**Bayesian modeling of a PK-PD relationship to support an adaptive dose-finding trial**

Sylvie Retout, Valérie Cosson, Nicolas Frey

Pharma Research and Early Development, Translational Research Sciences, Modeling and Simulation Group, F. Hoffmann-La Roche, Basel, Switzerland

**Context: **An adaptive sequential, within patient, dose-escalation design is proposed for a phase I study (N=12) to establish the relationship between the concentrations of a drug and the effects on a biomarker. Adaptive decisions are planned to be guided by a Bayesian modeling of the PK-PD relationship.

**Objective:** To investigate by simulation the feasibility and the efficiency of an adaptive dose-finding trial using Bayesian modeling of the PK-PD relationship.** **

**Method: **Twelve individuals, split into 4 cohorts of 3 patients, are planned to be treated with 3 sequentially escalating IV doses. The study starts from a predefined sequence of 3 doses. PK and PD measurements are collected for each dose. After each new cohort, Bayesian estimation is used to derive the posterior distribution of each population PK-PD parameters. Based on the medians of those posterior distributions, we estimate the dose - response curve as well as the doses at which 25%, 50% and 75% inhibition is reached. Those 3 doses, rounded to the nearest possible doses, define the new dose sequence for the next cohort.

We assume a two compartment first order elimination for the PK model, and an indirect response model for the PD, with inhibition of the production rate of response. Different scenarios are simulated based on possible values of *IC _{50}*, the concentration at which 50% of inhibition is reached, and

*k*, the first order loss rate of response. We also investigate different sampling strategies, with either only one PD measurement per dose or two. For each scenario, we simulate 30 replications of the trial; the Bayesian estimation is performed using WinBUGS

_{out}^{1}via the R2WinBUGS library

^{2}of R

^{3}.

**Results: **Whatever the scenario, two PD measurements per dose allow adequate estimation of *IC _{50 }*(mean and inter-patients variability) at the end of the 4

^{th}cohort, whereas only one measurement per dose leads to an inaccurate estimation, and, as a consequence, to an inaccurate prediction of the time course of response. Regarding

*k*, it is sometimes poorly estimated, especially for scenarios with low

_{out}*k*value; however, it has less impact on the prediction of the time course of response.

_{out}**Conclusion: **That work demonstrates the feasibility and the efficiency of that adaptive dose-finding trial, increasing the chance to correctly estimate the PK-PD relationship early in the development of the drug, even on a few number of patients. It is expected to result in more streamlined Phase II/Phase III trial plan.

**References:**

1. Lunn, D.J., Thomas, A., Best, N., and Spiegelhalter, D. (2000) WinBUGS -- a Bayesian modelling framework: concepts, structure, and extensibility. *Statistics and Computing*, **10**:325-337.

2. Sturtz, S., Ligges, U., and Gelman, A. (2005) R2WinBUGS: A Package for Running WinBUGS from R. *Journal of Statistical Software,* **12**(3):1-16.

3. The R project for statistical computing, http://www.r-project.org/