Using mathematics to make better decisions around Standards of Care, Clinical Guidelines, and Health Strategies

Mathematics of Medical Decisions provides a unified mathematical framework for analyzing the unique challenges of medical choices, from individual patient care decisions to population-level healthcare policies.

The text begins by establishing a formal foundation for the concepts of probability and utility, going on to describe essential tools such as decision trees, Bayesian analysis, and utility theory. It progresses to Markov models, screening policies, and prospect theory, amongst other advanced topics. The author demonstrates how mathematical reasoning can guide diagnostic, therapeutic, and policy decisions in medicine - enabling readers to evaluate trade-offs, quantify uncertainty, and design rational approaches to patient care decisions.

Combining theoretical rigor with practical application, Mathematics of Medical Decisions:

• Provides mathematical foundations for designing and evaluating predictive models used in diagnostic and treatment decisions
• Places special emphasis on how underlying assumptions can be tested to validate an analysis
• Integrates survival modeling and cost considerations into comprehensive decision frameworks
• Highlights the interplay between normative and descriptive theories of medical treatment and diagnosis decision making
• Addresses quantitative modeling and clinical reasoning to support both patient-specific and policy-level medical decisions
• Includes a wealth of clear examples linking abstract mathematical principles to real-world scenarios, including health policy design

Ideal for medical students, health economics students, and those in biomedical engineering or applied mathematics, Mathematics of Medical Decisions is a key resource for graduate and advanced undergraduate curricula in medical and quantitative sciences. It is particularly well suited for courses in medical decision analysis, health policy modeling, and biostatistics.

Michael C. Higgins is Adjunct Professor in the Division of Computational Medicine at Stanford School of Medicine. His research focuses on quantitative methods for clinical decision analysis and the development of mathematical models to improve medical outcomes.