• cancer
• car-t
• differential evolution
• johnson&johnson
• markov chain
• mcmc
• metropolis-hasting
• monte carlo
• ode
• parameter estimation

The thesis provided by Johnson & Johnson (Basel, CH) under the guidance of Gang Mu, PhD, addresses a crucial aspect of medical research—parameter estimation in CAR-T cell therapy. This advanced therapy is a groundbreaking approach in treating hematologic cancers that are resistant to conventional treatments. The thesis employs a combination of mathematical modeling and Bayesian statistics to enhance understanding and efficacy of CAR-T cell therapies.

Mathematically, the thesis explores the interactions of CAR-T cell phenotypes and their antitumor effects using ordinary differential equations (ODEs) to model cell proliferation and cytotoxic activities. Central to this is the use of Bayesian methods for parameter estimation, enabling the adjustment of models based on data from actual patient treatments. Markov chains play a pivotal role in the stochastic modeling within this thesis, aiding in the representation of biological processes and treatment responses.

This research extends into advanced stochastic modeling techniques, including Monte Carlo simulation and Markov Chain Monte Carlo (MCMC) methods, to capture the probabilistic nature of these interactions. Special emphasis is placed on the Metropolis-Hastings algorithm and its extensions, DEMetropolis and DEMetropolisZ, which integrate Differential Evolution to enhance convergence rates in the Bayesian inference process.

The application of these methodologies is demonstrated through numerical analyses performed on a real dataset of CAR-T cell therapy using Python and Jupyter Notebooks. The PyMC library is employed to construct MCMC samplers, which facilitates a thorough Bayesian analysis. This allows for rigorous assessment and optimization of the mathematical model, aligning it more closely with real-world data and potentially leading to more tailored and effective patient-specific treatments.