Population-Based Pharmacodynamic Modeling of Omalizumab in Pediatric Patients with Moderate to Severe Persistent Inadequately Controlled Allergic Asthma

Study Design and Patient Population

Study IA05 was a randomized, double-blind, placebo-controlled, multicenter evaluation of efficacy, safety, pharmacokinetic (PK), and PD of omalizumab in children (6–11 years) with moderate-to-severe, persistent, inadequately controlled allergic asthma. Study design and patient population for Study IA05 have been previously published (5). In summary, a total of 627 patients (421 omalizumab and 206 placebo patients) were randomized in the study. Omalizumab 75 to 375 mg (or placebo) was administered subcutaneously (SC) every 2 or 4 weeks over a period of 52 weeks (24-week steroid-stable phase followed by a 28-week steroid-adjustable phase). The dose and dosing frequency of omalizumab were determined based on body weight and serum IgE level at screening (details in omalizumab US package insert), which was designed to achieve individualized dosing for optimal clinical efficacy (4).

Study IA05 was conducted according to US FDA regulations, the International Conference on Harmonisation E6 Guidelines for Good Clinical Practice, and other national requirements. All sites obtained institutional review board approval to conduct this study and obtained signed informed consent from study participants before enrollment.

Data Used in the Population Pediatric IgE–FEV1 Model

Data collected during the steroid-stable period (first 24 weeks) of Study IA05 were used to develop the pediatric IgE–FEV1 model to control for the confounding effect of steroid use on FEV1. During this period, serum free IgE (i.e., IgE not bound to omalizumab) and total IgE (i.e., free IgE and IgE bound to omalizumab) were sampled at week 0 (randomization), week 1, and week 24, before the administration of omalizumab or placebo. Given omalizumab’s mechanism of action, it binds to IgE and lowers free IgE levels. So, before omalizumab treatment, free IgE is the same as total IgE. Free and total IgE assays were measured using enzyme-linked immunosorbent assays described previously (6, 7). FEV1 was sampled at weeks 0, 12, and 24, prior to omalizumab or placebo administration. The measured FEV1 (in milliliters [mL]) was expressed as a percentage of predicted FEV1 (mL) (FEV1 % predicted = FEV1 / predicted FEV1 × 100%) as is conventionally done in FEV1 data analysis (8), where the predicted FEV1 (FEV1pred, mL) was calculated for each patient based on their most recently measured height instead of the baseline height and was calculated using the Polgar formula (9).

Model Development and Covariate Analysis

The previously developed population IgE–FEV1 model with data from adults/adolescents (3) (referred as adult/adolescent model) was used as the starting point for these updated analyses. The adult/adolescent model was then adjusted and refined as necessary to characterize FEV1 and IgE in a pediatric population (e.g., alternative structural models, random-effect structures, and covariate models were tested). The adult/adolescent model described the relationship between free IgE and FEV1 (% predicted) in both omalizumab and placebo groups as:

$$\frac_i}=\textrm}_i\times \textrm1\textrm}_i\times \left(1-\frac}_i\times _^(t)}5_i^\times _^(t)}\right)-\textrm}_i\times \textrm_i\ (t)$$

where for the ith subject, FEV1i is FEV1 (% predicted). Kdeti is the rate constant reflecting FEV1 (% predicted) improvement and deterioration. FEV1maxi is the theoretical maximum steady-state FEV1 (% predicted) that can be achieved given a free IgE concentration of 0. Imaxi is the maximum IgE inhibitory effect. IC50i is the serum free IgE concentration causing 50% of the maximum inhibitory effect. The γ is the Hill coefficient reflecting the steepness of the sigmoidal curve for the IgE-FEV1 relationship. CIgE,i (t) is the free IgE serum concentration in the ith individual, at time t. Population and individual model parameters were estimated using the first-order conditional estimation with interaction (FOCEI) method. The population IgE-FEV1 analyses were conducted via mixed-effect modeling with a qualified installation of the nonlinear mixed-effect modeling (NONMEM) software, Version 7.4 or above (ICON Development Solutions, Hanover, MD) (10). Same as the adult/adolescent model (3), this model is not an indirect response (IDR) model (11), and this model is used to describe both the omalizumab and placebo responses. In contrast to a typical IDR model, FEV1 is not assumed to be in equilibrium before and after treatment. Moreover, this single model can describe each individual’s FEV1 response in both the omalizumab and placebo groups that can show an increase, decrease, or no change in FEV1.

The IgE–FEV1 model used the serum IgE concentrations as model input to describe the dynamics of FEV1. Similar to the adult/adolescent model (3), for patients in the placebo group, the model input was the average total IgE level over the steroid-stable period of the trial, as it was considered more representative of the subject’s IgE in the absence of a drug effect (3). For patients receiving omalizumab, total IgE measurements at baseline and free IgE measurements post-treatment were used. Omalizumab was expected to rapidly and extensively suppress free IgE within 1 day of a SC dosing (6, 12), but the first post-treatment IgE observation occurred weeks after treatment. To appropriately capture the early and rapid IgE suppression effect, IgE was imputed at 0.1 week by back-extrapolating from the first post-treatment free IgE value. Moreover, FEV1 (i.e., the dependent variable in the model) was measured more frequently than IgE, so the free IgE was derived, at each FEV1 observation time point, using interpolations (both linear and log-linear interpolations were tested). A similar approach (linear interpolation) was used when developing the adult/adolescent model (3).

Assessment of model adequacy and decisions about increasing or decreasing model complexity were driven by the data and guided by goodness-of-fit criteria, including visual inspection of diagnostic scatter plots (observed vs. predicted concentration, residual/weighted residual vs. predicted concentration or time, and histograms of individual random effects), successful convergence of the minimization routine with at least 2 significant digits in parameter estimates, plausibility of parameter estimates, precision of parameter estimates, and the Akaike information criterion (AIC), given the minimum objective function value and number of estimated parameters (10).

Exploratory investigation of covariate-parameter relationships were undertaken as part of the population PD modeling. Based on scientific interest, the covariates considered for evaluation included age, body weight, baseline FEV1, and baseline IgE. Given the different response pattern (in both magnitude and onset) observed in pediatrics and the collinearity between covariates (e.g., high correlation between age and body weight in pediatric subjects), only the age effect was examined during the pediatric model development and was modeled using a power model (covariate normalized by reference value). An attempt was made to characterize the impact of age on Imax, IC50, and FEV1max. Exploratory assessments of any remaining trends were conducted by graphical inspection of all covariate effects.

Model Evaluation

The adequacy of the final model and parameter estimates was assessed with a visual predictive check (VPC) method. The basic premise is that a model and parameters derived from an observed dataset should produce simulated data that are similar to the original observed data. Using the final model, 500 Monte Carlo simulations with the original model building dataset from Study IA05 were generated by stochastic simulation to include inter-individual variability (IIV) in the simulated data, which was then summarized to find the median, 10th, and 90th percentiles, along with their 90% CI. Observed FEV1 data at each nominal time and the median, 10th, and 90th percentiles were overlaid with the simulated data for comparison. VPCs were also stratified by IgE value at screening (≤ 700 IU/mL or > 700 IU/mL) or body weight (≤ 30 kg or > 30 kg) to examine the model robustness in describing the data at extreme body weight and IgE values.

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