Medical Decision Analysis (Introduction to Medical Informatics) (http://www.cpmc.columbia.edu/edu/textbook) LAST REVIEWED: 24 October 1996 need to come to a decision despite uncertain prospects heart disease 59 yo man with CAD, s/p CABG, recurrent pain operate again (higher mortality, less chance work) or treat with medication influenza 65 yo women with diabetes 35 yo women with no other disease vaccinate or not diagnose pulmonary embolism V/Q scan is easy to do but not certain pulmonary arteriogram is definitive but dangerous measuring the utility or value of several alternatives is especially difficult in medicine because of the emotional implications of the alternatives goal is to figure out the utility of each alternative, and then choose the one with the highest utility ("best") utility = measure of preference of a given alternative utility can be measured in terms of years of life years of life corrected for disability (eg, how many healthy years = years without a leg) cost (actual expense, put monetary value on years) (if it cost $100,000 to save a life with prenatal care) ... simple example assume 2 treatments for a disease, and all patients die within 4 years problem is that deaths are spread out over time ____probability_of_death____ years (util) treatment A treatment B ------------------------------------------- 1 0.2 0.05 2 0.4 0.15 3 0.3 0.45 4 0.1 0.35 "expected value" of A and B multiply probability by utility for each alternative sum over all alternatives A = .2*1 + .4*2 + .3*3 + .1*4 = 2.3 B = .05*1 + .15*2 + .45*3 + .35*4 = 3.1 therefore choose treatment B but expected value does not tell all ____probability_of_death____ years (util) treatment A treatment B ------------------------------------------- 1 0.0 0.5 2 0.0 0.0 3 1.0 0.0 4 0.0 0.0 5 0.0 0.5 method (to solve a more complex problem) 1. draw decision tree organize problem into a series of decisions & alternatives often can follow temporal order outcome nodes (dots) possible outcome for the chosen path eg, cure chance nodes (circles) wherever more than one outcome may occur eg, death vs cure decision nodes (boxes) wherever a choice must be made among alternatives there is often more than one way to draw the same tree 2. label outcomes need probabilities for branches at chance nodes need utilities at outcome nodes 3. average out expected value at each chance node = sum of (product of probability x value for each branch) 4. fold back at decision node, prune all but most preferred branch; assign it the expected value of that branch (ie, make the best choice) 5. repeat for next decision if more than one in tree example (from the Shortliffe textbook, page 102) 66 yo man crippled with arthritis, can walk only with canes. Knee surgery might cure him, do nothing, kill him, or, if the knee replacement gets infected, require an emergency second operation that will either leave him unable to walk or kill him. relative utilities for outcome nodes death = 0 no walking at all = 3 (ie, 10 years not walking = 3 years healthy) walk with canes = 6 cure = 10 probabilities for chance nodes P(perioperative death) = 0.05 P(infection|survive) = 0.05 P(cure|no infection) = 0.6 death +----------------------------------death 0 | 0.05 | death | +------------death 0 surgery | | 0.05 +-----------O D=7.72 infection | | | +-----------O A=2.85 | | | 0.05 | | | | | survive | | | +----------no walk 3 | | survive | 0.95 | +---------O C=8.12 | 0.95 | cure [] | +------------walk 10 | | | 0.6 | | no infect | | +-----------O B=8.4 | 0.95 | | | failure | +-------------cane 6 | 0.4 | no surgery +-----------------------------------------------cane 6 therefore surgery (7.72) is preferred over not (6) sensitivity analysis problem is that values for utility are often inexact how dependent is the decision on my choice of values for utilities and for probabilities on chance nodes For each parameter, find the value at which the decision is even. If your estimate of the value is near where the decision changes, then the decision is sensitive to your choice of that parameter. Eg, look at the probability of perfect mobility after surgery (estimated to be 0.6). Want to find probability of success necessary so that value of surgery decision is 6. Simply solve for the probability (p), and get 0.125. Therefore, even if my guess is way off, the patient should still have surgery. 6 = .95( .95( 6(1-p)+10(p) ) + .05(2.85) ) p = ((6/.95-.05*2.85)/.95 - 6)/4 = 0.125 Can also apply this to the choice of values for outcomes. related reading: Raiffa H. Decision analysis: introductory lectures on choices under uncertainty. M.D. Computing 1993;10(5):312-28.