Daren Austin and Stefano Zamuner
Clinical Pharmacology - Modelling and Simulation, GlaxoSmithKline, Stockley Park, UK
Objectives: Many clinical trials demonstrate a profound placebo response once patients enter the trial, which may invalidate interpretation of trial outcome. The intent of this work is to develop a simple, semi-mechanistic, disease progression model that has validity in multiple diseases, in order to provide an alternative tool for model-based inference..
Methods: Disease status is characterized using a simple linear turnover model and patients assumed to enter the trial at equilibrium. The action of entering the trial resets the equilibrium to a new set-point, which reflects the action of placebo and drug intervention. Subsequent disease trajectories are assumed to follow deterministic dynamics to the new equilibrium. The model is applied to two instances: Rituximab for Idiotypic Membranous Glomerular Nephropathy (IMGN) where placebo response is inferred[1], and aOSM for Rheumatoid Arthritis (RA), where the Proof of Concept study is analyzed to make inference of drug activity[2].
Results: Assuming that disease status, D(t), is described by the simple linear ordinary differential equation dD(t)/dt = Kin – Kout D(t), at trial entry patients are assumed to be at equilibrium D0 = Kin/Kout. Once the trial has begun, the parameters are assumed to change and the equilibrium point is modified such that Kout’ = Kout (1+Pi), where Pi is a random effect defining the magnitude of the treatment interaction (including placebo). Solution of this model is straightforward; D(t) = D0(1-1/(1+Pi))exp(-(1+Pi) Kout t)+D0/(1+Pi). Since the effect of the intervention, Pi, is a random variable, the simple model has the advantage over traditional mixture models, in that individual patients can deteriorate whilst the population improves. The population dynamics (including weighted mean response) is captured in a closed-form. The model was used to adequately describe two clinical trial scenarios, and was fitted to data using SAS and NONMEM. The model is extended to cases where disease progression parameters may be time-dependent and infer both relapse and progression.
Conclusions: A simple set-point model can be used to describe disease progression in Proof of Concept trials. The observation that entering a trial changes the disease equilibrium has been validated in two clinical settings. A closed-form solution makes model implementation simple and allows for inference of treatment effects when considering trial design and simulation.
References:
[1] Fervenza et al. (2008) 73 :117 – 125.
[2] Zamuner et al. (2012) PAGE abstract.
Reference: PAGE 21 () Abstr 2528 [www.page-meeting.org/?abstract=2528]
Poster: Other Drug/Disease Modelling