Functions & Formulae

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

Basket-of-countries reference price and currency conversion function

r(p_i, e_i, f) = P_ref

Maps the prices of one medicine observed in a basket of reference countries, each in its own currency, and the exchange rates or purchasing power parities that express them in one currency, to a domestic reference price under an aggregation rule and to a ceiling for a proposed domestic price. The same conversions move any cost record between currencies. A cost from another year is first moved to the common price year with the live price-year adjustment HE-FM-COST-002 of the resource costing function HE-FN-COST-001, and the index itself belongs to the Consumer Price Index concept. A basket price reflects what other countries list, while the economically justifiable price HE-FM-EJP-001 and the break-even price HE-FM-BEA-001 give the highest price at which a technology is cost-effective at home. Notation follows the Basket of Countries article.

  • Foreign price or cost converted to the home currency at a market exchange rate

    c_i = p_i * e_i

    Multiplies a price or cost observed in another country's currency by the exchange rate expressed as home-currency units per unit of that currency, the p_i e_i term of the article's reference-price rule. The same step converts any cost record between currencies. A rate published the other way round, as local currency units per US dollar in the GLOBE Model final rule, is divided into the price instead. The converted prices feed the basket aggregates of HE-FM-BOC-003, and conversion at purchasing power parity is HE-FM-BOC-002.

  • Cost converted between currencies at purchasing power parity

    C_t = C_s / PPP_s * PPP_t

    Divides a cost in the source currency by the source country's PPP conversion factor, which gives international dollars, and multiplies by the target country's factor, which gives the target currency. Both factors are local currency units per international dollar, so the route through international dollars follows from their units (derived here), and a target factor of 1 returns international dollars. The World Bank describes PPPs as eliminating differences in price levels between countries in the process of conversion, and the CCEMG-EPPI-Centre Cost Converter page notes that pure exchange-rate conversion, the market rate of HE-FM-BOC-001, does not. Where the cost also comes from another price year, the year is moved first with HE-FM-COST-002 and HE-CF-BOC-001 sets out the two orders.

  • Basket mean, lowest and highest price from five converted reference prices

    P_mean = (c_1 + c_2 + c_3 + c_4 + c_5) / 5; P_low = min(min(min(min(c_1, c_2), c_3), c_4), c_5); P_high = max(max(max(max(c_1, c_2), c_3), c_4), c_5)

    Combines the converted prices c_1 to c_5 of a five-country basket, each from HE-FM-BOC-001, into the mean, the lowest and the highest price, three of the aggregation rules f in the article's P_ref. Kanavos and colleagues report that the lowest price in the basket is often used and that the average or the median is not uncommon, and Rémuzat and colleagues found the average price in use in 15 European countries and the lowest price in 7. The highest price is the PMPRB's highest international price. The median, baskets of other sizes and countries without a price are handled by HE-CF-BOC-002, and HE-FM-BOC-004 turns a reference price into a ceiling.

  • Basket ceiling as a multiple of the reference price and the margin of a proposed price

    T = k * P_ref; D = P_prop - T

    Multiplies a basket reference price by a multiplier k to give a ceiling and subtracts the ceiling from a proposed domestic price. A positive margin means the price is above the ceiling and is cut or reviewed, and a margin of zero or below means it is accepted. The article's illustrative rule takes k = 1.25 on the basket mean, modelled on Japan's foreign average price adjustment, whose adjusted price is HE-FM-BOC-005, while the PMPRB test is k = 1 on the highest international price. The reference price comes from HE-FM-BOC-003 or HE-CF-BOC-002.

  • Japanese foreign average price adjustment of a calculated new drug price

    P_adj = min(max(P_calc, min(P_calc / 3 + P_fap / 2, 2 * P_calc)), P_calc / 3 + 5 * P_fap / 6)

    Moves a price calculated by cost accounting, or by similar efficacy comparison for a product without a similar pharmacological action, towards the foreign average price when it is far from it, as the 2021 MHLW slide sets out. Above 1.25 times the foreign average the price becomes P_calc/3 plus 5 P_fap/6, below 0.75 times it becomes P_calc/3 plus P_fap/2 up to twice P_calc, and between the two it is unchanged. The single line writes the slide's branches with min and max (derived here); the branches meet the unchanged price at exactly 1.25 and 0.75 times P_fap, so a tie at either threshold gives the same price whichever branch is applied. P_fap is the mean of the converted prices of the four-country basket after the slide's trimming of an outlying highest price, a mean that HE-CF-BOC-002 computes for any number of countries, and the threshold test is HE-FM-BOC-004.

Basket of Countries — Functions & Formulae | HealthEconomics.wiki