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Xavier Martinez-Giralt

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  • 1. Technology adoption in health care Pedro Pita Barros Universidade Nova de Lisboa and CEPR ppbarros@fe.unl.pt and Xavier Martinez-Giralt Institut d’An` lisi Econ` mica, CSIC and a o Universitat Aut` noma de Barcelona o xavier.martinez.giralt@uab.es AES, Valencia - June 2010 – p.1/21
  • 2. Introduction Motivation General consensus: tech develop primer driver HC expenses → adoption; New techs spread with different rhythms in HC sector → diffusion Literature Empirical literature: Vast documentation of impact of innovation on HC expenditure Theoretical literature: very scarce Aim of the paper Provide a theoretical model to study the role of reimbursement systems on the rate of technology adoption by providers in HC. AES, Valencia - June 2010 – p.2/21
  • 3. Theoretical literature Tech innovation on health insurance market: Goddeeris (1984a,b), Baumgardner (1991), Selder (2005) Feed-back effects between HC and R&D sectors: Miraldo (2007) Tech diffusion, network externalities, oligopoly & DRG: Grebel and Wilfer (2010) Tech adoption & payment system: THIS PAPER AES, Valencia - June 2010 – p.3/21
  • 4. Our model: General overview Elements of the model model of uncertain demand technological shift driven by the increased benefit for patients, financial variables, and the reimbursement system to providers. Objective: assess the impact of the payment system to providers on the rate of technology adoption. Payment schemes: Cost reimbursement according to the cost of treating patients, DRG payment system where the new technology may or may not be reimbursed differently from the old technology. DRG: patient class. system relating types of patients (given by common demographic and therapeutical attributes) to costs incurred by hospital. AES, Valencia - June 2010 – p.4/21
  • 5. Our model: Conclusions Role of patients’ benefits CR&DRGhom: large enough patient benefits are necessary for adoption to occur DRGhet: with discriminatory reimbursement, adoption occurs even in the absence of patients’ benefits CR vs. DRG CR leads to higher adoption of the new technology if the rate of reimbursement is high relative to the margin of new vs. old DRG. Whenever adoption occurs under both regimes, larger patient benefits favors more adoption under CR AES, Valencia - June 2010 – p.5/21
  • 6. Notation and assumptions Semi-altruistic hospital U (R, B) = V (R) + B net revenues: V (·), V ′ (·) > 0, V ′′ (·) < 0 patients’ benefits (B ) Population of individuals: q ∗ Uncertain number of patients treated q; F (q), f (q) ∈ [0, q ∗ ] Hospital 2 tech: new, old new tech capacity q patients ¯ cost per unit of capacity p marginal cost per patient treated θ old tech treats remaining q − q (when positive) ¯ marginal cost per patient treated c p + θ > c [new tech not cost saver; driver of cost inflation] AES, Valencia - June 2010 – p.6/21
  • 7. Notation and assumptions (2) Hospital reimbursement R: prospective, retrospective, mixed 2 payment systems total cost reimb; partial cost reimb; fixed fee/capitation DRG patients’ benefits new tech: b old tech: ˆ b b > ˆ b > p + θ; ˆ > c b; b new tech approval [HTA]: b − ˆ > p + θ − c > 0 b AES, Valencia - June 2010 – p.7/21
  • 8. Hospital’s expected welfare (W ) Sum of: Valuation of financial results profits from patients treated with new tech q ¯ 0 V (R − p¯ − θq)f (q)dq q profits from patients treated with old tech q∗ q V (R − p¯ − θ q − c(q − q ))f (q)dq ¯ q ¯ ¯ Valuation of patients’ benefits benefits to patients treated with new tech q ¯ 0 bqf (q)dq benefits to patients treated with old tech q∗ q ¯ (q − q )ˆ + q b f (q)dq ¯b ¯ Hospital’s problem: choice of q ¯ AES, Valencia - June 2010 – p.8/21
  • 9. Tech Adoption under cost reimbursement Cost reimbursement system R = α + βT C T C ≡ total cost α > 0 fixed component β ∈ [0, 1] cost sharing component β = 0 means capitation Total cost p¯ + θq q if q ≤ q ¯ TC = p¯ + θq + c(q − q ) q ¯ ¯ if q > q ¯ AES, Valencia - June 2010 – p.9/21
  • 10. Tech Adoption under cost reimbursement (2) Notation ∆ ≡ b − ˆ incremental patients’ benefits w/ new tech. b R1 (q) ≡ α − (1 − β)(p¯ + θq) net revenues if q < q . q ¯ R2 (q) ≡ α − (1 − β)(p¯ + θq + c(q − q )) net revenues if q > q . q ¯ ¯ ¯ H’s welfare function q ¯ q∗ W =b qf (q)dq + (q − q )ˆ + q b f (q)dq ¯b ¯ 0 q ¯ q ¯ q∗ + V R1 (q) f (q)dq + V R2 (q) f (q)dq 0 q ¯ H’s problem: maxq W ¯ AES, Valencia - June 2010 – p.10/21
  • 11. Tech Adoption under cost reimbursement (3) Proposition Full adoption is never optimal for the provider. Patients’ benefits above a threshold ensure positive adoption for every level of reimbursement. Proof ∂W q∗ q ′ ¯ ∂q ¯ =∆ q ¯ f (q)dq − (1 − β)p0 V (R1 (q))f (q)dq q∗ ′ −(1 − β)(p + θ − c) q V (R2 (q))f (q)dq = 0. ¯ For q → q ∗ , f.o.c. is negative. Therefore, q < q ∗ . ¯ ¯ Let q = 0. Then, f.o.c. reduces to ¯ q∗ ′ ∆ − (1 − β)(p + θ − c) 0 V (R2 (q))f (q)dq > 0 for β suff. high. Or equivalently, for each ∆ there is a critical β such that q > 0. ¯ AES, Valencia - June 2010 – p.11/21
  • 12. Tech Adoption under cost reimbursement (4) Intuition first term is marginal gain from treating one additional patient with the new technology when q > q .¯ other terms are the marginal cost of treating an extra patient with the new technology. Remark 1 Assumption p + θ > c and common reimbursement for both technologies yield that patients’ benefits are necessary for adoption. Given p + θ > c, if ∆ = 0, f.o.c. is always negative. Therefore, q = 0. ¯ AES, Valencia - June 2010 – p.12/21
  • 13. Comparative statics w.r.t α and β Concavity of V and assumption p + θ − c > 0 yield: d¯ q ∂2W sign dβ= sign ∂ q∂β ¯ >0 increasing cost-sharing leads to more adoption. d¯ q ∂2W sign dα= sign ∂ q∂α ¯ >0 Higher α means lower mg cost of investing more (in utility terms). For the same benefit, more investment will result. Remark 4 Under risk neutrality, adoption insensitive to α. Then, cost-sharing only instrument of payment system to affect technology adoption. Summarizing Higher transfers lead to higher levels of adoption by hospital because ↑ patients’ benefits (∆) are assumed to offset ↑ mg cost (p + θ − c), [HTA] AES, Valencia - June 2010 – p.13/21
  • 14. Comparative statics w.r.t dR = 0 ⋆ Trade-off between α and β with risk aversion Computing dR = 0, and totally differentiating f.o.c. yield ambiguous result. Solution is: d¯ q d¯ q dβ = Υ−ΛΦ and dα = − ΛΨ+ΓΥ Ψ+ΓΦ Υ−ΛΦ If properties of V (·) are s.t. Υ/Φ > Λ, then d¯/dβ > 0, d¯/dα < 0. q q BUT = hospitals, = properties of V (·). Issue behind difficulties to interpret empirical work on tech adoption. ⋆ Trade-off between α and β with risk neutrality Computing dR = 0, and totally differentiating f.o.c. dα + Γd¯ + Λdβ = 0 ⇒ α adjusts q ′ −Ψ d¯ + Υ′ dβ = 0 ⇒ d¯/dβ > 0. q q ⋆ Impact on welfare: dW = ∂W dR + ∂W d¯ = 0 ∂R ∂q q ¯ ⋆ Summary: [1.] ↑ β, ↑ q because ↑ patients’ benefits. ¯ [2.] Given dR = 0, ↑ β requires ↓ α , and [3.] given dW = 0, ↑ patient’s benefits, ↓ hosp. surplus. AES, Valencia - June 2010 – p.14/21
  • 15. Tech Adoption under DRG payment Types of DRG reimbursement Homogenous DRG reimbursement: Hospital receives same reimbursement under both technologies, i.e. technology used does not change DRG R = Kq Heterogenous DRG reimbursement: New technology leads to coding sickness in a different DRG, and receives different reimbursement. K1 q if new tech R= K2 q if old tech and K1 > K2 . AES, Valencia - June 2010 – p.15/21
  • 16. Heterogenous DRG payment Notation ∆ ≡ b − ˆ incremental patients’ benefits w/ new tech. b R5 (q) ≡ K1 q − p¯ − θq net revenues if q < q . q ¯ R6 (q) ≡ K1 q + K2 (q − q ) − p¯ − θq − c(q − q ) net revenues if ¯ ¯ q ¯ ¯ q > q. ¯ Assumption: K1 − p + θ > K2 − c, i.e. margin with new tech. larger than margin with old tech. H’s welfare function q ¯ q∗ W =b qf (q)dq + (q − q )ˆ + q b f (q)dq ¯b ¯ 0 q ¯ q ¯ q∗ + V R5 (q) f (q)dq + V R6 (q) f (q)dq 0 q ¯ AES, Valencia - June 2010 – p.16/21
  • 17. Heterogenous DRG payment (2) Proposition Full adoption is never optimal for the provider. Assumption K1 − K2 − (p + θ − c) > 0 sufficient for adoption even under absence of patients’ benefits. Proof ∂W q∗ ∂q ¯ =∆ q ¯ f (q)dq + V (R5 (¯)) − V (R6 (¯)) f (¯) q q q q ′ ¯ q∗ −p 0 V (R5 (q))f (q)dq+(K1 −K2 −p−θ+c) q ¯ V ′ (R6 (q))f (q)dq = 0. For q → q ∗ , f.o.c. is negative. Therefore, q < q ∗ . ¯ ¯ Let ∆ = 0. Then, ∃ parameter values satisfying f.o.c. AES, Valencia - June 2010 – p.17/21
  • 18. Heterogenous DRG payment (4) s.o.c. imply q < 1 ¯ Assumption K1 − K2 − (p + θ − c) > 0 is sufficient to achieve optimal adoption. Not necessary if ∆ large enough. Patients’ benefits are not necessary for adoption as long as assumption K1 − K2 − (p + θ − c) > 0 holds. Patients’ benefits are necessary for adoption when assumption K1 − K2 − (p + θ − c) > 0 does not hold. Patients’ benefits raises adoption rate. Adoption may even take place when assessment criterion goes against new tech approval (i.e. ∆ < p + θ − c), but K1 − K2 sufficiently large. AES, Valencia - June 2010 – p.18/21
  • 19. Comparing payment regimes Assume V ′ (·) = 1, unif. distr., q ∗ = 1, and λ ≡ K1 − K2 . ¯drg ¯dgr qhom < qhet ¯drg qhom < q cr ¯ ¯drg q cr ≶ qhet ¯ ¯ q 0 ¯drg qhom ¯drg qhet 1 β λ≷∆ q cr ¯ 1−β AES, Valencia - June 2010 – p.19/21
  • 20. Comparing payment regimes (2) λ β (∆, θ, c) given λ=∆ 1−β DRG ↑∆ adopts more CR adopts more 0 β 1 Optimal adoption: CR vs. heterogenous DRG. AES, Valencia - June 2010 – p.20/21
  • 21. Caveats 1. On assumptions HTA criterion for new tech. approval: ∆ > p + θ − c > 0 hospital can treat all patients. Only decision is capacity q ¯ no capacity constraints. individuals fully insured single sickness (single technology) AES, Valencia - June 2010 – p.21/21

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