Estimating Value-Based Price and Quantifying Uncertainty around It in Health Technology Assessment: Frequentist and Bayesian Approaches

Background: Although several statistical methods have been developed to inform decision making on reimbursement under uncertainty (e.g., expected net benefit, cost-effectiveness acceptability curves, and expected value of perfect information [EVPI]), those for value-based pricing are limited. This research develops methods for estimating the value-based price and quantifying the uncertainty around it in health technology assessment. Methods: We defined the value-based price of a medical product under assessment as the price at which the incremental cost-effectiveness ratio is just equal to a cost-effectiveness threshold. According to this definition, we derived an explicit form of the value-based price. Using this explicit form, we developed frequentist and Bayesian approaches to value-based pricing under uncertainty. Our proposed methods were illustrated via 2 hypothetical case studies. Results: The value-based price can be expressed explicitly using cost, effectiveness, and a cost-effectiveness threshold and is a linear function of a cost-effectiveness threshold. In the frequentist framework, point estimation, interval estimation, and hypothesis testing for the value-based price are available. In the Bayesian framework, the best estimate of the value-based price under uncertainty is the weighted median value-based price with the weight of the expected consumption volume of a medical product under assessment. This is based on the opportunity loss incurred by a decision error in value-based pricing. This opportunity loss also provides a basis for the calculation of EVPI associated with value-based pricing. These methods provided estimates of the value-based prices of medical products and the uncertainty around them in 2 hypothetical case studies. Conclusions: Our developed methods can improve decision making on value-based pricing in health technology assessment.