Assessing drug effect from distributional data: A population approach with application to Duchenne Muscular Dystrophy treatment.

ABSTRACT

BACKGROUND AND OBJECTIVE: In Duchenne Muscular Dystrophy (DMD) treatment, muscle fiber size can be considered as an indicator of muscle health and function. In particular, the statistical distribution of fibers cross-sectional areas (CSAs) has been used as quantitative efficacy endpoint. For each patient, assessment of treatment effect relies on the comparison of pre- and post-treatment biopsies. Since biopsies provide "distributional data", i.e. empirical distributions of fibers CSA, the comparison must be carried out between the empirical pre- and post-treatment distributions. METHODS: Here, distributional fiber CSA data are analyzed by means of a hierarchical statistical model based on the population approach, considering both the single patient and the population level. RESULTS: The proposed method was used to assess the histological clinical effects of Givinostat, a compound under study for DMD treatment. At the single patient level, a two-component Gaussian mixture adequately represents pre- and post-treatment distributions of log-transformed CSAs; drug effect is described via a dose-dependent multiplicative increase of muscle fiber size. The single patient model was also validated via muscle composition data. At the patient population level, typical model parameters and inter-patient variabilities were obtained. CONCLUSIONS: The proposed methodological approach completely characterizes fiber CSA distributions and quantifies drug effect on muscle fiber size, both at the single patient and at the patient population level. This approach might be applied also in other contexts, where outcomes measured in terms of distributional data are to be assessed.