This document summarizes a theoretical model that examines the role of reimbursement systems on the rate of technology adoption by healthcare providers. The model considers an uncertain demand for healthcare services and a technological shift that provides increased benefits to patients. It analyzes how different reimbursement schemes, including cost reimbursement and DRG payment systems, impact a hospital's decision to adopt a new technology. The conclusions indicate that cost reimbursement can lead to higher adoption rates if reimbursement levels are high relative to the costs of the new technology. Discriminatory DRG payments that reimburse the new technology differently can also encourage adoption.

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
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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.
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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.
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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
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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)
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