Bounded outcome score modeling: application to treating psoriasis with ustekinumab

Abstract

Disease status is often measured with bounded outcome scores (BOS) which report a discrete set of values on a finite range. The distribution of BOS data is often non-standard, e.g., J- or U-shaped, thus making standard analysis methods that assume normality inappropriate. Data transformations aiming to achieve normality with BOS can be much more difficult than with many other types of skewed distributions, and application of methodologies explicitly dealing with this problem has not been previously published in pharmacokinetic/pharmacodynamic modeling literature. In this analysis, a coarsened latent variable (CO) approach is augmented with flexible transformations and applied for the purpose of demonstrating ustekinumab effects on four clinical components (involved body surface area, induration, erythema, and scaling) in patients with moderate to severe psoriasis from two Phase 3 studies. Patients were randomized to receive placebo or ustekinumab 45 or 90 mg, followed by randomized withdrawal and long-term extension periods. The approach was used together with a previously established novel semi-mechanistic, mixed-effect exposure-response model integrated with placebo effect and disease progression, and with potential influence of dropout investigated. An additional transformation further modifying both tails of the standard logit transformation in the original CO approach was shown to be necessary in this application.

Population exposure-response model to support dosing evaluation of ixekizumab in patients with chronic plaque psoriasis

“…Two clinical endpoints most commonly employed for determination of efficacy in clinical trials for psoriasis are 75% reductions in PASI score and the static Physician Global Assessment (sPGA). Exposure–response models have been developed for both endpoints . The structure employed in the current model largely resembled that from Zhou et al where an indirect‐response model was tested for characterizing the effect of ixekizumab because it is anticipated that there would be a time delay between observations of maximal ixekizumab concentrations relative to maximal drug effect on psoriatic lesions, as represented by PASI scores.…”

A semi‐mechanistic model to characterize the pharmacokinetics and pharmacodynamics of brodalumab in healthy volunteers and subjects with psoriasis in a first‐in‐human single ascending dose study

“…It has been shown that an equivalently sized study could provide dose-response information with negligible loss of proof-of-concept power by apportioning subjects with disease to a range of dose levels and employing model-based analysis. 13 Semi-mechanistic pharmacokinetic-pharmacodynamic (PK-PD) models in psoriasis have been published for a few biologic compounds based on PASI score (treated as a continuous variable), 14,15 categorical scores such as PASI75, 16 the Physicians Global Assessment (a 6-point score) 17 and PASI component scores (as an improved way of modeling bounded outcome scores) 18 and inhibition of biomarkers CD11a 19 and CD4þ/CD8þ. 20 These examples were based primarily on Phase 3 data, and only the CD11a inhibition model 19 was based on Phase 1 data alone.…”

Modeling of Bounded Outcome Scores with Data on the Boundaries: Application to Disability Assessment for Dementia Scores in Alzheimer’s Disease

“…A coarsened grid approach has been proposed for bounded outcome scores with data on boundaries (14,18). This approach assumes that an underlying latent process (variable, U) within a bounded interval gives rise to observed scores with data at the boundaries via a coarsening mechanism.…”

“…At the boundaries, y* ij = 0 when 0<U ij <0.5/m and y* ij =1 when (m−0.5)/m<U ij <1. Other normalization transformation (e.g., Czado transformation) can be also used with the CO approach (18).…”

“…More recently, zero-and one-inflated beta regression models (ZOI) have been proposed to circumvent the problem associated with boundary data (10,12). Coarsening (CO) models have been shown to be another viable option to model the bounded outcome data (14,18).…”