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he is indifferent between the two choices, finding it very difficult to say which he would prefer. His utility for diabetes is calculated as 22 divided by 24, meaning the twenty-two years in perfect health divided by his life expectancy of twenty-four years with diabetes. The utility of diabetes is 91.7. This proportion is life in the better health state divided by life expectancy in the worse health state. The time trade-off method breaks down when a person states that he or she is not willing to trade off any years of life, even though those years are lived in an imperfect health state. If that was the case, then the imperfect health state has a utility of 100 percent, meaning that it is equivalent to perfect health, which clearly it is not.

This back-and-forth assessment of time traded for perfect health is used to identify “preferences” of people without the imperfect health condition by asking them to imagine, in the cases of prostate cancer treatment, being impotent or incontinent. A utility number is calculated this way, and the highest utility indicates “preference.” All of the pitfalls in forecasting are amplified in the setting of asking people who have no experience of the health condition to trade off time to regain “perfect health.” Yet the time trade-off method is widely used in guiding clinicians; see Julia H. Hayes et al., “Active surveillance compared with initial treatment for men with low-risk prostate cancer,” JAMA 304 (2010), pp. 2373–2380; Ian M. Thompson, Laurence Klotz, “Active surveillance for prostate cancer,” JAMA 304 (2010), pp. 2411–2412.

To apply the standard gamble calculation for diabetes, researchers would ask a patient if she prefers living with diabetes to a treatment that results in perfect health in 90 percent of patients and death in 10 percent. Say she does not like these odds but ultimately is willing to accept a 94 percent chance of perfect health and a 6 percent chance of death. Her utility then for diabetes is 0.94. Some researchers who favor the standard gamble method point out that it incorporates the patient’s risk attitude, and the odds the patient selects reflect her tolerance for risk. But there are clear difficulties with the standard gamble. A gamble involving death seems to be too “high stakes” to be reasonable for some patients. This indeed proved to be the case in trying to use the standard gamble in the setting of decisions around treatment of prostate cancer. Some patients refused to gamble and therefore would not accept any odds despite living with incontinence and impotence. This would mean that incontinence and impotence are equivalent to perfect health and have utility of 100 percent; see Sara J. Knight et al., “Pilot study of a utilities-based treatment decision intervention for prostate cancer patients,” Clinical Prostate Cancer (September 2002), pp. 105–114.

For more detailed critiques of utility methodology, see Heather P. Lacey et al., “Are they really that happy? Exploring scale recalibration in estimates of well-being,” Health Psychology 27 (2008), pp. 669–675; Peter A. Ubel et al., “What is perfect health to an 85-year-old? Evidence for scale recalibration in subjective health ratings, Medical Care 43 (2005), pp. 1054–1057; Paul Dolan, Daniel Kahneman, “Interpretations of utility and their implications for the valuation of health,” Economic Journal 118 (2008), pp. 215–234.

Bernoulli’s formula could be applied to the other patients we have met. Susan Powell, in assessing the first part of the formula on outcomes of elevated cholesterol, might ask: What kind of heart attack? Some heart attacks are minor, others lead to chronic debility with heart failure. Does the imagined heart attack lead to problems with her heart rhythm, so that she needs to take multiple medications with multiple side effects to keep her heart beating at a steady and safe pace ? Is she left short of breath? Must she enter a cardiac rehabilitation program to regain her endurance ? Can she return to work and spend productive days, or is she left homebound and dependent on others? Then,