Risk Adjustment in Social Health Insurance

1
Risk Adjustment in Social Health Insurance

• European Science Days, Steyr, Austria
• July 18, 2007
• Konstantin Beck website css-institute.chCSS
  Institute for Empirical Health Economics
  Socioeconomic Institute, University of Zurich

2
Managed Competition (Enthoven Plan)

• Mandatory basic package Minimal package of
  services, equal for all consumers
• Periodic open enrollment

Provider
Reimbursing costs (Fee for serviceor capitation)
Free access
Consumer
Insurer
(Flat rate ) premium
Incentive for selection / to expensive for low
income people / in conflict with cost reducing
strategies (MC, deductibles..)
3
Managed Competition (Enthoven Plan)

• Mandatory Basic package Minimal package of
  services, equal for all consumers
• Periodic open enrollment

Provider
Reimbursing costs (Fee for serviceor capitation)
Access
Consumer
Insurer
Flat rate premium or risk rated premiums
Tax money /premium subsidy
Sponsor
4
Managed Competition (Enthoven Plan)

• Mandatory Basic package Minimal package of
  services, equal for all consumers
• Periodic open enrollment

Provider
Reimbursing costs (Fee for serviceor capitation)
Access
Consumer
Insurer
Flat rate premium or risk rated premiums
Tax money /premium subsidy
Risk adjustment (internal system)
Sponsor
Sponsor
5
Managed Competition (Enthoven Plan)

• Mandatory Basic package Minimal package of
  services, equal for all consumers
• Periodic open enrollment

Provider
Reimbursing costs (Fee for serviceor capitation)
Access
Consumer
Insurer
Flat rate premium or risk rated premiums
Tax money /premium subsidy
Sponsor
Risk adjustment (external system)
6
Agenda

• The theory of managed competition
• The theory of risk adjustment
• Switching behavior
• Progress in the empirical research and reform
  models
• Empirical results
• Impact of reforms / total redistributive effect

7
The Theory of Risk Adjustment

• Incentive for risk selection
• Ideal risk adjustment
• Zero sum rule
• Prospective versus retrospective formulas
• Impact of imperfect risk adjustment
• Problem of premium differentiation
• OLS versus cell based approach
• R versus C variables
• Impact of growth and demographic changes

8
An Appropriate RA Scheme Has to Meet the
Following Conditions

• RA has to adjust for risks not for costs
• The RA scheme must not give wrong incentives
  (e.g. reduction of the incentive to economies
  costs)
• The factors of the RA-formula must be resistant
  to manipulation.
• The factors must be effective and sufficient.
• The formula should be simple and transparent.
• The RA calculation itself should be efficient.
• The formula should refer to a market with flat
  rate premiums, or reflect the premium structure
  of the market

9
The Ideal Risk Adjustment
bi is the contribution per risk class i into
RA-fund when negative or from the RA fund, when
positive (E.. stands for expected value C for
costs, EC overall average costs) Given bi
each insurer j is able to calculate its debt or
its contribution (RAj) out of the RA-fund. For
each class i the insurer multiplies its number of
insured within this class (nij) by the
contribution bi.
Zero sum rule
10
The Swiss RA Formula (to Start With)

• Contribution per risk class
• Total payment per insurer

11
A Counter Productive Cost Saving Model
Situation Before Saving Costs
Costs of Good risks bad risks

Cost saving model
Flat rate premium Average costs

Ordinary insurance
12
and After Saving Costs
Costs of Good risks bad risks
Cost saving model
Ordinary insurance
The savings ( ) reduce average costs of
all insured ( ). This reverses the flow of
risk adjustment payments ( ).
13
OLS-Regression and Cell Based Approach
Cell based approach
Proof Beck (2004) Appendix 2.
14
R Versus C Factors

• The insurer should be compensated for cost
  driving influences it cannot be held responsible
  for
• All factors that influence costs can be divided
  into R-variables (insurer is held responsible
  for) and C-variables (insurer is compensated
  for).
• How can we implement this distinction?
• And how do we deal with overlapping risk classes?
  
• Simply omitting R-variables will lead to
  estimation bias!

15
16 Individuals in 4 Risk Classes
16
Overcompensated Insurer

• OLS and cell based approach yield the same result
• Insurer is compensated for all (!) differences in
  expected costs
• OLS gt
• Total redistributed RA-Volume 1722.50

17
Geographic Variable Omitted
18
Biased Estimation

• OLS and cell based approach yield the same result
• Insurer is not compensated for geographic
  differences, but RA estimation is biased, due to
  the negative correlation between region and
  risk-type.
• OLS gt
• Total redistributed RA-Volume only 2.50

19
Simultaneous Estimation with Neutralized Impact
20
Simultaneous Estimation with Neutralized Impact

• Cell based approach is not working (overlapping
  risk groups)
• Insurer is only compensated for cost differences
  it is not held responsible for. OLS estimation is
  unbiased.
• Step 1 OLS gt
• Step 2
• Total redistributed RA-Volume 1151.67

21
Empirical Illustration HCE per Capita and Month
Swiss Basic Insurance
1400
1200
2003 and 1996
1000
800
600
400
200
0
19/25 26/30 31/35 36/40 41/45 46/50 51/55
56/60 61/65 66/70 71/75 76/80 81/85 86/90 91
22
Dynamics of Solidarity in Basic Insurance
0



Annual growth of HCE 5.6, and of transfers
6.8
23
Results of a Total Differential Analysis

• Growth in the number of young people will inflate
  solidarity transfer ? does not happen
• Growth in the number of elderly people will
  reduce solidarity transfer ? happens but
  dominated by 4
• Growth in the HCE of young people will reduce
  solidarity transfer ? happens but dominated by 4
• Growth in the HCE of elderly people will inflate
  solidarity transfer ? dominant influence

24
Agenda

• The theory of managed competition
• The theory of risk adjustment
• Switching behavior
• Progress in the empirical research and reform
  models
• Empirical results
• Impact of reforms / total redistributive effect

25
The Winner in the New Market Will Be the Risk
Selecting Fund
Monthly premium in CHF
not selecting fund
140
118.-
120
100
80
61.-
60
40
selecting fund
20
0
1. year
2. year
3. year
4. year
5. year
Source Beck and Zweifel (Prediction from 1995)
PD Dr. Konstantin Beck
Universität Zürich
26
Reaction of the Market Conglomerates
Middle-Risk-Fund
High-Risk- Fund
Low-Risk- Fund
27
Market Shares of 6 Largest Insurer 1996 to 2006
The really successful insurer is the risk
selecting insurer

• insured

1'400'000
1'200'000
1'000'000
800'000
600'000
400'000
200'000
-
1999
2000
2001
2002
2003
2006
1996
1997
1998
2004
2005
28
Index of Risk Selection
Conglomerate- Premium
( )
Insurer A Insurer B Insurer C
Flat rate premium of the conglomerate weighted
average premium
Index Sum of the blue area within the
conglomerate as percentage of the premium
deviations of the whole market
29
Index of Risk Selection 1997 - 2003

• The index measures the minimum impact risk
  selection has on solidarity

14.7
16.0
14.0
12.2
12.0
10.0
7.2
8.0
5.5
4.9
6.0
4.2
4.0
1.7
2.0
0.0
1997
1998
1999
2000
2001
2002
2003
30
Agenda

• The theory of managed competition
• The theory of risk adjustment
• Switching behavior
• Progress in the empirical research and reform
  models
• Empirical results
• Impact of reforms / total redistributive effect

31
Explanatory Power of HCE-Models (R2)

• Models prior to 1990 1
• Demographic model (year 2000) 10.9
• Region (urban / rural) 11.1
• Prior hospitalization 16.2
• Voluntary deductible 16.8
• Nursing home 22.9
• birth in preceding year (-) 23.2
• prior expenditures (3 preceding years) 46.3
• (Beck, 2004)

32
Predicting HCE of 20 Most Expensive Insured

• Simple average 23.3
• Demographic model (year 2000) 39.9
• Region (urban / rural) 40.2
• Prior hospitalization 45.3
• Voluntary deductible 46.6
• Nursing home 49.3
• birth in preceding year (-) 49.7
• prior expenditures (3 preceding years) 69.3
• (Beck, 2004)

33
Swiss Risk Adjustment Scheme Divides the
Population into 30 Risk Classes
Costs per head and month
700
600
500
400
300
Average
200
100
0















19-
26-
31-
36-
41-
46-
51-
56-
61-
66-
71-
76-
81-
86-
91
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Risk classes according to age and gender
34
Problem with Chronically Ill
AIDS 2'080 Fr./Mon.
From RA 1'900 Fr./Month
A young man with AIDS costs the insurer about
CHF. 2000.-/Mon. In addition payments into the
RA of . A morbidity oriented RA will identify
extreme diagnoses and recompensate them fairly (
)
Costs per head and month
700
600
500
400
300
Average
200
100
0















19-
26-
31-
36-
41-
46-
51-
56-
61-
66-
71-
76-
81-
86-
91
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Risk classes according to age and gender
35
Risk Adjustment with Prior Hospitalization
Divides into 60 Risk Classes (Remaining
Calculation is Similar)
Costs per head and month
700
600
500
400
300
Average
200
100















19-
26-
31-
36-
41-
46-
51-
56-
61-
66-
71-
76-
81-
86-
91
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Risk classes according to age and gender and
prior hospitalization
36
Contributions for 13 Different Most Expensive PCG
CHF per month (1 1.5 CHF)
900
700
500
300
100
Epilepsy
HIV / AIDS
Cardiac disease
Malignancies
Respiratory illness, Asthma
Transplantations
Acid peptic disease
Diabetes insulin-dep.
Parkinson's disease
Renal disease, ESRD
Diabetes non-insulin-dep.
Rheumatologic conditions
Crohn's and ulcerative colitis
0 - 18
19 - 35
36 - 50
51 - 65
66 - 80
81
Age Group
37
Average Costs in an APDRG - Model
3'500
3'000
average costs according to age and gender
2'500
2'000
1'500
1'000
500
-
Contributions to average costs given one or more
of 17 hospital diagnoses, a hospital or nursing
home stay
38
Comparing the Models by Holly et al. (2004)
39
Stability of Coefficients
2001
2000
1999

• SQLape10 1655 321 2867
• SQLape11 1395 443 1302
• SQLape14 -108 -117 -1887

40
Dataflow
Today existing dataflow
Funds
Hospital
Individuals Age, Sex, Costs, Months
Fed. Off. of Statistics Matching calculate
averages
Individual Diagnoses
Grouped and anonymous Info
Office for risk adjustment
41
Spychers Formula with Costs of the Preceding Year
Costs per head for...
insured with precedingcosts below CHF
6000.
insured with precedingcosts above CHF
6000.
19-
25
42
Agenda

• The theory of managed competition
• The theory of risk adjustment
• Switching behavior
• Progress in the empirical research and reform
  models
• Empirical results
• Impact of reforms / total redistributive effect

43
Motivation

• Existing empirical research on risk adjustment
  formulas is focused mainly on short run
  explanatory power
• If profits of risk selection are considered (e.g.
  Shen and Ellis, 2002) the analysis is often
  limited to one year

44
Research Strategy

• Calculation of a five-year Expected Individual
  Profit or
• Loss (based on prior utilization) and
  derivation of a risk
• selection strategy

'97
'98
'99
reality
prediction
Prediction-model
45
The Rational of the Insurer
Calculation for each individual taking prob. of
dying and switching into account
B-customer low profit
A-customer high profit
C-customer Low loss
D-customer high loss
preferred customer
Versicherer verhält sich neutral
unwanted customer
insurer is neutral
46
The Data
47
Compared Risk Adjustment Formulas

• Benchmark calculation with no risk adjustment
• All formulas with age gender as risk factors (
  status quo R2 9 - 11)
• plus pooling of high risks (10 of total HCE)
• plus identifying high risks according to prior
  HCE
• above/below a certain threshold(threshold at
  13333 or 10000 or 6666 or 3333)
• above/below a randomly set threshold
• plus prior hospitalization (R2 18 21)
• plus prior hospitalization and PCGs (R2 30)

48
Five-Year Expected Individual Profits or Losses

• Individual Expected Net Present Value 01.01.2000
  

49
Five-Year Expected Individual Profits or Losses

• Estimation of expected HCE
• - OLS including age, gender, deductible and
  prior utilization 1997- 99
• - High R2 46 /48, prediction considers
  regression to the mean
• Estimation of probability to opt-out
• - Logistic regression including age, contract
  period, amount of
• supplementary coverage and premium relative to
  average premium
• Premiums and RA subsidies are estimated on 2000
  data (more accurate than individual HCE because
  of the Law of Large Numbers)
• Probability of death is provided by the federal
  statistical office

50
Distribution of Expected Individual Profits or
Losses (Sample 2)
Expectation without any RA
Insured
CHF

51
Distribution of Real Individual Profits or Losses
(Sample 2)
Real Profits without any RA
Insured
CHF
52
Distribution of Expected Individual Profits or
Losses (Sample 2)
Expectation with RA based on prior
hospitalization and PCG
Insured
CHF
53
Distribution of Real Individual Profits or Losses
(Sample 2)
Real Profits with RA based on prior
hospitalization and PCG
Insured
CHF
54
Segmentation of the Distribution (Ad hoc
Threshold at CHF 1000 per Year)
Real Profits with RA based on prior
hospitalization and PCG
Insured
C
A
B
D
CHF
0
55
Segmentation
60
No Risk Adjustment
50
Demographic RA
40
Demographic RA prior hospitalization
30
Demographic RA prior hospitalization
Pharmaceutical Cost Groups
20
10
0
A
B
C
D
56
Decreasing Reliability of Prediction
All figures in
PCG
Hospitalization
Demographic
No RA
Category
40.4
27.4
AA
12.0
15.9
7.3
AB
3.0
3.8
12.0
1.5
1.7
1.6
1.8
AC
3.6
AD
3.5
4.4
2.1
20.1
25.8
40.2
56.2
Total
57
Wrongly Categorized A Customers
All figures in
60
50
40
AD
AC
30
AB
AA
20
10
0
plus prior hosp.and PCG
plusprior hosp.
No RA
Demogr. RA
58
Decreasing Reliability of Prediction
59
Wrongly Categorized D Customers
All figures in
25
20
DD
15
DC
DB
10
DA
5
0
plus prior hosp.and PCG
plusprior hosp.
No RA Demographic Hospitalization PCG
No RA
Demogr. RA
60
Impact of Pushing Off D Customers on Premiums
No RA

46
(status quo)
Demographic RA
32
(Bundesrat)
..plus high risk pool
30
.. prior HCE threshold of 13333.- 21
.. prior threshold of 10000.- 19
..prior hospitalization
19
(Ständerat)
..randomly set threshold 17.5
.. threshold of 6666 16
(Ständerat plus)
..plus hosp. PCG 16
.. threshold of 3333 14
(Benchmark)
Managed Care
25
0
5
15
25
35
45
61
Impact of Selectively Enrolling A Customers on
Premiums (x 4)
No RA

41
(status quo)
Demographic RA
32
(Bundesrat)
..plus high risk pool
31
..plus prior HCE ( 133333.-)
23
..threshold of ( 10000.-)
21
..threshold randomly set 18
..threshold ( 6666) 17
(Ständerat)
..prior hospitalization 15
(Ständerat plus)
..plus PCG 14
..thresh. (3333) 10
(Reference)
Managed Care
25
0
5
15
25
35
45
62
Impact of Selectively Enrolling A Customers
63
Characterizing A and D Type Insured Comparing
Average HCE per Month (Real Values 2000 2004)
64
Conclusions

• Improved risk adjustment reduces the share of
  desired and not desired customers in a long term
  prospect.
• makes identification of desired and not desired
  customers more risky itself. The probability of
  wrong decisions increases.
• reduces the impact selection has on premiums
  and makes managed care a comparably better
  option.
• Even pragmatic formulas as taking prior
  hospitalization into account, improve the
  effectiveness substantially

65
Redistribution of HCE Through Flat Rate Premium
1.) Beck/Trottmann (2007) 2.) According RA
statistic3.) According to Zweifel/Eugster/Sennhau
ser (2007)