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 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 Decision –Square node, two arcs and options Sequence of events –Circle node, arcs and events –Probabilities Consequences –Utilities or costs

Continue as is Join PPO Decision

Continue as is Join PPO Hospitalized Not hospitalized Hospitalized Not hospitalized Clinic visit No visit P1P1 P2P2 P3P3 Hospitalized Not hospitalized Hospitalized Not hospitalized Clinic visit No visit P4P4 P5P5 P6P6 Events Time Decision

Continue as is Join PPO P3P3 P2P2 Hospitalized Not hospitalized Hospitalized Not hospitalized Clinic visit No visit P1P1 Clinic visit No visit P4P4 Hospitalized Not hospitalized P5P5 Hospitalized Not hospitalized P6P6 Events Time DecisionConsequences C1C1 C3C3 0 C2C2 C1C1 C3C3 0 C2C2

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 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 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

Continue as is Join PPO Clinic visit P2P2 Hospitalized Mental health visit Outpatient visit Meets deductible Claims Less than deductible P1P1 C1C1 C3C3 0 C2C2 P3P3 P4P4 P5P5 Clinic visit P7P7 Hospitalized Mental health visit Outpatient visit Meets deductible Claims Less than deductible P6P6 C4C4 C6C6 0 C5C5 P8P8 P9P9 P 10 Cost to employer

Estimating Probabilities from Data, Experts & Literature

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)

Continue as is Join PPO Clinic visit.46 Hospitalized Mental health visit Outpatient visit Meets deductible Claims Less than deductible *4,796 / * * Clinic visit.44 Hospitalized Mental health visit Outpatient visit Meets deductible Claims Less than deductible.37 7, * *

Analysis of Trees Folding back –Replace a node with its expectation Continue until the decision node

Continue as is.44 Hospitalized Outpatient visit Meets deductible Claims Less than deductible.37 7, * $ *$192 = $ Continue as is Meets deductible Claims Less than deductible * $7, * $ = $3, Continue as is.37 * $3, * 0 =$1,468.94

Net Impact Expect cost under continue: Expected cost after joining PPO: $ Savings per family per year: $ 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 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 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