Brandeau Margaret L, Zaric Gregory S
Department of Management Science and Engineering, Stanford University, Stanford, CA 94305, USA.
Health Care Manag Sci. 2009 Mar;12(1):27-37. doi: 10.1007/s10729-008-9074-7.
This paper develops a mathematical/economic framework to address the following question: Given a particular population, a specific HIV prevention program, and a fixed amount of funds that could be invested in the program, how much money should be invested? We consider the impact of investment in a prevention program on the HIV sufficient contact rate (defined via production functions that describe the change in the sufficient contact rate as a function of expenditure on a prevention program), and the impact of changes in the sufficient contact rate on the spread of HIV (via an epidemic model). In general, the cost per HIV infection averted is not constant as the level of investment changes, so the fact that some investment in a program is cost effective does not mean that more investment in the program is cost effective. Our framework provides a formal means for determining how the cost per infection averted changes with the level of expenditure. We can use this information as follows: When the program has decreasing marginal cost per infection averted (which occurs, for example, with a growing epidemic and a prevention program with increasing returns to scale), it is optimal either to spend nothing on the program or to spend the entire budget. When the program has increasing marginal cost per infection averted (which occurs, for example, with a shrinking epidemic and a prevention program with decreasing returns to scale), it may be optimal to spend some but not all of the budget. The amount that should be spent depends on both the rate of disease spread and the production function for the prevention program. We illustrate our ideas with two examples: that of a needle exchange program, and that of a methadone maintenance program.
本文建立了一个数学/经济框架来解决以下问题：给定特定人群、特定的艾滋病毒预防计划以及可投入该计划的固定资金数额，应投入多少资金？我们考虑预防计划投资对艾滋病毒充分接触率的影响（通过生产函数来定义，该函数描述了充分接触率随预防计划支出的变化），以及充分接触率变化对艾滋病毒传播的影响（通过一个流行病模型）。一般来说，随着投资水平的变化，避免每例艾滋病毒感染的成本并非恒定不变，所以在一个计划中某些投资具有成本效益这一事实并不意味着对该计划增加投资也具有成本效益。我们的框架提供了一种正式方法来确定避免每例感染的成本如何随支出水平变化。我们可以如下使用这些信息：当该计划的每例感染边际成本递减时（例如，在疫情不断蔓延且预防计划具有规模报酬递增的情况下会出现这种情况），最优选择要么是在该计划上不投入资金，要么是投入全部预算。当该计划的每例感染边际成本递增时（例如，在疫情不断缩小且预防计划具有规模报酬递减的情况下会出现这种情况），最优选择可能是投入部分而非全部预算。应投入的资金数额取决于疾病传播速度和预防计划的生产函数。我们用两个例子来说明我们的观点：一个是针头交换计划的例子，另一个是美沙酮维持治疗计划的例子。
