Functions & Formulae

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

Case weight derivation, case-weighted payment and casemix cost comparison function

w_g = c_bar_g / c_bar; P_i = w_g * B * a_h; P_i = NWAU_i * NEP; R_h = C_h / (CM_h * c_bar)

Maps the mean costs of patient classification groups, such as diagnosis-related groups (DRGs), to relative case weights, and uses the weights to price hospital cases and to compare hospital costs for a given casemix. The records follow the notation of the Case Weight article, where w_g is the weight of group g and c_bar the mean cost per case across all groups, so a weight of 1 marks a group whose cases cost the same as the average case.

  • Relative cost weight of a case group from group mean costs

    c_bar = sum_(k=1)^K [n_k * c_bar_k] / sum_(k=1)^K [n_k]; w_g = c_bar_g / c_bar

    Divides the mean cost per case in one group by the mean cost per case across all groups of the costing sample, the calculation that the European Observatory study of DRG systems describes in greatly simplified terms. The overall mean is the case-weighted mean of the group means, so the case-weighted average of the weights equals 1 in the costing year. Real systems refine the ratio, for example with IHACPA's inlier and outlier cost model for each AR-DRG, but keep the same scaling to a reference cost.

  • Case-weighted payment per hospital case

    P_i = w_g * B * a_h

    Converts a case weight into money by multiplying it by a base rate, the money paid per unit of weight, and by any adjustment factor for the hospital. In the Medicare inpatient prospective payment system, the base payment rate, with its labour-related share adjusted by the area wage index, is multiplied by the DRG relative weight. Summed over a hospital's cases, the payment equals its casemix multiplied by the base rate and the adjustment.

  • Casemix-adjusted cost ratio of a hospital

    CM_h = sum_(g=1)^G [n_hg * w_g]; R_h = C_h / (CM_h * c_bar)

    Divides a hospital's actual total cost by the cost expected if each of its cases cost the reference amount for its group. The ratio has the form of an indirect standardisation, as in the SMR (an analogy drawn here). CM_h is the hospital's casemix, the sum of the weights of its cases, so the ratio equals cost per weighted case divided by the reference cost of one unit of weight. A value above 1 means spending above the reference for that casemix. HE-FM-ALOS-004 applies the same structure to bed-days.

  • Price of an Australian admitted acute episode from national weighted activity units

    NWAU_i = PW_g * A_paed * (1 + A_res + A_ind + A_rt + A_dia) * (1 + A_treat) + A_icu * h_i; P_i = NWAU_i * NEP

    Applies IHACPA's adjustments to the price weight of an AR-DRG to give the episode's national weighted activity units (NWAU), the Australian case weight in which the average hospital service is worth 1, and multiplies the result by the national efficient price (NEP). The formula is the 2026-27 admitted acute formula without the private patient deductions and without the hospital-acquired complication and avoidable readmission terms, which the 2026-27 determination states are shadow priced rather than applied as penalties.