Mathematica Modeling & Simulation Support for Clinical Trials

Experience and Examples from Phase Ib Studies of Hepatitis C Direct Antiviral Therapy

Robert B. (Nachbar^(1* )), Jeffrey S. (Saltzman^1), Julie (Stone^2), Paul (Panorchan^2)

(( )^1)Applied Computer Science and Mathematics, Merck Research Laboratories, Rahway, NJ
(( )^2)Clinical PK/PD, Merck Research Laboratories, West Point, PA

Abstract

The design, execution, and analysis of a successful clinical trial requires many decisions to be made in a timely manner, often without all the hard data one would like to have to make informed choices. Modeling and simulation (M&S) is playing an expanding role to fill this gap. Mathematica offers many tools for M&S methods that can provide decisive information, visualization tools to effectively communicate the information, and documentation tools to adequately record, store, and retrieve the data and information. This presentation will describe many of the tasks undertaken with Mathematica to design a clinical trial, analyze the results, and modify the model in response to new information derived from the trial. We began by constructing a model for hepatitis C viral (HCV) infection based on the known biology of the infection process, and then converted it to a dynamical differential equation model. The model was combined with data from the literature for the antiviral interferon and used to predict the outcome of several Phase Ib trial designs for a Merck HCV NS3/4A protease inhibitor (PI). After the trial was completed and the data unblinded it was obvious that the model needed several changes to account for the pharmacokinetics of the PI and the emergence of resistance mutants. Interactive exploration of model and parameter values allowed us to quickly revise the kinetic model. A segmented regression model was constructed to allow nonlinear least squares fitting of both total viral load and the distribution of viral mutants. Lastly, we used Monte Carlo methods to generate a large cohort of virtual patients, and visualization of the outcome of the simulated trial demonstrated that the model was able to predict the median and range of response to treatment in a dose-proportional way.