Signature
C_vial = n_v * p_v; C_share = D * p_v / v; C_waste = C_vial - C_share
| Inputs | Definition | Unit |
|---|---|---|
n_v | Dose divided by vial content, rounded up to a whole number | vials |
p_v | Price paid per vial | pounds |
D | Dose given at one administration | mg |
v | Amount of drug in one vial | mg |
C_vial | Cost of the vials opened for one administration | pounds |
|---|---|---|
C_share | Cost in proportion to the dose given | pounds |
C_waste | Whole-vial cost minus shared cost | pounds |
Function
Dose-response curves and the dose-dependent drug cost behind incremental cost per extra responder
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.
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Implementations
Excel
Whole-vial, shared and wasted drug cost from named cells
With AdminDose, VialMg and VialPrice named, ROUNDUP returns the vials opened into VialsOpened, and the formulas return the whole-vial cost, the shared cost and the wasted cost, held in VialCost, SharedCost and WasteCost.
=ROUNDUP(AdminDose/VialMg,0); =VialsOpened*VialPrice; =AdminDose*VialPrice/VialMg; =VialCost-SharedCost
Assumptions
One vial size and no sharing of opened vials
All vials hold v mg at p_v pounds and any drug left in an opened vial is discarded; with several vial sizes the cheapest combination covering the dose replaces n_v times p_v.
Worked examples
150 mg dose from 100 mg vials at 300 pounds
A 150 mg dose needs two 100 mg vials, 600 pounds, against 450 pounds with sharing, so 150 pounds of drug is discarded each time; over 12 administrations the course costs 7,200 pounds, as in the article.
n_v = 2; p_v = 300; D = 150; v = 100; C_vial = 600; C_share = 450; C_waste = 150
200 mg dose from 100 mg vials at 300 pounds
A 200 mg dose uses the same two vials with nothing wasted, so both costs are 600 pounds, as in the article.
n_v = 2; p_v = 300; D = 200; v = 100; C_vial = 600; C_share = 600; C_waste = 0
Common errors
Costing single-use vials per mg used
Bach and colleagues note that leftover drug in a single-dose vial still has to be paid for even when discarded, and NICE's PMG24 asks for drug wastage to be taken into account in drug costs; per-mg costing prices the article's 150 mg course at 5,400 instead of 7,200 pounds.
Treating the available vial sizes as fixed
Hatswell and Porter estimated, with UK population data, that supplying pembrolizumab in 70 mg and 100 mg vials instead of 50 mg and 100 mg would cut wastage from 13.3 per cent to 8.7 per cent, so the vial sizes assumed can change drug costs.
Sources
Leftover drug in single-dose vials still has to be paid for
Bach PB, Conti RM, Muller RJ, Schnorr GC, Saltz LB. Overspending driven by oversized single dose vials of cancer drugs. BMJ. 2016;352:i788. doi:10.1136/bmj.i788 (full text read). Opening section: patients' body sizes are unlikely to match the amount of drug in a single-dose vial, so there is nearly always some left over, and the leftover drug still has to be paid for, even when discarded.
Vial sizes and wastage for pembrolizumab
Hatswell AJ, Porter JK. Reducing drug wastage in pharmaceuticals dosed by weight or body surface areas by optimising vial sizes. Applied Health Economics and Health Policy. 2019;17(3):391-397. doi:10.1007/s40258-018-0444-0 (abstract read). Abstract (Results): changing the available vial sizes for pembrolizumab (50 mg and 100 mg vials) to 70 mg and 100 mg could cut wastage from 13.3 per cent to 8.7 per cent, using UK population data.
NICE PMG24 on drug wastage in drug costs
National Institute for Health and Care Excellence. Single technology appraisal and highly specialised technologies evaluation: user guide for company evidence submission template (PMG24). London: NICE; 2015, last updated 31 March 2026 (full text of the cost-effectiveness chapter read). Section 3.5.6: drug wastage should be taken into account in calculating drug costs; oral treatments dispensed in tablet packs are costed per pack unless clinical experts or other evidence suggest there would be no wastage.
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