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Background  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).    Methods  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.    Result  The proof shows that a proportional rule sets reimbursement prices of new drugs in a mathematically consistent way.    Conclusion  Based on the proof and the underlying assumptions a proportional relationship between costs and health benefits ensures mathematical consistency in VBP of drugs.

A proportional rule for setting reimbursement prices of new drugs and its mathematical consistency