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Infinite or at least 27382738 1060 what can

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Unformatted text preview: es depend on underlying disease probability distribution I Tx V(I) U V(U) W V(W) Modeling treatment Utilities: improved: 5000 unchanged: -2500 worse: -5000 Modeling test: transfemoral arteriography How large is the tree? • Infinite, or at least (27+3+8)^(27+3+8), ~10^60 • What can we do? – Assume any action is done only once – Order: • questions • tests • treatments • 27! x 4 x 3 x 2 x 8, ~10^30 • Search, with a myopic evaluation function – like game-tree search; what’s the static evaluator? – Measure of certainty in the probability distribution How many questions needed? • How many items can you distinguish by asking 20 (binary) questions? 2^20 • How many questions do you need to ask to distinguish among n items? log2(n) • Entropy of a probability distribution is a measure of how certainly the distribution identifies a single answer; or how many more questions are needed to identify it Entropy of a distribution For example: H(.5, .5) = 1.0 H(.1, .9) = 0.47 H(.01, .99) = 0.08 H(.001, .999) = 0.01 H(.33, .33, .33) = 1.58 (!) H(.005, .455, .5) = 1.04 H(.005, .995, 0) = 0.045 (!) -- should use logn P j Interacting with ARF in 1973 Question 1: What is the patient's age? 1 0-10 2 11-30 3 31-50 4 51-70 5 Over 70 Reply: 5 The current distribution is: Disease Probability FARF 0.58 IBSTR 0.22 ATN 0.09 Question 2: What is the patient's sex? 1 Male 2 Pregnant Female 3 Non-pregnant Female Reply: 1 . . . ARF in 1994 Local Sensitivity Analysis Case-specific Likelihood Ratios Therapy Planning Based on Utilities Assumptions in ARF • Exhaustive, mutually exclusive set of diseases • Conditional independence of all questions, tests, and treatments • Cumulative (additive) disutilities of tests and treatments • Questions have no modeled disutility, but we choose to minimize the number asked anyway...
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