We use a simple lifetime utility maximization model to study the problem of medical resource allocation. This model leads to a welfare specification with a QALY (quality-adjusted life-year) component that captures an individual's preferences over both life expectancy and health status. The goal of medical cost-effectiveness analysis (CEA) is characterized as maximizing the QALY measure for a given total medical expenditure. We show that the CEA with such a goal has a longevity bias: the CEA-based division of a given total medical expenditure between extending life and improving health gives the former a larger share than is called for by welfare maximization.