Bounded outcome score modeling: application to treating psoriasis with ustekinumab

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.