Rules for Economic Efficiency by Paul Leigh Professor of Health Economics Center for Health Services Research in Prima

1. Rules for Economic Efficiencyby Paul LeighProfessor of Health EconomicsCenter for Health Services Research in Primary CareandDepartment of Public Health SciencesUC Davis Medical School

2. Health Economics: How to re-allocate scarce medical resources to save the greatest number of lives Focus of today’s talk: Medical interventions subject to Law of Diminishing Returns. Do not put all your eggs (population or individual health) in one basket (one intervention)

3. Outline for today’s talk I Health Production Function, Concave Downward Curve 1. inputs and outputs 2. cardiovascular fitness and exercise 3. draw curve; slope 4. other examples of concave downward curve: bacteria colony growth; learning biology in school shooting free throws; restoring people to health in hospital keep low birthweight babies alive in neo-natal intensive care units colon cancer screen; cervical cancer screen

4. II Total Product, Marginal Product, Slope III Rule marginal product/price curves for cholesterol, exercise, and diet numerical example mix and match exercise and diet numerical example for colon cancer screen and mammogram mix and match the two screenings IV Conclusion Outline, continued

5. I Health Production Function Output = f(input) Suppose output = cardiovascular fitness Input = exercise Hold everything else constant; “other things being equal.” What will relation look like for most people most of time? How does nature work?

11. The “S” Growth Curve J.J. Sepkoski, a paleontologist at the University of Rochester, has recently found that a plot of increasing organic diversity versus time from the late Precambrian to the end of the “explosion” conforms to our most general model of growth – the so-called sigmoidal (S-shaped) curve. Consider the growth of a bacteria colony on a previously uninhabited medium: each cell divides every twenty minutes to form two daughters. Increase in population size is slow at first. (Rates of cell division are as fast as they will ever be, but founding cells are few in number and the population builds slowly towards its explosive period.) This “lag” phase forms the initial, slowly rising segment of the sigmoidal curve. The explosive, or “log” phase follows as each cell of a substantial population produces two daughters every twenty minutes. Clearly this process cannot continue indefinitely: a not-too-distant extrapolation would fill the entire universe with bacteria. Eventually, the colony guarantees its own stability (or demise) by filling its space, exhausting its nutrients, fouling its nest with waste products, and so on. This leveling puts a ceiling on the log phase and completes the S of the sigmoidal distribution. “Survival of fittest” taken from economist, Thomas Malthus

16. Tendency in medicine to move into “negative returns” Has a name: “technology creep” Definition: increasing use of expensive procedures to increasingly wider groups of patients, many of whom may not benefit and even be harmed. Example on handout: Medicare may OK expensive lung surgery.

17. Other examples Learning most physical skills driving bicycling playing 8-ball playing video games Learning most cognitive skills academic subjects: physics, biology, chemistry, economics chess cards Monopoly Learning physical and cognitive skills Surgery Piloting airliner The Learning Curve is concave downward. “Practice makes Perfect.”

19. An Application: The Sixth Stool Guaiac (“Goo-Y-ack”)Test, Screening for Colon Cancer 1975 protocol was six sequential stool tests for occult blood: called guaiac tests. Barium-enema procedure administered if any tests are positive. (Now given colonoscopy) Authors assumed 72 persons out of 10,000 persons screened have colon cancer and probability of 91.66 from any single test, with false positive rate of 36.51%. Authors calculated second test will detect 99.3% of all cancer cases.

22. II Total Product, Marginal Product, Slope Total product = output for given input, curve itself Average product = total product/input Marginal product = ?total product / ?input To maximize efficiency, marginal product is more important than total product Marginal product ? average product Also... Slope = ?output / ?input = marginal product Slope = ?fitness / ?exercise = marginal product

24. Example using Math Fitness = ß x Ln (exercise hours + 1)

28. III Rule Ten hours, study for a final Imagine not yet spent $ on two interventions = X, Y Arbitrarily plan to allocate 50 to X, 50 to Y If (marginal productX/priceX) > (marginal productY/priceY) then take planned spending from Y and give to X If (marginal productX/priceX) < (marginal productY/priceY) then take planned spending from X and give to Y Continue to apply rules until (MPx/Px) = (MPy/Py)

30. III Rule Example 1. Begin with cholesterol at 300. Let exercise and diet be expressed in hours per week. (1 hour diet means substitute healthy for unhealthy meal). Price exercise = price diet. Assume maintain exercise and/or diet for one year.

31. Suppose have 5 hours per week for one year to allocate 5 on exercise only: -105 5 on diet only: -75 3 on exercise, 2 on diet: -120 If only used exercised, would have missed opportunity to reduce cholesterol even more - by -15 with same resources (5 hours). Missed opportunity: Opportunity Cost; Opportunity Lost Do not fall into Total Product or Average Product trap

32. III Rule Example 2. Spending on colon cancer screening (fecal occult blood test) and mammograms. Assume can rank people according to benefit. We start with people at high risk in the first 10,000 and gradually move to people with lower risk for last 10,000. Risk factors for colon cancer: blood type A, history of colon cancer or polyps, history of chronic inflammatory bowel disease, over age 50, high fat diet, family history of colon cancer. Risk factors for breast cancer among women: family history, patient history, no children, hormone replacement therapy, obesity, over age 50.

34. Suppose can only screen 50,000 additional people. 50,000 on colon cancer screen: 76 lives saved 50,000 on mammogram: 47 lives saved 30,000 on colon cancer screen and 20,000 on mammogram: 54 + 32 = 86 lives saved By spending only on colon cancer screen, you kill 10 people. Opportunity Cost: What was next best available alternative? Do not fall into Total Product or Average Product trap.

35. Another example: Train all physicians to be cardiologists? Or mix and match across specialties?III Rule If MPx/Px > MPy/Py, move resources from Y to X If MPx/Px < MPy/Py, move resources from X to Y MPx/Px = MPy/Py ? optimum Mix and match

36. Conclusion Medical interventions subject to Law of Diminishing Returns. Do not put all your eggs (population or individual health) in one basket (intervention. Mix and match among interventions according to Marginal Product divided by Price; i.e., According to Marginal Benefit and Marginal Cost. Application of rules from economics saves lives.