Expectation and preparation

The key rule for evaluating options that include outcomes that are uncertain is the expectation principle: the value of being exposed to the possibility of an outcome is determined by the value of the outcome and the frequency with which it would be experienced if you were exposed to the possibility repeatedly. For example, facing an one-in-twelve chance of losing a year of life expectancy should be evaluated as facing a certain loss of one month (1/12th of a year) of life expectancy. The expected value of such an option is loss of a month of life.

At the level of a population of patients, this principle is easy to understand. If 1,200 patients face the option, about 100 of them (one-in-twelve) will lose a year of life, while the other 1,100 do not. The net result is 100 years of life lost to the group of 1,200 patients, or, on average, a loss of one month per patient.

What makes the expectation principle counterintuitive, however, is that no individual patient in that group ever loses a month of life; each loses either a year or nothing. But because we do not know in advance, at the time of the decision, whether a particular patient will be one of the lucky ones or one of the unlucky ones, each patient is in an identical state of uncertainty and faces the same expected, or average, loss of one month of life if they must face this option.

The expectation principle is useful when comparing treatment choices. A treatment that has an expected loss of one month of life is likely to be preferable to one that has an expected loss of a year of life.

But the expectation principle is only useful before a decision is made. Once a patient has committed to a decision, they will experience one of its actual outcomes, not the average outcome. Consider a more extreme example: a 55-year-old patient facing a one-in-twelve chance of losing a 12 years of their 20-year life expectancy. This patient would not be well-served by preparing for a life shortened by one year. If they need to get their affairs in order before they die, they must do so under the assumption that they may only live to 63.

This is why patients should respect fairly small probabilities of death or permanently disabling outcomes.[i] Although such chances may not greatly diminish the expected value of a treatment (and perhaps should not actually weigh against choosing the treatment), once chosen, a patient may be wise to plan ahead of the possibility of catastrophe (by preparing their will, signing an advance directive, doing things they’d always meant to do, etc.)

That is, once a decision has been made, one must plan for actual outcomes. We might call this the preparation principle.

[i] In this context, “fairly small” means larger than the patient is exposed to regularly. If the chance of death is smaller than what they experience during their daily commute, for example, it’s probably too small to trigger estate planning (or perhaps they should be making those plans before their next work week!)

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