Functions & Formulae

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

Resource costing function

c(q_i,p_i) = C

Maps the resources used by an option, and the unit cost of each, to a single cost expressed in one currency, one price year and one time basis. Costing identifies the resources that differ between options, measures how much of each is used and values each with a unit cost; costs from other years are moved to the common price year, and capital used over several years is spread as an equivalent annual cost. Future costs are then discounted, as set out on the Discount Rate page.

  • Total cost from resource quantities and unit costs

    C = sum_(i=1)^n [q_i * p_i]

    Multiplies the quantity of each resource used by its unit cost and adds the products over all resource types. Keeping quantities and unit costs separate shows whether a cost difference comes from different resource use or from different prices, and lets an analyst in another setting substitute local unit costs. The same sum over options gives the cost terms C_j used in the ICER and net monetary benefit.

  • Price-year adjustment of a cost with an inflation index

    C_b = C_a * I_b / I_a

    Moves a cost observed in price year a to price year b by multiplying it by the ratio of an appropriate price index in the two years. When the index is published as annual percentage increases, as the NHS Cost Inflation Index is, the index is built by chaining: each year's value is the previous value multiplied by one plus that year's increase. The NICE manual names the NHS Cost Inflation Index and the PSS Pay and Prices Index, both reported in the Unit Costs of Health and Social Care manual, or the ONS consumer price index.

  • Equivalent annual cost of a capital asset

    E = (K - S / (1 + r)^n) / ((1 - (1 + r)^(-n)) / r)

    Spreads the cost of a capital asset, such as equipment or a building, over its useful life as an equal annual amount whose present value equals the purchase cost less the discounted resale value. The annuity factor A(n,r), one minus (1 + r) to the power minus n, all divided by r, is the present value of 1 a year for n years at rate r. Unlike straight-line depreciation, the equivalent annual cost includes the opportunity cost of the funds tied up in the asset.