Healthcare decision-making can be complex, often requiring decision makers to weigh serious trade-offs, consider patients' values, and incorporate evidence in the face of uncertainty. Medical decisions are made implicitly by clinicians and other decision-makers on a daily basis. Decisions based largely on personal experience are subject to many biases. Decision analysis and cost-effectiveness analysis are systematic approaches used to support decision-making under conditions of uncertainty that involve important trade-offs. These mathematical tools can provide patients, physicians and policy makers with a useful approach to complex medical decision making.