Calculating willingness-to-pay with discrete cost and random coefficients in discrete choice experiments

Objectives 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. Methods 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. Results 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. Conclusion This study highlights the importance of incorporating discrete cost and selecting appropriate distribution assumptions for cost parameters to accurately derive the WTP.