Casemix-adjusted cost ratio of a hospital

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.

Signature

CM_h = sum_(g=1)^G [n_hg * w_g]; R_h = C_h / (CM_h * c_bar)
Inputs
InputsDefinitionUnit
n_hgNumber of cases of hospital h in group g, one value per groupcount
w_gWeight of group g, one value per group in the same order as n_hgratio
C_hTotal actual cost of the cases of hospital h included in the comparisoncurrency
c_barReference cost of one unit of weight, the mean cost per case of the costing samplecurrency per weighted case
Output
CM_hCasemix of hospital h, the sum of the weights of its casesweighted cases (units of the average case)
R_hActual cost of hospital h divided by its expected cost at the reference cost per unit of weightratio, 1 meaning cost as expected for its casemix
  • G Number of groups, equal to the length of the n_hg and w_g lists (count)

Function

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

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.

Try this function

Implementations

  • Excel

    Casemix-adjusted cost ratio with SUMPRODUCT

    With the hospital's cases per group in a range named HospitalCases, the group weights in a range of the same size named GroupWeights, and named cells for the hospital's total cost and the reference cost per unit of weight, Excel returns the ratio.

    =HospitalCost/(SUMPRODUCT(HospitalCases,GroupWeights)*RefUnitCost)

Assumptions

  • Weights, reference cost and hospital cost on one costing basis

    The weights and c_bar come from one costing sample and year, and C_h is measured on the same cost scope, for example with capital and direct teaching costs treated the same way, so that the costing sample itself scores 1.

  • Comparable coding and complexity within groups across hospitals

    Cases are coded on the same rules in every hospital and complexity within each group does not differ systematically. Up-coding raises CM_h and lowers R_h with no change in efficiency.

Worked examples

  • Cost ratio of illustrative Hospital X in the case weight article

    Hospital X treats 200, 50 and 10 cases in groups A, B and C, a casemix of 195 weighted cases. Its expected cost at £4,000 per unit of weight is £780,000 against an actual £858,000, a ratio of 1.10, or 10% above the reference.

    n_hg = [200, 50, 10]; w_g = [0.5, 1.25, 3.25]; G = 3; c_bar = 4000; C_h = 858000; CM_h = 195; R_h = 1.1

  • Cost ratio of illustrative Hospital Y in the case weight article

    Hospital Y treats 50, 100 and 60 cases, a casemix of 345 weighted cases and an expected cost of £1,380,000. Its actual cost of £1,311,000 gives a ratio of 0.95, or 5% below the reference.

    n_hg = [50, 100, 60]; w_g = [0.5, 1.25, 3.25]; G = 3; c_bar = 4000; C_h = 1311000; CM_h = 345; R_h = 0.95

Common errors

  • Ranking hospitals on crude cost per case

    Crude cost per case is £3,300 for Hospital X and about £6,243 for Hospital Y, so Y looks nearly twice as costly. Per weighted case the order reverses, £4,400 for X and £3,800 for Y, and the cost ratios are 1.10 and 0.95. The crude comparison favours X only because it treats mostly cheap cases.

  • Reading a casemix-adjusted cost ratio as efficiency

    The ratio compares cost for a given mix of cases, not health produced. A hospital can score below 1 through generous coding or shorter stays with worse outcomes, so coding, complexity within groups and outcomes are checked before a ratio is read as efficiency.

Sources

  • Casemix as the sum of cost weights and the case mix index

    Busse R, Geissler A, Quentin W, Wiley M, editors. Diagnosis-Related Groups in Europe: Moving towards transparency, efficiency and quality in hospitals. Maidenhead: Open University Press, European Observatory on Health Systems and Policies Series; 2011. Chapter 14 (Geissler et al.), p. 250: the casemix equals the sum of the cost weights of all DRGs in a period, and the average case weight is the casemix divided by the number of cases.

    View source →

  • Recurrent cost per weighted separation in Australian public hospitals

    Productivity Commission. Report on Government Services 2026, Section 12: Public hospitals. Canberra: Productivity Commission; 2026. Recurrent cost per weighted separation, the average cost of an admitted patient adjusted for casemix, and the key term casemix adjusted separations.

    View source →

Canonical Identity

Persistent URI
https://healtheconomics.wiki/formula/casemix-adjusted-cost-ratio-of-a-hospital

Stable URI · Machine-readable · Resolvable · CC BY 4.0