An Introduction to Decision Analysis

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An Introduction to Decision Analysis

• Adam Rothschild, M.D.
• DBMI Intensive Course
• 25 May 2005

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Agenda

• Brief lecture on decision analysis
• What is it?
• When is it useful?
• How you do it?
• Hands-on decision analysis exercise
• Analyze the treatment decision in your breast
  cancer case study
• Use TreeAge software to build decision tree model

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What is decision analysis?

• Decision analysis is
• Fun and easy!
• A formal process that yields a quantitative model
  for decision making under conditions of
  uncertainty
• What is a model? A simplified representation of a
  real-world situation
• What is uncertainty? Well, I dont know...
• When does one have to make decisions under
  conditions of uncertainty? Nearly always!

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Decisions under uncertainty examples

• Everyday examples
• How should I travel downtown this evening (e.g.,
  drive or take the subway)?
• What career path should I take (e.g., law school,
  medical school, investment banking)?
• Should I play the lottery today?
• Medical examples
• What is the best test to diagnose this patient?
• What is the best treatment option for this
  patient?

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The difference between decisions and outcomes

• Bad decision, good outcome
• Decision spending 1 to play the lottery
• Outcome winning 10,000,000
• Good decision, bad outcome
• Decision not buying the extended warranty on DVD
  player
• Outcome DVD player breaks right after regular
  warranty expires

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Why use decision analysis?

• It helps you make good decisions
• What is a good decision?
• One that maximizes the expected utility
• What is expected utility?
• Utility the value of a particular outcome
• Expected the probability of achieving that
  outcome under particular circumstances
• Expected utility utility(outcome) x
  probability(outcome)
• This is the essence of decision analysis!

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Decisions, outcomes and utilities

• Decision Should I drive to work or take the bus?
• Possible outcomes
• Arrive at work early
• Arrive at work on-time
• Arrive at work late
• Utility
• time
• money

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The basic pieces of a decision model

• Decision to be made
• Possible outcomes
• Probabilities of the outcomes
• Utilities of the outcomes (if the outcomes are
  terminal)
• The structure of the model (i.e., how the various
  outcomes are connected to the decision and the
  other outcomes)

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A simple decision tree

• Scenario You are trying to decide whether to buy
  a scratch-off lottery ticket.
• It costs 1 to play.
• If you play, you have a 1 in 1000 chance of
  winning.
• The prize for winning is 1000.
• If you lose, you get nothing and are out the
  dollar you paid to buy the ticket.

possible outcomes
utilities of outcomes
probabilities of outcomes
decision to be made
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Probabilities

• Probability is the chance of an event occurring
• Probabilities in decision analysis are derived
  from empiric data where possible (e.g., published
  literature, local databases) and estimations
  where necessary

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Outcomes

• Outcomes in decision analysis are essentially
  anything that can happen
• Outcomes can be terminal or non-terminal
• Only include outcomes in your model that are
  relevant

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Utility

• Definition quantitative measure of the strength
  of a persons preference for an outcome
• Remember goal of a decision is to maximize
  utility (or minimize disutility)
• Common measures of utility
• Money
• Time
• A given decision can involve more than 1
  attribute of utility

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Utility in medicine

• Medical decisions frequently require more complex
  measures of utility because of multiple
  attributes of utility
• Quality of life is often an issue
• E.g. elderly patient with severe back and leg
  pain from spinal stenosis might choose surgery
  even if it carries a 20 risk of death
• Due to preferences, two individuals facing the
  exact same decision and health state can have
  widely differing utilities
• Frequently need to use special techniques to
  assess utility for various health states

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Assessing utility in medicine

• Common techniques
• Rating scale / visual analog scale
• Standard gamble (a.k.a. reference gamble)
• Time trade-off
• In practice, the decision analyst frequently
  applies more than one
• Complicating factors in assessing utility
• Risk aversion
• Preference of a certain outcome of lower value
  over a gamble with a higher average value (but
  RISK of a poor outcome)
• Time preference
• Years of life farther in the future are valued
  less

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Putting it together Doing the math

• Integrating the data in the model to determine
  the best decision is called rolling back or
  averaging out
• Procedure
• Start from the right (i.e., terminal nodes)
• Multiply the expected utility of each node by its
  probability
• Sum the values at each branching point

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Rolling back example
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Next steps

• Demo TreeAge software
• Introduce in-class decision analysis exercise
• Mention PROACTIVE framework
• Demonstrate sensitivity analysis
• Give caveat