Signature
V = G * TP / n - L * FP / n
| Inputs | Definition | Unit |
|---|---|---|
G | Net monetary benefit of intervening for a patient who would have the event, for example from a decision model at a stated cost-effectiveness threshold | currency per case |
TP | Patients classed positive who have the event | patients |
n | Number of patients in the validation sample | patients |
L | Net monetary loss from intervening for a patient who would not have the event | currency per patient |
FP | Patients classed positive who do not have the event | patients |
V | Expected value per patient of the classifications compared with intervening in no one | currency per patient |
|---|
Function
Decision curve net benefit of a risk model or test across threshold probabilities
Maps a risk model's or test's classifications in a validation sample, at a chosen threshold probability, to net benefit: true positives per patient minus false positives per patient weighted by the odds at the threshold, so that both are counted in units of true positives. Repeating the calculation over a preset range of thresholds, for the model and for intervening in everyone or no one, gives the decision curve. The notation follows the Decision Curve Analysis article; the economic net benefit of an option at a cost-effectiveness threshold is a different quantity (HE-FM-NMB-001).
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Implementations
Excel
Decision curve monetary gain per patient from named counts and values
With BenefitCase, HarmNonCase, TruePos, FalsePos and SampleSize named, the formula returns the gain per patient, held in GainPerPatient.
=BenefitCase*TruePos/SampleSize-HarmNonCase*FalsePos/SampleSize
Assumptions
Classifications made at the threshold implied by G and L
The equality V = G x NB holds when patients are classed at p_t = L / (G + L); at another threshold V still values the classifications but no longer matches the curve.
Decision curve monetary values cover the whole pathway after classification
G and L include downstream costs and health effects valued at a stated cost-effectiveness threshold, and the cost of running the model is excluded unless added. A cost-effectiveness analysis relaxes these simplifications.
Worked examples
Model A at the implied 25 per cent threshold
With 1,500 pounds per admission-prone patient reached and 500 pounds lost per unnecessary intervention, model A's 22 true and 28 false positives per 100 are worth 190 pounds per patient, matching 1,500 times its net benefit of 0.1267.
G = 1500; L = 500; TP = 22; FP = 28; n = 100; V = 190
Intervening in everyone at the implied 25 per cent threshold
Intervening in all 100 patients gives 26 true and 74 false positives and is worth 20 pounds per patient, matching 1,500 times 0.0133.
G = 1500; L = 500; TP = 26; FP = 74; n = 100; V = 20
Common errors
Treating the decision curve monetary gain as a full economic evaluation
The figure inherits the decision curve's simplifications: one benefit and one harm for everyone, no discounting and no uncertainty analysis. A cost-effectiveness analysis models the pathway after testing.
Comparing models at different thresholds after conversion
Money values from two thresholds use different implied ratios of harm to benefit, so their difference is not a valid comparison; convert at one threshold.
Sources
Population net benefit in units of the benefit to a case
Kerr KF, Brown MD, Zhu K, Janes H. Assessing the clinical impact of risk prediction models with decision curves: guidance for correct interpretation and appropriate use. Journal of Clinical Oncology. 2016;34(21):2534-2540. doi:10.1200/JCO.2015.65.5654. Section on decision curves: the expected net benefit of a policy is B times TPR times P minus C times FPR times (1 minus P); measuring it in units of B gives the decision curve expression, and with R/(1 minus R) = C/B it becomes TPR times P minus R/(1 minus R) times FPR times (1 minus P).
Canonical Identity
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