Frankfurt School of Finance & Management, Adickesallee 32-34, 60322, Frankfurt am Main, Germany.
BMC Health Serv Res. 2020 Mar 23;20(1):240. doi: 10.1186/s12913-020-5055-4.
Value-based pricing (VBP) of new drugs has been suggested both as a way to control health expenditures and to maximize health benefits based on the available resources. The purpose of this work is to present a simple mathematical proof showing that prices of new drugs are set in a mathematically consistent way when the sum of intervention and downstream costs is proportional to the size of health benefits. Such proportional relationship underlies the efficiency-frontier method used by the German Institute for Quality and Efficiency in Health Care (IQWiG).
A proof by contradiction is presented that is based upon the following three premises: 1) total costs (intervention plus downstream costs) of existing non-dominated drugs and interventions are acceptable to decision-making bodies; 2) new drugs with health benefits in-between those of the most and second most effective existing interventions are not automatically excluded from reimbursement and are acceptable if prices are sufficiently low; and 3) value is measured on a cardinal scale.
The proof shows that a proportional rule sets reimbursement prices of new drugs in a mathematically consistent way.
Based on the proof and the underlying assumptions a proportional relationship between costs and health benefits ensures mathematical consistency in VBP of drugs.
新药品的基于价值的定价（VBP）既被建议用于控制医疗支出，也被建议用于根据现有资源最大化健康收益。本研究的目的是提供一个简单的数学证明，表明当干预和下游成本之和与健康收益的大小成比例时，新药品的价格是以一种数学上一致的方式确定的。这种比例关系是德国医疗保健质量和效率研究所（IQWiG）使用的效率前沿方法的基础。
提出了一个反证法，该方法基于以下三个前提：1）现有非主导药物和干预措施的总成本（干预和下游成本之和）为决策机构所接受；2）具有介于最有效和第二有效的现有干预措施之间的健康收益的新药品不会自动被排除在报销之外，如果价格足够低，则是可以接受的；3）价值是在基数尺度上进行衡量的。
该证明表明，比例规则以一种数学上一致的方式确定新药品的报销价格。
基于该证明和基础假设，成本与健康收益之间的比例关系确保了药品 VBP 的数学一致性。
