Factored stochastic tree modeling for medical decision making

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Factored stochastic tree modeling for medical
decision making

• Gordon Hazen
• Northwestern University
• Rowland Chang
• Northwestern University
• James Pellissier
• Loyola University/Merck Pharmaceuticals

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Outline of talk

• What is a stochastic tree?
• Basic concepts..
• Stochastic tree transformation and rollback.
• Approximating human survival.
• Factoring out mortality..
• Factoring stochastic trees.
• Discounting / Risk aversion.
• Influence diagrams for stochastic models
• Our THA model...
• The StoTree modeling environment.
• Cost-effectiveness for THA..

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What is a stochastic tree?

• A stochastic tree is
• A decision tree with stochastic nodes added
• A continuous-time Markov chain with chance and
  decision nodes added
• A multi-state DEALE model
• A continuous-time version of a Markov cycle tree

Stochastic Trees
Decision Trees
Continuous-time MCs
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What is a stochastic tree?
Matchar Pauker (1986) Transient ischemic
attacks in a man with coronary artery disease
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What is a stochastic tree?
Roach et al. (1988) Prostate cancer in a man
with asymptomatic HIV
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Markovcycletree
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Transforming stochastic trees

• Superposition / Decomposition

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Transforming stochastic trees

• Eliminating self-transitions

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Transforming stochastic trees
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Stochastic tree rollback

v(x) Quality rate at x L(x) Mean
quality-adjusted duration beginning at
x Recursive formula
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Stochastic tree rollback
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Approximating human survival
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Coxian approximation to human mortality
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Coxian approximation to human mortality
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Factoring out mortality
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Factoring out mortality
Background mortality
Stroke morbidity
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Factoring out mortality
Background mortality
Stroke morbidity
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Equivalent product tree
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Rollback with Coxian mortality
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Factored stochastic trees
Cancer
AIDS
Background mortality
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Factoring stochastic trees
Tsevat et al. (1986) Warfarin for dilated
cardiomyopathy

• Systemic embolism

Pulmonary embolism
Systemic hemorrhage
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Discounting / Risk aversion

• Utility function yielding quality-adjusted
  duration

• Utility function yielding discounted
  quality-adjusted duration

• Rollback with discounting

G
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Modeling risk attitude
Vaccine scenario What chance p of immediate
death would you take to reduce your ongoing
mortality rate by a percentage c?

Undiscounted quality-adjusted duration forces p
c
Discounted quality-adjusted duration allows p lt c
(risk aversion)
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Continuous-risk utility assessment
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Influence diagrams
Decision tree
Influence diagram
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Influence diagrams with stochastic nodes
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THA model
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ACR functional status
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THA vs. Conservative Management
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ACR Functional Status / Initial THA Outcome
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Prosthesis Status After THA
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Last Surgery
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Conservative Management
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The StoTree modeling environment
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StoTree modeling environment
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...StoTree modeling environment
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Rollback in the THA model
85-year-old white male
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Cost-effectiveness for THA
85-year-old white male
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THA Cost-Effectiveness Results