Functions & Formulae

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

Dose-response curves and the dose-dependent drug cost behind incremental cost per extra responder

E_D = E_0 + E_max * D^h / (ED_50^h + D^h)

Links the expected response to the dose through the sigmoid Emax curve and the dose to the drug cost actually paid, through whole single-use vials and relative dose intensity, so that doses can be compared by the incremental cost per extra unit of effect. The incremental ratio between adjacent doses is HE-FM-ICER-001 with the sequential rules of HE-FM-CEA-001 and HE-FM-DOM-002, and the average ratio against placebo HE-FM-ACER-002. Notation follows the Dose Response article.

  • Expected response at a dose under the sigmoid Emax model

    E_D = E_0 + E_max * D^h / (ED_50^h + D^h)

    The sigmoid Emax model, the standard four-parameter dose-response curve, rises from the placebo response E_0 towards E_0 plus E_max, reaching half the maximum added effect at the dose ED_50; the Hill coefficient h sets how steeply it rises around ED_50, and with h = 1 it reduces to the hyperbolic Emax model. Because acquisition cost usually rises in proportion to dose while the effect flattens, each extra milligram buys less response than the one before once the dose is past the steep part of the curve.

  • Drug cost of one administration with whole single-use vials and with vial sharing

    C_vial = n_v * p_v; C_share = D * p_v / v; C_waste = C_vial - C_share

    When the dose is set by weight or body surface area and the drug comes in single-use vials, the amount paid for is the vials opened: n_v is the dose divided by the vial content rounded up to a whole number. With vial sharing, or payment per mg used, the cost is in proportion to the dose, and the difference is the cost of the drug discarded. The calculator has no rounding-up function, so n_v is entered.

  • Drug cost per cycle scaled by relative dose intensity

    C_drug = C_planned * RDI

    Relative dose intensity (RDI) is the delivered dose per unit of time divided by the planned dose per unit of time, and models multiply the cost of the planned dose for a cycle by it to reflect dose reductions, delays and missed doses.