Yasunori Aoki: Mathematical and Computational challenges in Pharmacometrics (joint with appl. and comp. mathematics)

Nonlinear mixed effect models have been shown to be an effective tool for the analysis of clinical trial data.  As a result, pharmacometric analysis based on nonlinear mixed effect models, also known as population approach, has become an essential step of drug development.  As the importance of pharmacometric analysis increases, more and more complex mathematical models are introduced and more complex challenges in mathematics and numerical computations start to arise.

In this talk we briefly describe the overview of pharmacometrics, then share the speaker’s experience of working in the field of pharmacometrics as an applied mathematician. We present a preconditioning method we have recently developed to address the computational instability issues [1], and a new parameter estimation strategy for the fixed-effect models with unidentifiable parameters [2].  Lastly, we introduce key mathematical and computational challenges in the field with (the hope for) potential collaboration opportunities with applied mathematicians at KTH.

[1] Aoki, Y., Nordgren, R., and Hooker, A.C. (2015). Preconditioning of Nonlinear Mixed Effect models for Stabilization of the Covariance Matrix Computation, PAGE 24 Abstr 3586   www.page-meeting.org/?abstract=3586  
[2] Aoki, Y., Hayami, K., De Sterck, H., and Konagaya, A.: Cluster Newton Method for Sampling Multiple Solutions of Underdetermined Inverse Problems: Application to a Parameter Identification Problem in Pharmacokinetics,  SIAM Journal on Scientific Computing, Volume 36, Issue 1, 2014, Pages B14-B44.