Dental Lifeline Network

Ordinary unrestricted national recipient donation. c is an explicit full-support cash-equivalent per nominal clinical case, including national and affiliate administration/fundraising and nonclinical portfolio burden; it is not a restricted DDS-only program-expense ratio. G=$10,000 is calculation normalization only. Donated clinician/lab opportunity cost and patient travel/time are excluded from donor cost, with separate resource-cost sensitivity. No medical savings or donated-service retail value is credited.

Domestic DDS patient eligibility and state-based delivery support g=1 for residents of50states/DC; pessimistic .98 allows rare boundary/residence misclassification. Licensee scope is an organizational attribution issue, not foreign health: it is addressed by conservative c and b, not by pretending those US patients live elsewhere. No overseas outcomes are credited.

q = q1 × sum[t=1..T](p^(t−1)/(1.03^t)). N_add = (G/c)×b. Q_all = N_add×(s×q−h). Q_USA = Q_all×g. Price per 10 =10G/Q_USA when Q_USA>0. q1 is a case-mix-average oral pain/function utility gain before alternative care; h is incremental treatment burden/harm for every added case and is not discounted by s.

G

10000 USD normalization (judgment). Arithmetic unit only.

National expense2025

2090255 USD (observed). Net recipient return expense, includes negative technical/administrative reimbursement. [dln-99025]

Group expense2025

3090873 USD (observed). Separate affiliated group return; program expense2621544 and DDS expense2592303. [dln-group25]

DDS annual individuals

4367 individuals (observed). Includes licensee states; served does not establish completed treatment or matched financial scope. [dln-ar25]

c

2000 USD full-support/nominal case (judgment). Approximate national+group expense5181128 divided by all4367 DDS patients is1186, but is not a matched denominator. Choose2000 to allow missing licensee support, clinical completion and nonclinical portfolio costs; range750–3000. Internal reimbursement detail remains unreconciled. Historical partial grant429/patient supports only an optimistic marginal possibility. [dln-99025] [dln-group25] [dln-ar25] [dln-nextfifty]

q1

0.03 utility gain/year per nominal case (judgment). Modest case-mix-average relief of oral pain and eating/function limitation. Not a measured treatment effect. GBD symptomatic severe tooth-loss disability weight.067 is a severity anchor, not a QALY identity; generic utility evidence is weak. Central below that severe profile; range.005–.067, with zero tested. [dental-denture-rct] [dental-welfare] [dental-utility] [dental-implant-rct] [gbd-oral]

p

0.85 annual retained benefit fraction (judgment). 15% annual attenuation for relapse, prosthesis problems, mortality and comparator catch-up; not observed DLN follow-up. [dln-terms]

T

3 years (judgment). Finite horizon, sensitivity1–5; ongoing maintenance not promised. [dln-terms]

b

0.5 additional funded treatment fraction (judgment). National-to-network flow, alternative donors/reserves and volunteer bottleneck discount. Range.2–.85; zero possible. [dln-99025] [dln-group25] [dln-help] [dln-blue26]

s

0.75 counterfactual health additionality (judgment). Benefits must be exhausted but alternative charity care or later care remain possible. Range.4–.9; zero tested. [dln-help]

h

0.001 QALY treatment burden per added case (judgment). Illustrative net short-term discomfort/complications, roughly.365 full-health-equivalent day. Not measured adverse-event rate; higher burden and zero benefit tested. [dln-terms] [dental-implant-rct]

g

1 USA resident benefit share (judgment). Domestic patient program; .98 pessimistic because residence data not published. [dln-help]

discount

0.03 annual (judgment). Analyst convention.

Additional resource cost

2000 USD/added case (judgment). Illustrative clinician/lab opportunity cost plus patient time, not retail donated value; no avoided cost credit.

Cautious oral pain and function judgment: Cost: $10K; USA QALYs: 0.13437144639054402; all-population QALYs: 0.13437144639054402. c=2000; q1=0.03; p=0.85; T=3; b=0.5; s=0.75; h=0.001; g=1; q=0.07299810474162348. Explicit judgment, not measured donor yield.

Efficient coordination of severe otherwise untreated oral disability: Cost: $10K; USA QALYs: 2.5679136215159533; all-population QALYs: 2.5679136215159533. c=750; q1=0.067; p=0.9; T=5; b=0.85; s=0.9; h=0.001; g=1; q=0.25286734851463594. Explicit judgment, not measured donor yield.

Low utility gain and weak additional capacity: Cost: $10K; USA QALYs: 0.0009419417475728158; all-population QALYs: 0.0009611650485436896. c=3000; q1=0.005; p=0.5; T=1; b=0.2; s=0.4; h=0.0005; g=0.98; q=0.004854368932038835. Explicit judgment, not measured donor yield.

No additional treatment capacity: Cost: $10K; USA QALYs: 0; all-population QALYs: 0. b=0: donation replaces existing funding or cannot add volunteer capacity.

Equivalent benefit elsewhere but additional treatment burden: Cost: $10K; USA QALYs: -0.0025; all-population QALYs: -0.0025. Central inputs except s=0; all2.5 added cases retain h=.001. No favorable price.

Central including illustrative noncash and patient resources: Cost: $15K; USA QALYs: 0.13437144639054402; all-population QALYs: 0.13437144639054402. Adds2000 per2.5 additional cases for donated clinical/lab opportunity cost and patient resources. This is an illustrative societal sensitivity, not a measured societal ICER.

Counterfactual: s is the fraction of oral-health benefit not achieved on a similar timeline through insurance, Medicaid, another charity or eventual self-financed care. Benefit-exhaustion eligibility supports high but not complete clinical access additionality. b separately represents the national donation's ability to produce extra network treatment rather than reserves, replacement funding, fixed administration or unfilled volunteer capacity. A shorter wait can provide partial benefit even if treatment eventually occurs elsewhere.

Attribution: Full-support c includes the whole recipient/network support burden rather than cherry-picking donated dentist time as free productivity. b=.5 is a substantial discount for uncertain national-to-affiliate marginal conversion. The model does not attribute all licensee production to the national recipient. q1 already averages severity, incomplete relief and treatment mix; there is no extra arbitrary success multiplier. Counterfactual health and treatment burden are kept separate.

The health utility bridge is an analyst valuation judgment, not measured DLN efficacy or a validated mapping of oral-health scores. External randomized evidence establishes benefit for selected denture patients only. Cost, case mix, clinical utility, alternative treatment and national funding additionality could all change the result by multiples. Scenarios are not confidence intervals; zero and adverse health remain possible. The favorable severity scenario is not the central patient profile.

Sensitivity

• At central c=2000,b=.5,s=.75,h=.001,g=1, achieving$100,000 per 10 requires q≥0.53467 QALY/case; achieving$1million requires q≥0.05467. Central q=.072998 meets the latter but not the former.
• At central health and additionality, maximum full-support cost is about $269 percase for the$100,000 threshold and$2,687 percase for $1million. A partial restricted grant cost is not evidence that these national all-support costs are achievable.
• One-year-only benefit with central q1 lowers q to.029126 and raises price to about $1.92million per 10; durability is a decisive assumption, not a finding.
• If national funding additionality b falls from.5 to.1, price increases fivefold to about $3.72million per 10. An unchanged waiting list cannot identify b.
• An observed year of 4367 patients is not 4367 donor-caused completions. Counting nonclinical outreach or licensee production without its costs would bias price downward.
• Using an additional$2000 of noncash/patient resources per added case increases central cost by50%, to about $1.12million per 10. Donated treatment retail value is not a valid opportunity-cost estimate.
• Zero clinical access additionality retains treatment burden, producing negative modeled health. No prevented deaths from medical clearance, systemic-disease reductions or employment gains rescue this case.

Unresolved inputs

• Consolidated national-plus-group audited cash expense with intercompany reimbursements/eliminations and licensee boundaries reconciled.
• Unique completed clinical cases within exactly that financial scope, including noncompletion, case mix and multi-year treatments.
• Marginal national unrestricted budget translating added dollars into coordinator capacity, volunteer matches and actual added completions; treatment capacity versus waiting-list constraints.
• Baseline and post-treatment generic health utility or credible patient-valued oral-function mapping, with unsuccessful cases and harms included.
• Counterfactual insurance/Medicaid/charity care availability and timing after the required benefits-exhaustion check.
• Duration of pain/function relief, prosthesis use, repeat dental disease and access to maintenance in this older/medically vulnerable population.
• Current unrestricted reserve availability and other grant commitments; audited treatment/opportunity costs rather than donated retail valuations.
• Resident geography and a verified measure of clinical severity among the otherwise undefined medical-clearance category.