Ong Clarence, Cook Alex R, Tan Ker-Kan, Wang Yi
Saw Swee Hock School of Public Health, National University of Singapore and National University Health System, Singapore, Singapore.
Department of Surgery, Yong Loo Lin School of Medicine, National University of Singapore, Singapore, Singapore.
Health Econ Rev. 2025 Jul 18;15(1):63. doi: 10.1186/s13561-025-00658-z.
This study provides step-by-step guidance to calculate willingness-to-pay (WTP) in discrete choice experiments that involve discrete cost. It highlights the limitations of assuming a linear disutility for cost in WTP calculation.
Five mixed-logit models were considered. Log-normal distributions were applied to cost parameters for four models under the assumption that utility (disutility) for cost should be negative (positive) or at least non-positive (non-negative) for all individuals. Piecewise linear utility in cost, using an iterative process, was proposed to calculate the WTP for the discrete cost models. Individual level simulations - considering individual random preference - were conducted to obtain the median WTP across all individuals and compared with the population mean WTP. A case study exploring preferences for colorectal cancer screening was used to demonstrate these models and methods.
Models utilising discrete cost exhibited higher disutilities in cost at lower costs relative to models using continuous cost, but lower disutilities in cost at higher costs. Modelling using continuous cost tended to overestimate the WTP at low costs and underestimate the WTP at high costs. Adding a quadratic cost term only partially solved the problem, as the quadratic functional form may not capture the sharp change in preference for cost at low-cost levels. Divergent policy recommendations emerged when comparing results from continuous and discrete cost models. Although WTP was calculated using the population mean and the median across individuals, no systematic pattern was identified.
This study highlights the importance of incorporating discrete cost and selecting appropriate distribution assumptions for cost parameters to accurately derive the WTP.
本研究提供了分步指导，用于在涉及离散成本的离散选择实验中计算支付意愿（WTP）。它强调了在计算支付意愿时假设成本的线性负效用的局限性。
考虑了五个混合逻辑模型。在假设所有个体的成本效用（负效用）应为负（正）或至少非正（非负）的情况下，对四个模型的成本参数应用对数正态分布。提出了使用迭代过程的成本分段线性效用，以计算离散成本模型的支付意愿。进行了个体水平模拟——考虑个体随机偏好——以获得所有个体的支付意愿中位数，并与总体平均支付意愿进行比较。一个探索结直肠癌筛查偏好的案例研究被用来展示这些模型和方法。
与使用连续成本的模型相比，使用离散成本的模型在低成本时成本的负效用更高，但在高成本时成本的负效用更低。使用连续成本进行建模往往会在低成本时高估支付意愿，而在高成本时低估支付意愿。添加二次成本项只能部分解决问题，因为二次函数形式可能无法捕捉低成本水平下成本偏好的急剧变化。比较连续成本模型和离散成本模型的结果时出现了不同的政策建议。尽管支付意愿是使用总体均值和个体中位数计算的，但未发现系统模式。
本研究强调了纳入离散成本并为成本参数选择适当分布假设以准确推导支付意愿的重要性。
