A STATISTICAL APPROACH TO COST-EFFECTIVENESS ANALYSIS UNDER UNCERTAINTY ABOUT THE WILLINGNESS-TO-PAY FOR HEALTH
Purpose: Although it plays a central role in cost-effectiveness analysis (CEA), society's willingness to invest for an additional unit of health is rarely known to policy makers. Our goal is to develop a statistical method to help decision-makers determine whether a new healthcare alternative is considered cost-effective in the absence of exact value for the willingness-to-pay for health (WTP).
Method: Our method utilizes a probability density function P to represent the policy maker's uncertain belief about the true value of WTP. The proposed method calculates a probability p that corresponds to the p-value of the hypothesis that the net monetary benefit (NMB) of a new alternative is less than or equal to that of an existing alternative when the true WTP value is randomly drawn from P. If p is less than a desired significance level, we reject this hypothesis, and consider the new alternative cost-effective under the WTP belief P. Our method also calculates the expected NMB gain under P if the new alternative is chosen. This information allows statistical comparison of the cost-effectiveness of multiple interventions. To demonstrate the application of our method, we consider two hypothetical alternatives, both of which present the same incremental cost-effectiveness ratio of $20,000 per unit of health but result in substantially different health and financial outcomes (Figure A-B). These alternatives also yield the same cost-effectiveness acceptability curves (CEAC) (Figure C-D), a popular tool used in CEA when the true value of WTP is unknown.
Result: When the policy maker's belief about the WTP value follows a Gamma distribution with mean $50,000 and StDev $5,000 (Figure E), both Alternatives 1 and 2 are considered cost-effective at significance level 0.05 (p-value < 0.01, Table). While CEACs suggests that Alternatives 1 and 2 perform equally well (Figure C-D), our method determines that Alternative 2 has significantly higher expected NMB gain, and hence, should be preferred to Alternative 1. In this example, when the policy maker's belief about the WTP value is uninformative (Figure F), neither of these alternatives is considered cost-effective (p-value > 0.2).
Conclusion: We developed a method to statistically evaluate and compare the cost-effectiveness of healthcare alternatives under uncertainty about the WTP value. We showed how our approach can overcome the limitations of CEACs commonly used in CEA.