DECISION ANALYSIS

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DECISION ANALYSIS

• Richard E. Hughes, Ph.D.
• Orthopaedic Surgery

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C-SPINE IMAGING

• Cervical spine evaluation
• Radiograph vs. CT
• CT costs more
• CT better
• Which is less costly overall, x-ray or CT?

Grogan et al. (2005) J. Am Coll. Surg.
200(2)160-165
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IMPORTANCE OF DECISION ANALYSIS

• Rigorous clinical decision making
• Health policy

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IMPORTANCE OF DECISION ANALYSIS

• Rigorous clinical decision making
• Health policy
• Reimbursement

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DECISION ANALYSIS IN ORTHOPAEDICS

• ACL reconstruction (Gottlob et al. 1999)
• Patella resurfacing in TKA (Zanger and Detsky,
  2000)
• Bankart reconstruction (Kailes and Richmond,
  2001)
• Acute Achilles tendon rupture (Kocher et al.,
  2002)
• Prophylactic pinning of the hip (Schultz et al.,
  2005)

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HISTORY OF DECISION ANALYSIS

• von Neumann and Morgenstern, Theory of Games and
  Economic Behavior, 1944
• Operations research
• Weinstein and Fineberg, Clinical Decision
  Analysis, 1980

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HISTORY OF DECISION ANALYSIS

• von Neumann and Morgenstern, Theory of Games and
  Economic Behavior, 1944
• Operations research
• Weinstein and Fineberg, Clinical Decision
  Analysis, 1980

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C-SPINE DECISION TREE
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WAGER EXAMPLE

• You have a choice of two options
• A Choose 10 with certainty
• B Bet 21 on heads in a fair coin toss
• Which yields the highest expected gain?

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PROBABILITY

• Consider event E
• PEProbability of event E happening
• Example
• Eroll of a six-sided die yields 2
• PE1/6

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EXPECTED VALUE

• Probability of an event times value of event
• Example
• Expected value of the roll of a six-sided die
• (1/6)x1 (1/6)x2 (1/6)x63.5
• In long run, expected value estimates the mean

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CONDITIONAL PROBABILITY

• PEAProbability of event E happening given A
• Example
• Probability that the sum of two die is 3 given
  the first die was 1
• Eevent that sum of two dice is 3
• Aevent that first die was a 2
• Psum of two dice3first die2 PEA 1/6

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SENSITIVITY
SensitivityP test disease TP / (TPFN)
DISEASE STATUS

-
TP
FP

TEST RESULT
-
FN
TN
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SPECIFICITY
SensitivityP- test - disease TN / (FPTN)
DISEASE STATUS

-
TP
FP

TEST RESULT
-
FN
TN
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DECISION ANALYSIS FORMULATION

• Identify and bound problem
• Structure problem (decision tree)
• Decision notes ( )
• Chance notes ( )
• Outcome nodes ( )
• Note not chronological
• Gathering data
• Analyzing decision tree
• Sensitivity analysis

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WAGER DECISION TREE
10
A
Heads
21
Pheads.5
B
Tails
0
Ptails.5
Outcome (utility)
Decision
Coin flip
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BACKWARD INDUCTION
10
A
B
Expected value0.5x21 0.5x011.5
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BACKWARD INDUCTION
10
A
B
Expected value0.5x21 0.5x011.5
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BACKWARD INDUCTION
B
Expected value0.5x21 0.5x011.5
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WAGER DECISION TREE MY VIEWPOINT
-10
A
Heads
-21
Pheads.5
B
Tails
0
Ptails.5
Outcome (utility)
Decision
Coin flip
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C-SPINE DECISION TREE
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C-SPINE DECISION TREE
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RADIOGRAPH AND FRACTURE
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RADIOGRAPH AND FRACTURE
Pfracture
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RADIOGRAPH AND FRACTURE
P radiograph fracture Sensitivity
Pfracture
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RADIOGRAPH AND FRACTURE
P radiograph fracture Sensitivity
Pfracture
P- radiograph fracture 1-P radiograph
fracture 1 - Sensitivity
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RADIOGRAPH AND FRACTURE
P radiograph fracture Sensitivity
Pparalysis
Pfracture
P- radiograph fracture 1-P radiograph
fracture 1 - Sensitivity
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RADIOGRAPH AND FRACTURE
P radiograph fracture Sensitivity
Pparalysis
Pfracture
P- radiograph fracture 1-P radiograph
fracture 1 - Sensitivity
Pno paralysis 1-Pparalysis
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C-SPINE DECISION TREE
2,142
554
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MODEL PARAMETERS

• Probability of fracture
• Sensitivity of radiograph
• Specificity of radiograph
• Sensitivity of CT scan
• Specificity of CT scan
• Probability of paralysis
• Cost of CT scan
• Cost of radiograph
• Cost of paralysis

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META-ANALYSIS

• Combine results of previous studies to
  systematically make conclusions about a body or
  research
• Used to estimate probabilities and utilities
• Widely used
• Not a substitute for good studies

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MODEL PARAMETERS
VARIABLE
LIT. RANGE
SIM. RANGE

• Probability of fracture 4-11.5 0-15
• Sensitivity of radiograph 44-84 0-100
• Specificity of radiograph 72-89 0-100
• Sensitivity of CT scan 95-97 0-100
• Specificity of CT scan 93-100 0-100
• Probability of paralysis 0-29 0-29
• Cost of CT scan NA 0-3k
• Cost of radiograph NA 0-3k
• Cost of paralysis 0-800k 0-1M

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SENSITIVITY ANALYSIS
Grogan et al. (2005) J. Am Coll. Surg.
200(2)160-165
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COST-EFFECTIVENESS ANALYSIS (CEA)

• Uses decision analysis to compare
  cost-effectiveness of treatments
• Compares alternative treatments
• Compares treatment to no treatment

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OUTCOME IN CEA

• Mortality - life expectancy
• Morbidity utility measure
• Utility is decision analysis term
• Quality adjusted life year (QALY) combines
  expected survival and quality of life
• Subjective measurement (Quality of Well Being
  scale, SF-36, etc.)

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C-SPINE CEA
/QALY outcome
CT more cost-effective for high risk patients
Blackmore, C.C. et al. (1999) Radiology
212117-125.
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CRITICISMS OF DECISION ANALYSIS AND CEA

• Utility
• Health-related quality of life (QALY)
• Discounting future costs
• Ignores risk preferences and utilities of
  individual patients
• Does not solve ethical issues
• Used by payors to limit procedures

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CEA FOR ORTHOPAEDICS
Treatment Comparison /QALY Endoscopic CTS
release Open CTS release 220-1100 THA No
treatment 4,300 ACL (patellar tendon graft) No
treatment 6,500 Hormone replacement therapy No
treatment 840,000 in 50 year old female
with average risk of hip fracture
Source The CEA Registry, Harvard School of
Public Health
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SUMMARY

• Decision Analysis
• Increasing use in medicine
• Part of evidence-based medicine
• Framework for cost-effectiveness studies
• Cost-effectiveness analysis (CEA)
• Used by payors
• Learn to use it or it will use you

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THANK YOU
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PROBABILITY OF NOT

• PEprobability of E
• Pnot E1-PE
• Example
• Eevent that my kid grows up to be taller than
  Scott Kaars. PE0.0001
• Pmy kid does not grow up to be taller than
  Scotts Pmy
  kid grows up to be shorter than Scotts 1-PE
  0.9999