Communicating Quantitative Information

1
Communicating Quantitative Information

• Decision Making

2
What is a Decision?

• A decision is an irreversible choice among
  alternative ways to allocate valuable resources

3
Expected Values

• Expected value if someone has a 1 in 4 chance of
  winning 100, the expected value of of the
  gamble (the gamblers expectation) is ¼ of 100,
  or 25

4
Expected Values

• A 20,000 lottery offers a 1-in-1000
• chance of winning. The expected value of
• playing this lottery ignoring the ticket
• price equals 0.001(20,000)0.999
• (0), or 20. Based on expected value,
• what will be a reasonable bet?

5
Expected Values
6
Neonatal Intensive Care Costs Estimate

• Neonatal cost premature boy-5,000, premature
  girl-4,800. If 51 of all premature births are
  boys, what will be expected intensive care cost
  of a single premature birth?

7
Neonatal Intensive Care Costs Estimate

• P(boy)0.51
• P(girl)0.49
• Cost(.494800)(0.515000) 4,902

8
Neonatal Intensive Care Costs Estimate

• A study of hospital predict 100 qualifying
  premature births in the coming year
• Q1what is the total expected cost of premature
  births for the coming year?
• Q2if a governmental agency offers a single lump
  sum payment of 350, 000 on June 30, should the
  hospital take it?
• Or should it seek reimbursement on case by case
  basis?

9
Back to guessing on the tests

• On standardized tests your penalty is .25 for a
• wrong answer.
• Assume 5 multiple choice answers.
• What is the expected value of a guess?
• What will be the expected value of a guess if we
• eliminate one answer as wrong?

10
A simple problem How should I invest 1000?

• Certificate of deposit (CD), risk free
• Equity investment, risk involve
• You will reconsider your investment
• decision at the end of one year, but not
• earlier.
• You have no fees or taxes to consider, just an
  identical 1,000 investment in either case.

11
How should I invest 1000?

• The CD pays simple interest at a rate of 5
  annually. What is your return?
• For equity investment
• a 30 probability that its market value will have
  gone up by 500
• a 40 probability of a modest 100 increase in
  value
• a 35 probability of a substantial drop in value,
  -600.

12
How should I invest 1000?

• Let's design the decision tree on paper.
• Expected value(5000.3) (1000.4)
  (-6000.3) 150 40 -180 10.

13
Decision Trees

• In building a decision tree, there are some
• basic guidelines to be considered
• In the tree, events are ordered from left
• to right.
• 2. Different kinds of events are distinguished
• using shapes called nodes.
• 3. A decision node (square) indicates a choice
  facing the decision maker.

14
Decision Trees

• 4.A chance node (circle) represents an event
  which has multiple possible outcomes and is not
  under the decision makers control.
• 5. A terminal node (triangle) denotes the
  endpoint of a scenario

15
Decision Trees

• 6. Branches emanating from a decision node
  represent the options. All available choices must
  be represented.
• Branches emanating from a chance node represent
  the possible outcomes of the event. All possible
  outcomes must be represented, none overlap.
• 8.Terminal nodes are assigned a value,
• usually referred to as a payoff.

16
Decision Tree(calculation)

• The value of a decision node is equal the value
  of its best option
• The value of a terminal node is equal to its
  payoff
• The value of chance node is equal to its expected
  value which is found by by weighting the values
  for all of each branches by their probabilities

17
In Class Exercise

• Your patient is 24 year old male who suffered an
  open ankle fracture in a rock climbing accident.
  The accident occurred during an unexpected
  snowstorm. A number of days passed before he was
  rescued.
• The wound is seriously infected and the foot is
  gangrenous. Oral antibiotics administered by the
  rescue team and in the ER have been ineffective.

18
In Class Exercise

• You are concerned that it may not be possible to
  save the foot and, further, that if the infection
  spreads, it can threaten the leg or even cause
  death. A decision must be made whether to
  amputate the foot or attempt to save it at the
  risk of more serious consequences.

19
In Class Exercise

• Based on your experience, supplemented by review
  of literature, you estimate that administration
  of high-dose intravenous antibiotics combined
  with surgical debridement offers 0.65 (65)
  probability of saving the foot, a 0.35 (35)
  probability infection spread. If it happens, the
  foot will be amputated at the knee, or a patient
  might die(0.15 (15) probability of death).
• Surgery at this time to amputate at the ankle
  poses no other material causes.

20
In Class Exercise

• Discuss payoff (utilities)
• Death - 0
• Foot saved 1
• Foot amputated 0.65
• Leg amputated 0.5
• Create a tree and calculate the expected values

21
Vanguard Software

• http//www.vanguardsw.com/decisionpro/jdtree.htm
• (you can request a 15 day trial copy of the
  software)
• Full software has optimization tools.