A Simulation Model of Consumer Driven

Health Care

Adam C. Powell

HCMG 903

April 12th, 2007

What is Consumer Driven Health Care?

• Consumer Driven Health Care (CDHC) is the pairing of:– A High Deductible Health Plan (HDHP) and– A Health Savings Account (HSA) or– A Health Reimbursement Arrangement (HRA)

• This presentation will not be exploring a CDHC arrangement involving HRAs, as HRAs do not make employees more sensitive to costs than they are under traditional insurance

High Deductible Health Plans (HDHPs)

• A High Deductible Health Plan is legally defined as a plan that has a deductible (in 2007) between:– $1,100 and $5,500 for single individuals– $2,200 and $11,000 for families

• HDHPs have lower premiums than traditional insurance offerings, as the insurer is not liable for the cost of care, up to the deductible

• HDHPs often have little or no coinsurance for in-network care, as if the deductible is reached, it is likely the care the subscriber is receiving is not elective

Health Savings Accounts (HSAs)

– HSAs hold funds to be used for medical expenditures. Their holdings roll over each year.

– Contributions are not subject to income tax, but can only be used to pay for medical expenses

• After age 65, funds can be withdrawn without penalty, although income taxes will apply if the funds are not used for medical purpose

• Funds in HSAs can be invested like funds in IRAs

– The maximum annual contribution to the HSA is the HDHP deductible. The 2007 maximum contribution limit is $2,850 for an individual and $5,650 for a family

Example: CDHC vs. Traditional Insurance

• Assumptions: You spend $200/month ($2,400/year) on healthcare and have actuarially-fair insurance. You start the year with $4,000 in the bank.

• CDHC plan– $1,200 premium– $1,200 deductible– No copay

• Traditional plan– $1,600 premium– $400 deductible– 20% copay

Note that the CDHC plan has a lower premium and higher deductible than the Traditional plan. Also, CDHC plans often have no copay after the deductible is met.

Example: CDHC vs. Traditional Insurance

CDHC Insurance Traditional Insurance

Month Bank Account Health Savings Account Medical Expenses Bank Account Medical Expenses

Dec $4,000.00 $0.00 $0.00 $4,000.00 $0.00

Jan $1,600.00 $1,200.00 $200.00 $2,200.00 $200.00

Feb $1,600.00 $1,000.00 $200.00 $2,000.00 $200.00

Mar $1,600.00 $800.00 $200.00 $1,960.00 $200.00

Apr $1,600.00 $600.00 $200.00 $1,920.00 $200.00

May $1,600.00 $400.00 $200.00 $1,880.00 $200.00

Jun $1,600.00 $200.00 $200.00 $1,840.00 $200.00

Jul $1,600.00 $0.00 $200.00 $1,800.00 $200.00

Aug $1,600.00 $0.00 $200.00 $1,760.00 $200.00

Sep $1,600.00 $0.00 $200.00 $1,720.00 $200.00

Oct $1,600.00 $0.00 $200.00 $1,680.00 $200.00

Nov $1,600.00 $0.00 $200.00 $1,640.00 $200.00

Dec $1,600.00 $0.00 $200.00 $1,600.00 $200.00

What are the advantages of CDHC?

• Lower insurance premiums due to a lack of first-dollar coverage

• A plan structure that discourages unnecessary first-dollar utilization, further reducing premiums

• A plan structure that provides consumers with a strong incentive to choose less costly interventions (generics) over more costly interventions (brand-name drugs) without forcing them to do so through a utilization management system

• Elimination of moral hazard for individuals who do not reach their deductibles (all unspent money in an HSA can be rolled-over into the next year)

The Model

(Derek Zoolander)

Patients

• In my model, I assume that there are essential two types of patients:– Emergency patients

• These consumers are not price-sensitive, as they require urgent care, and likely will reach their deductible anyway. They choose the nearest hospital.

– Non-emergency patients• These consumers seek treatment at hospitals that

offer the best overall value. They prefer hospitals that are both nearby and have low prices.

Hospital Selection Criteria

• Emergency patients– They pick a hospital based on

min(distance)

• Non-emergency patients– They pick a hospital based on

min(hospitalScore)hospitalScore = q * (hospitalDistance / averageHospitalDistance) +

(1-q) * (hospitalPrice / averageHospitalPrice)

q is a weighting constant

Hospitals

• The hospitals in this model set their prices each period based upon their volume of patients in the previous period.

• Hospitals have the following cost, marginal cost, and price functions:

MCmP

xMC

Fxx

xC

*

1)10ln(

100

)10ln(

)ln(100)(

x = patient volume

F = fixed costs of operation

m = markup

The incremental cost of adding a patient decreases with volume, at a decreasing rate.

Closure

• Hospitals begin the simulation with $1,000 of “profit” in their coffers.

• Each year, a hospital recalculates its profitprofitnow = profitlast year + p*x – C(x)

• When profitnow ≤ 0, a hospital closes. After closure, a hospital reports a price, quantity, and profit of 0.

Spatial Orientation of Hospitals

• Hospitals and patients are randomly situated along a line.

• Unlike the firms in the Hotelling Model, hospitals cannot easily relocate in order to increase demand

• Due to zoning and size constraints, it is unlikely that hospitals can optimize their locations

• In the model, a dozen hospitals are initially randomly situated along a line that is 100 units long

H H H H H H H H HH HH

Spatial Orientation of Patients

• In the model, the city contains 5,000 citizens• Each citizen has a probability of becoming ill and

requiring medical care• Each citizen has a probability of requiring

emergency or non-emergency care

H H H H H H H H HH HH

E N

NE

Differences in Hospital Quality

• Two experiments were performed to determine whether subtle differences in hospital quality effected the evolution of the market

• Experiment 1: Uniform Hospitals– When more than one hospital provides a patient with the highest

possible utility, the patient randomly selects one of the hospitals (Hospital0 = Hospital1 = Hospital2)

• Experiment 2: Ranked Hospitals with a Flagship– Hospital0 is considered far superior to the other eleven hospitals;

its distance and price are evaluated as worth 85% of their actual values

– When more than one hospital provides a patient with the highest possible utility, the patient selects the hospital with the lowest index (Hospital0 > Hospital1 > Hospital2)

Input Variables

• For all years:– Iterations (50)– Years (20)– Markup (1.5 or 2.0)– Fixed costs (100)– Starting “profit” (1000)– Weighting constant q (.25 or .50)

q * (hospitalDistance / averageHospitalDistance) + (1-q) * (hospitalPrice / averageHospitalPrice)

– Probability a person is sick (.50)– Probability a person has an emergency (.50)

• For each year– Whether the market is CDHC (TRUE) or not (FALSE)– Whether the simulator sees all hospitals as equal or ordered

The Monte Carlo Method

• Monte Carlo simulations use random numbers and multiple trials to study complex interactions

• The Monte Carlo Method emphasizes the use of random (or pseudorandom) numbers for parameter values

Variables Determined Randomly

• Number generation– A pseudorandom number generator was used to run the

simulation– In each of the variations of the experiment, the pseudorandom

number generator was given the same seed. Thus, while the values assigned to the hospitals and patients vary from iteration to iteration of one trial, they do not vary across trials.

– The pseudorandom number generator provided numbers from a uniform distribution

• Variables determined randomly– Patient

• Emergency / non-emergency• Location• Sick / well

– Hospital• Initial price• Location

Sample of Data CapturedRowID H0profit H1profit H2profit H3profit H4profit H5profit CDHC Iteration Year

1 1095 630 634 914 906 802 TRUE 1 1

2 981 542 561 732 716 679 TRUE 1 2

3 836 466 498 556 552 539 TRUE 1 3

4 685 376 433 369 359 399 TRUE 1 4

5 550 309 358 184 167 236 TRUE 1 5

6 446 228 274 8 -8 126 TRUE 1 6

7 319 165 226 -133 0 142 TRUE 1 7

8 177 110 358 0 0 320 TRUE 1 8

9 49 31 451 0 0 455 TRUE 1 9

10 -65 -25 539 0 0 556 TRUE 1 10

11 0 0 803 0 0 878 TRUE 1 11

12 0 0 1080 0 0 1165 TRUE 1 12

13 0 0 1340 0 0 1449 TRUE 1 13

14 0 0 1609 0 0 1723 TRUE 1 14

15 0 0 1889 0 0 1996 TRUE 1 15

16 0 0 2180 0 0 2257 TRUE 1 16

17 0 0 2413 0 0 2557 TRUE 1 17

18 0 0 2664 0 0 2828 TRUE 1 18

19 0 0 2952 0 0 3110 TRUE 1 19

20 0 0 3222 0 0 3393 TRUE 1 20

Data Captured

• Firm level– Price, quantity, quantity emergency, quantity non-

emergency, and profit

• Market level– Average price, average quantity, average quantity

emergency, average quantity non-emergency, average profit, number of active hospitals, Herfindahl-Hirschman Index (HHI)

• Environmental– Year, status of CDHC (yearly)

Implementation

• An application was written to take the inputs, specified as comma separated value files, run the model on them, and then return the results in a series of comma separated value files.

• Comma separated value files may be opened in Excel, R, and any other tools that can process spreadsheets

• The application was written in the Processing programming language, which runs on top of Java

Results

Experiment 1: Equal Hospitals

Price Over Time

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

Year

Pri

ce

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

Quantity Over Time

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

0 5 10 15 20 25

Year

Qu

anti

ty

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

Profit Over Time

0

500

1000

1500

2000

2500

0 5 10 15 20 25

Year

Pro

fit

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

Number of Hospitals Over Time

0

2

4

6

8

10

12

14

0 5 10 15 20 25

Year

# o

f H

osp

ital

s

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

HHI Over Time

0

500

1000

1500

2000

2500

3000

3500

4000

0 5 10 15 20 25

Year

HH

I

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

Recall:

HHI < 1,000:

Effective or Monopolistic Competition

1,000 < HHI < 1,800:

Monopolistic Competition or Oligopoly

HHI > 1,800:

Oligopoly, Dominant Firm with a Competitive Fringe, or Monopoly

Results

Experiment 2: Ordered Hospitals

Price Over Time

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25

Year

Pri

ce

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

Quantity Over Time

0

5000

10000

15000

20000

25000

0 5 10 15 20 25

Year

Qu

anti

ty

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

Profit Over Time

0

500

1000

1500

2000

2500

3000

0 5 10 15 20 25

Year

Pro

fit

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

Number of Hospitals Over Time

0

2

4

6

8

10

12

14

0 5 10 15 20 25

Year

# o

f H

osp

ital

s

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

HHI Over Time

0

500

1000

1500

2000

2500

3000

3500

4000

4500

0 5 10 15 20 25

Year

HH

I

C m1.5 q.5

C m1.5 q.25

C to NoC m1.5 q.5

C to NoC m1.5 q.25

NoC m1.5

NoC to C m1.5 q.5

NoC to C m1.5 q.25

Recall:

HHI < 1,000:

Effective or Monopolistic Competition

1,000 < HHI < 1,800:

Monopolistic Competition or Oligopoly

HHI > 1,800:

Oligopoly, Dominant Firm with a Competitive Fringe, or Monopoly

Findings

• The impact of changes in plan design is far greater when hospitals are heterogeneous than when they are homogeneous– When faced with homogeneous hospitals, randomly dispersed

consumers either pick the closest hospital (no CDHC), or the hospital with the best distance/price combination (CDHC)

– Although there are economies of scale, in a perfectly random environment, each hospital will receive around the same number of patients on average under both CDHC and no CDHC

– Hospitals in a CDHC market have similar prices as on average each receives about the same volume, and thus achieves about the same economies of scale

Findings

• In the heterogeneous hospital scenario, when patients are more price-sensitive (q=.25), the HHI of the market is the greatest– High price sensitivity makes firms more willing to seek lower

priced hospitals during non-emergency situations– The flagship hospital is always considered to be 15% cheaper in

terms of distance and/or price than an equivalent hospital in the same location

– As a result, the flagship hospital achieves the greatest volume, enabling it to offer a lower price. The lower price leads to it receiving more patient volume, and charging a yet lower price. Eventually, competing hospitals must close, and it is able to grab their market share

– Idiosyncratic differences in initial prices are most strongly propagated under strong CDHC, as consumer-directed patients are more willing to travel to receive a lower price

Findings

• Strong CDHC causes more hospital closure than weak CDHC or no CDHC– Hospitals that had a relatively low volume in

the previous year cannot set prices at a level that will likely attract enough business in the next year to be able to offer competitive prices

– After a year of low volume, under strong CDHC, hospitals are likely to enter a death spiral, unless they have the random luck to receive a lot of emergency patients

Findings

• CDHC increases the profitability of surviving hospitals in a region– If a region has a fixed number of patients and

hospitals close, the remaining hospitals will have to treat a larger quantity of patients

– Although the hospitals will then be able to provide cheaper care (due to the returns to scale), as the marginal cost decreases at a decreasing rate, their change in quantity outweighs their change in price

Limitations

• This model assumes a scenario of market consolidation; no new hospitals ever open

• As hospitals leave the market, hospitals continue to price their services competitively, and are unable to charge monopoly rents

• Hospitals are situated in a non-strategic fashion• The hospitals all compete using the same markup; in a

competitive market, firms would reduce their markup to increase their market share

• The hospitals receive the same payment for emergency and non-emergency care, and their probability of receiving payment for both types of care is the same (100%)

Q & A