A Conceptual Framework for Advancements in Clinical Pharmacology: Integrating Pharmacokinetics, Pharmacodynamics, Personalized Medicine, and Artificial Intelligence with Bayesian Inference and Global Sensitivity Analysis

This paper presents a conceptual framework for advancing clinical pharmacology, emphasizing drug efficacy, safety, pharmacodynamics (PD), pharmacokinetics (PK), and the integration of artificial intelligence (AI). The framework incorporates mathematical derivations, computational simulations, global sensitivity analyses, hierarchical Bayesian inference, and uncertainty quantification to facilitate the development of individualized therapeutic strategies. Simulations are conducted using reproducible Python code with parameters sourced from peer-reviewed literature, supplemented by applications to real-world drugs for validation. This approach serves as a rigorous resource for clinicians, researchers, and educators to investigate the complex interactions between pharmacotherapeutics and biological systems, with implications for drug development and patient-centered care. In this revised version, we introduce novel hybrid AI-mechanistic models, full hierarchical Bayesian inference, comprehensive global sensitivity analysis, and a corrected reference list, enhancing the framework's originality and applicability.