OBJECTIVES: In value-based pricing (VBP), an optimal price is adjusted by comparison with a threshold of incremental cost-effectiveness ratio (ICER). Our objective is to extend it to an algorithmic theory for VBP specially focused on the difference of prices of a product and its comparator, called a premium of price in Japan, and to examine the validity of Japanese ICER-based pricing as a real-world case.

METHODS: Regarding the definition of ICER, we derive a mathematical expression to formulate the incremental cost ⊿C in terms of a function of ⊿P (=p₁ – p₀; difference of a product price p₁ and the comparator price p₀) , i.e., ⊿C = f (⊿P) , in decision-tree or Markov model. Then the ICER definition, by substituting f (⊿P) for ⊿C, leads to a formula for ⊿P as a variable: ICER = f (⊿P) /⊿E. Furthermore, algorithmic procedures for VBP will be developed from the formula.

RESULTS: In decision-tree or Markov model, it was mathematically proved that the cost estimation can be generally expressed in terms of a linear function of price: C₁ = a₁p₁ + b₁ for costs of a product and C₀ = a₀p₀ + b₀ for the comparator, where the coefficients, a₁, b₁, a₀, b₀, are constant. Based on such expressions, the ICER formula resulted in a linear function of ⊿P, i.e., ICER = h⊿P + k, where h = a₁/⊿E and k = ((a₁ - a₀)p₀ + (b₁ – b₀))/⊿E. Consequently the algorithmic procedures for VBP developed with this linear formula contradicted the VBP operations in Japan with a step function of ⊿P intuitively employed, which illuminated science and art of the Japanese methods with a hypothetical example.

CONCLUSIONS: The ICER definition can be formulated with a linear function of price difference, and this fact does not theoretically comply to the Japanese methods for VBP.