous composite measures under tocilizumab treatment which should be taken into account to avoid misassessment of disease activity.

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.