Optimization and variability analysis of a pharmacokinetic model with dual-randomness caused by medication non-adherence.

Non-adherence to prescribed medications, typically manifested as random dosing times and variable dosages, is a significant obstacle in disease treatment. Existing model-based studies often rely on assumptions as dose omissions or random dosing times, which fails to represent the multifaceted nature of non-adherence. In this study, we propose a one-compartment stochastic pharmacokinetic model incorporating dual-randomness in dosing times and dosages. Our objective is to analyze how dual-randomness affects drug concentration variability, and to develop dosage adjustment strategies for the desired concentration. Leveraging the renewal process, the law of total expectation, and the theory of second-type Volterra integral equations, the statistical properties of drug concentrations under general distributions in dosing times and dosages are derived, including characteristic function, expectation, variance, and so on. Given specific uniform and exponential distributions of inter-dose time intervals, the explicit expressions of statistical characteristics are obtained, and the dosage adjustment strategies to acquire the desired concentration are theoretically proposed. Our findings establish a theoretical foundation for understanding drug concentration variability within a dual-randomness framework, thereby providing critical insights for risk prevention and process control in drug therapy during disease treatment.