Problem_Session_8

Problem_Session_8 - MS&E 252 Decision Analysis I Problem...

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MS&E 252 Decision Analysis I Problem Session 8
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What concepts do we expect you to master for the Final Exam? Medical DA The Foundations of DA PIBP, PISP Relevance The Five Rules U-Curves The Delta Property Sensitivity Analysis Information Gathering, Value of Information Decision Diagrams Probability Encoding Rain Bets
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Medical Decision Analysis Some problems with how medical decisions are usually made: Procedures are generalized for all individuals not taking into consideration their own preferences. Moreover, few decisions are actually made by the patient. Medical Decision Analysis provides us with a framework that can help us tackle life and death issues.
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24 hour Pain, then Cure B A Pay a certain amount X , then Cure We calculate your micromort value by setting up two deals. (1) You should be just indifferent between the two alternatives – you are measuring your PIBP for pain relief.
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p 1-p 24 hour Pain, then Cure Cure Death C A We calculate your micromort value by setting up two deals. (2) Again, you should be just indifferent. p cannot be 0 – why? p cannot be 1 – why?
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p 1-p 24 hour Pain, then cure Cure Death C A Pay a certain amount X , then cure We calculate your micromort value by setting up two deals. (3) B Form the ratio (X/p)/1,000,000 The ratio (X/p)/1,000,000 is your $-value per micromort. Indifference
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Why do we evaluate micro- probabilities? A micromort is a chance of one in a million of dying. This unit is usually more appropriate when we cope with life and death issues. We are interested in evaluating the dollar value per micromort ($/μmt).
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Micromorts provide us with a scale against which it is natural to assess risks. Such a table is very useful to measure a certain level of risk against risks you are more familiar with. Proba of Death Type of Accident in μmt year, in the US Motor Vehicle 270 Falls 100 Fire and Explosion 40 Drowning 28 Firearms 13 Machinery 10 Aircraft 7.5
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Why is the value per micromort useful? There is a range of small risks over which these two curves are linear. Payment to Avoid Death Risk 1 10 100 1000 10000 100000 1000000 10000000 100000000 0 0 1 10 100 1,000 10,000 100,000 1,000,000 Micromorts (1 in a million chance at death) Payment ($) Payment to Accept Death Risk 1 10 100 1000 10000 100000 1000000 10000000 100000000 0 0 1 10 100 1,000 10,000 100,000 1,000,000 Micromorts (1 in a million chance at death)
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Here is a simple example showing how you would use the constant range. Leo is your typical American; as such, he considers he faces 270 μmt a year from auto accidents. His value per micromort in the constant range is about $20. How much should he be willing to pay for a full “auto death prevention” policy? Answer: 20 * 270 = $5,400 a year!
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Why did we have the 24 hour pain alternative? To give you an incentive to put down a number. To be a transition stage between the two other alternatives – some people do not feel comfortable with the concept of trading a probability of death with money.
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What concepts do we expect you to master for the Final Exam?
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This note was uploaded on 06/16/2010 for the course MS&E 252 taught by Professor Howard during the Fall '08 term at Stanford.

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Problem_Session_8 - MS&E 252 Decision Analysis I Problem...

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