Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Supply-side threshold function

s(Delta_B,Delta_H) = k

Maps a change in health-care expenditure under a fixed budget, and the change in population health that results, to the cost at which the health system gains or loses one unit of health at the margin. This is the opportunity-cost basis of the threshold, distinct from a demand-side value placed on health.

  • Supply-side threshold from marginal spending and health

    k = Delta_B / Delta_H

    Divides a change in health-care expenditure by the change in health it produces through the services funded or displaced. The result is the additional cost that has to be imposed on the system to forgo one QALY through displacement, the definition Claxton and colleagues used to estimate the threshold for the English NHS.

  • Incremental net health benefit at threshold k

    H_d = Delta_C / k; INHB = Delta_E - Delta_C / k

    Converts the incremental cost of an intervention into the health expected to be displaced elsewhere, Delta_C divided by k, and subtracts it from the incremental health gain. A positive value means population health increases overall; a negative value means the health gained does not offset the health lost from care not funded elsewhere. It gives the same decision as incremental net monetary benefit at the same threshold.