The equivalence of cost-effectiveness analysis (CEA) and cost-benefit analysis (CBA) has been vigorously debated in the health economic literature. In this paper we review and refine the conditions for the equivalence of CEA and CBA. The previously stated conditions require that 1) each individual's willingness to pay (WTP) per quality-adjusted life year (QALY) is constant and does not vary with the magnitude of QALY gains, and 2) the WTP per QALY is identical for every individual in society. Based on mathematical programming formulations of CEA and CBA, we note that condition 2 can be replaced with two other conditions, which together are less restrictive than the requirement that every individual have the same WTP per QALY. Even with this less restrictive set of conditions, CEA and CBA are unlikely to be equivalent under real world conditions. When CEA and CBA do lead to different resource allocation decisions, the most appropriate framework for health economic analysis depends on the perspective regarding distribution issues. We also examine the equivalence of two different definitions of CEA provided in the literature and discuss the problems that could arise when there are multiple optima.