Judgment and decision making (JDM) are fundamental human activities, and in many ways, among the most interesting and useful to study. Every moment of every day, we're faced with judgments and decisions. Some are relatively inconsequential, such as which way to walk to work. Some are easy or habitual, such as what time to wake up in the morning or whether to buy a bottle of soda for 50 cents or the same bottle for $1. But many are both consequential and novel, and nowhere more so than in medical decisions.

In this course, we'll discuss both decision making and judgment. A decision is the process of choosing a course of action in a given situation, to achieve some goals. A judgment is the process of trying to determine an unknown state based on known cues.

• Alternatives: actions that can be taken. Not acting is usually also an alternative. Example: treat a man with localized prostate cancer with surgery, treat with radiation therapy, or leave untreated.
• States of the world: conditions that may or may not be present, that are relevant to the results of the decision, and that are not under the control of the decision maker. For example, whether the cancer will respond to radiation therapy, whether it has metastasized, whether it will recur, how soon the man would die of natural causes.
• Outcomes: Each pairing of a chosen alternative with a state of the world results in outcomes. For example, if radiation therapy is chosen, and the cancer responds to radiation therapy, the outcomes might include increased life expectancy for the patient, decreased money in the patient's wallet, side effects of the therapy, etc. Outcomes can be immediate or delayed. Here's an example of a small outcome matrix:

• Utilities: A utility is the psychological or subjective value of an outcome. For example, if one outcome of the radiation therapy is nausea, some people will find that outcome worse than other people. An outcome's utility (or disutility) is a measure of how good (or bad) the outcome is to decision maker. While having a good appetite might be very important to me, it might be less so to someone else.
• Objectives: Finally, the decision maker has objectives, values, or goals, that they would like to achieve when making the decision. Sometimes these goals are explicitly stated: "I want to live as long as I can. I want to be able to function the way I function now. I want to be as rich as possible." As you can see, sometimes these objectives can conflict, and tradeoffs become necessary -- a shorter life with higher functioning vs. a longer life with less functioning, for example.

• An unobservable state of the world: For example, whether a patient has a virus or an infection.
• Cues: Observable features that may be more or less predictive of the unobservable state. For example, duration of fever, color of phlegm, white blood cell count, etc.
• Note that there's variation in both how well the cues reflect the unobservable state (their "validity") and how well the judge uses the cues (their "utilization"). None of the cues may be very good, but the judge may get the most s/he can out of them; at the other extreme, there may be a perfect cue, but the judge doesn’t use it.

We'll return to judgment next week. For now, let's focus on decision making.

Decisions can be thought of as being made under one of four conditions:

1. Certainty: The states of the world are known. The problem is to determine the outcomes that will result from each alternative (easy), to decide what the utilities of those outcomes are (harder), and to decide how to resolve tradeoffs when one alternative better achieves objective A, and another alternative better achieves objective B.
2. Risk: The states of the world are unknown, but their probabilities are known. For example, I don't know if the cancer will respond to radiation therapy, but I know that in 45% of patients like mine, it does. So in addition to the problems associated with decisions under certainty, we must also evaluate probabilities, and combine information about probabilities and outcomes.
3. Uncertainty: The states of the world are unknown, and even their probabilities are unknown. There may be no clinical trials about the effectiveness of some treatment, for example. Now we have all the problems of decisions under risk, but we must also estimate probabilities somehow.
4. Conflict: The states of the world also include other peoples' choices. Their choices may depend on your choices (or their beliefs about your choices). We have all the problems of decisions under uncertainty, and we have to think about strategy - how to respond to or influence someone else's actions. The study of decision under conflict is usually called game theory, and is fascinating, but we won't spend much time on it in this course.

There are three main approaches to studying JDM:

• Normative: The normative approach to JDM attempts to answer the question, "How should decisions be made?" It seeks to identify rules of decision making which, if followed, will result in the best possible decisions on average or in the long run.
• Descriptive: The descriptive approach to JDM attempts to answer the question "How do people make decisions?" It recognizes that people do not always follow normative rules and tries to characterize their actual behavior.
• Prescriptive: The prescriptive approach to JDM attempts to help decision makers. It says, "Given the way people actually make decisions differs from the way they should, how can we help people make better decisions?"

The medical decision making literature contains examples of all three approaches, and this course will explore them all. We'll look at how we should make decisions, how we actually make decisions, and how we can make better decisions. Which brings us to an important question for discussion:

• Considers both positives and negatives of alternatives, and allows positives to compensate for negatives (is "compensatory")
• Considers present and future outcomes
• Considers the objective/values/outlook of decision makers
• Makes appropriate use of all available relevant information

A probability is a numerical estimate of the likelihood of an event. For example, the probability of rain is a number that represents how likely it is that it will rain. Because probabilities are numerical, they can be dealt with mathematically, a great advantage over other ways of expressing likelihood (e.g., "it'll probably rain"). Probabilities range from 0 (impossible) to 1 (certain).

Most everyone agrees with the above, but there is a long-standing controversy over how to assess and interpret a probability. Frequentists argue that probabilities are standardized frequencies: we know the probability of snow on January 20 is 0.6 because it snowed on 60 of the last 100 January 20s. To a frequentist, it's meaningless to speak of the probability of an event when its frequency has never been observed. For example, what is the probability that there is extraterrestrial intelligence? We've never encountered any, but we haven't sampled the whole universe yet. The frequentist responds that the question can not be answered.

Bayesians disagree. To a Bayesian, a probability represents a subjective judgment of likelihood, and need not be based on observed frequencies. A Bayesian can answer that she believes the probability of extraterrestrial intelligence is 0.01, because this number reflects her opinion of the likelihood. As long as these estimates obey the laws of probability, Bayesians argue, we can treat them as probabilities and take advantage of them as sources of information, rather than restrict ourselves only to frequencies. (Bayesians are named for the Reverend Thomas Bayes, an 18^th century theologian. Bayes' work on probability was published posthumously. During his life, he published Divine Benevolence, or an Attempt to Prove That the Principal End of the Divine Providence and Government Is the Happiness of His Creatures (1731) and An Introduction to the Doctrine of Fluxions, and a Defence of the Mathematicians Against the Objections of the Author of The Analyst (1736), which countered the attacks by Bishop George Berkeley on the logical foundations of Isaac Newton's calculus.)

If you hold a Bayesian view that probability judgments are statements of belief, one approach to eliciting them is to consider your willingness to bet on your beliefs, and to compare them to your willingness to bet on a truly random game.

A discussion of the probability estimates brought in by the students. Where did they come from? Are they based on frequencies found in studies? Expert judgment? Something else?

Whether probabilities are beliefs or frequencies, they should obey some normative mathematical rules, called probability theory. Suppose A and B are uncertain events. Here are the most important terms and rules:

• The probability of event A happening is written p(A).
• The probability of event A not happening is written p(not-A)
• The probability of event A happening, given that event B has happened, is referred to as the conditional probability of A, given B, and written p(A|B). Note that p(A|B) is not the same as p(B|A): the probability that a child has a fever given that the child has meningitis is very high, but the probability that a child has meningitis given that the child has a fever is quite low.
• If whether or not B happens doesn't affect whether or not A happens, then p(A|B) = p(A), and events A and B are said to be independent.

• p(A) + p(not-A) = 1. It is certain (1) that an event either happens or does not happen.
• p(A and B) = p(A)p(B|A) = p(B)p(A|B). The probability that both A and B occur is the probability that A occurs, multiplied by the probability that B occurs, given A. Or, the probability that B occurs, multiplied by the probability that A occurs, given B. This is going to turn out to be very important in the next few weeks.
• p(A or B) = p(A) + p(B) - p(A and B). The probability that A or B (or both) occur is the sum of the probability that A occurs and the probability that B occurs, minus those cases where both occur.

Discuss questionnaire question #8 (boys and girls)

Let's step away from the normative theory of probability and take a brief foray into the descriptive theory: how do the ways in which people use probability differ from the normative theory and how can we tell?

Accuracy of probability judgment is usually measured with calibration curves. If you tell me that there's a 0.3 probability of an event (or that you're 30% sure that the event will occur) and I go out and find that the event does indeed occur 30% of the time, your judgment is well-calibrated.

Let's take an example from the questionnaire I handed out last week. Discuss #5 (folding paper).

People tend to be overconfident in their estimates, tend to underweight very high probabilities, and tend to overweight very low probabilities. Very low probabilities pose an especially difficult and important problem in medicine, particularly when it comes to informed consent. What does it mean that the risk of a dangerous side effect from a drug is 0.0001 or 0.01%? Ron Howard offers a solution to this problem: microrisks.

Student presentation of Howard paper.

Discussion: Should we present risks to patients as micromorts, along with a comparison table like Howard's p. 361?

If people are interested, I have a paper and a spreadsheet that explains how to calculate your own micromort value. It's difficult and messy, though.

There's another common way to represent likelihood without using probabilities that also gets around some of the "small probabilities" problems: odds.

A probability of 1 in 100 means that in 100 chances for the event to occur, it occurs once. The equivalent of this in odds is odds of 99 to 1 against the event: the event will fail to occur 99 times for every 1 time that it occurs. This is usually written 99:1 against. Or it could be written 1:99 in favor.

Probability can easily be converted into odds, and vice versa:

• Odds(A) = Odds in favor of A = p(A)/p(not-A) = p(A)/(1-p(A))

• Odds(not-A) = Odds against A = p(not-A)/p(A) = (1-p(A))/p(A)

• p(A) = Odds(A) / (1+Odds(A))

Later on, we'll see some situations in which representing likelihood as odds makes some calculations easier. For now, let's consider whether this is a better representation of uncertainty than probability for the purposes we've been discussing, such as informed consent.