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Decision Trees. Farrokh Alemi, Ph.D. Coming Up. How to construct a decision tree? Components of a tree Interviewing decision makers How to analyze a decision tree? Mathematical expectations. Folding back . Example.

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decision trees

Decision Trees

Farrokh Alemi, Ph.D.

coming up
Coming Up
  • How to construct a decision tree?
    • Components of a tree
    • Interviewing decision makers
  • How to analyze a decision tree?
    • Mathematical expectations.
    • Folding back
example
Example
  • A preferred provider organization (PPO) has approached the benefit manager of a company of 992 employees.
  • The PPO offered to discount hospitalization services by 6% and outpatient services by 15% if the company would remove co-payments for employees utilizing the PPO
components of a tree
Components of a Tree
  • Decision
    • Square node, two arcs and options
  • Sequence of events
    • Circle node, arcs and events
    • Probabilities
  • Consequences
    • Utilities or costs
slide5

Decision

Join PPO

Continue as is

slide6

Decision

Events

P2

Hospitalized

Hospitalized

Join PPO

Clinic visit

P1

P3

Not hospitalized

Not hospitalized

No visit

P5

Hospitalized

Clinic visit

P4

Continue as is

Not hospitalized

P6

Hospitalized

No visit

Time

Not hospitalized

slide7

Decision

Events

Consequences

P2

C1

C1

Hospitalized

Hospitalized

Join PPO

C2

C2

Clinic visit

P1

P3

C3

C3

Not hospitalized

Not hospitalized

0

0

No visit

P5

Hospitalized

Clinic visit

P4

Continue as is

Not hospitalized

P6

Hospitalized

No visit

Time

Not hospitalized

the analysis process matters
The Analysis Process Matters
  • It informs that a decision is looming
  • Reassures that the analysis is fair
  • It removes decision makers from day-to-day concerns
  • It provides new insights while facilitating discussion
process
Process
  • Interview decision makers and construct a preliminary tree
  • Present tree and show how various concerns are captured
  • Solicit a list of new concerns
  • Revise tree
new concerns
New Concerns
  • Separate general outpatient care from mental health care
  • Focus on employees who file claims
  • The PPO clinic might have less efficient practices
  • Lower co-pay may lead to over utilization
  • Group practices are more efficient than solo practices
  • Clinicians may generate their own demand
  • Show discounts
slide11

Cost to

employer

P2

Hospitalized

C1

Meets deductible

P4

Clinic visit

C2

P1

P3

Outpatient visit

Join PPO

P5

Mental health visit

C3

Claims Less than deductible

0

P7

Hospitalized

C4

Meets deductible

P9

Clinic visit

C5

P6

P8

Outpatient visit

Continue as is

P10

Mental health visit

C6

Claims Less than deductible

0

estimating costs
Estimating Costs
  • Review of cases at the employer site
    • Average cost of the sample
  • Review of cases at the PPO
    • Adjusted for case mix difference (PPO patients 30% sicker)
slide14

.46

Hospitalized

.94 *4,796 / 1.3

Meets deductible

Clinic visit

.98

.85 *1085

.37

.83

Outpatient visit

Join PPO

.05

Mental health visit

.85 * 252

Claims Less than deductible

0

.44

Hospitalized

7,549

Meets deductible

Clinic visit

.98

.80 *1009

.37

.81

Outpatient visit

Continue as is

.05

Mental health visit

.80 * 240

Claims Less than deductible

0

analysis of trees
Analysis of Trees
  • Folding back
    • Replace a node with its expectation
  • Continue until the decision node
slide16

1

.44

Hospitalized

7,549

Meets deductible

.98 * $807.2 + .05 *$192 = $800.66

.37

.81

Outpatient visit

Continue as is

Claims Less than deductible

0

.44 * $7,549 + .81 * $800.66 = $3,970.09

2

Meets deductible

.37

Continue as is

Claims Less than deductible

0

3

.37 * $3,970.09 + .63 * 0 =$1,468.94

Continue as is

net impact
Net Impact
  • Expect cost under continue:
  • Expected cost after joining PPO: $871.08
  • Savings per family per year: $597.86
  • Sensitivity analysis
    • Not sensitive to 5% changes in hospitalization rate
    • Not sensitive to 5% changes in clinic visit rate
    • Sensitive to changes in calculation of cost of hospitalization and case mix differences
myth of analysis
Myth of Analysis
  • All options are depicted
    • Wait for a better offer
  • All consequences are enumerated
    • Other health care organizations were on the board of the employer
    • Assess utilities and fold back using expected utilities
  • Data are valid
    • Sensitivity analysis: see if small differences in estimates will change conclusions
make your own
Make Your Own
  • Think through what is the unit of analysis (who decides)
  • Start with the decision
  • Think through possible events and consequences
  • Think through issues that should be captured
  • Make a draft
  • Revise to incorporate new issues