Where do we draw the line between where statistics applies and where it doesn’t? If you are in a casino, and you trust the house to play fair, we’d probably all agree that the outcomes of future card games can be statistically analyzed. When creating actuarial tables to price insurance, the risks and prices are all based on carefully computed relative frequencies. The insurance company has found this mindset useful enough to build a business on top of it for centuries. But if a doctor is operating on a patient with an extremely uncommon condition, is that statistics too? In a sense, we can only define the term ’uncommon’ in statistical terms. It refers to a relative frequency of occurrence. However, in these cases where experiences do seem wholly new, how can we map past rates onto how to act?
There is clearly a spectrum between when pure statistics can guide action (e.g., betting on blackjack) and where perhaps there is something else that must be applied (e.g., surgery on a novel condition).
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Meehl highlights a dozen other studies in his book and continued to track examples throughout his career. No matter how much he looked, he kept finding the same thing: statistical rules were seldom worse and often much better than clinical predictions. In a reflection on his book, Meehl wrote in 1986, “There is no controversy in social science that shows such a large body of qualitatively diverse studies coming out so uniformly in the same direction as this one.”
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What can we make of these results? Many feel like a doctor can assess more than what is fed into the computer. That a counselor can see subtle cues that are valuable for prediction. That there are edge cases that statistical algorithms can’t catch. Why does the empirical evidence not bear this out? Why does clinical judgment repeatedly fare worse on average?
The key to the entire clinical-statistical puzzle is those last two words.
The trick that Meehl plays is in the quantification of “better.” By better, we of course mean on average. This is a subtle point: Meehl discusses in Chapter 4 that a clinician may be able to detect a variety of exceptional cases that don’t appear in the original data seen by the statistical algorithm. His famous example is where an actuarial table determines that Professor Glotz attends the movies 90% of all Fridays, but this Friday he has a broken leg. The broken leg impels the clinician to change their predicted probability to near zero. What if clinicians are adept at finding such idiographic oddities as broken legs? Meehl doesn’t deny this possibility, but asserts that, regardless of how clinicians incorporate new knowledge, their performance should be evaluated actuarially. [...]
Actuarial evaluation seems innocuous: how else would we compare two decision-makers but by the body of their work? However, once all parties decide that predictions will be evaluated by averages, the game is up. If prediction is possible, meaning that the past and the future are similar, and the evaluation is based on rates of future success, then the best predictor will be the one that maximizes success rate among some class of possible algorithms. You should find a rule that accurately predicts the past and use it to make predictions about the future. Since you will be evaluated based on averages, this is effectively the optimal thing to do.
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If I pick a statistical evaluation, I can derive the optimal decision. I call this phenomenon, where the metric fixes optimal actions, Metrical Determinism. The evaluation ties our hands. Once we decide what is best in the future, the problem of optimal action is mechanical. It should thus not be surprising that statistics wins when we evaluate predictions and decisions using statistics.
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Meehl provides clinicians with clearly delineated conditions for when statistical methods are useful: answering clear, multiple-choice questions about simple actions from machine-readable data. This characterization is useful in of itself. Moreover, I cannot emphasize enough here that just because statistical prediction is never worse and often better than clinical judgment, that doesn’t mean that it isn’t possible to poorly implement statistical prediction. Careful statistical prediction remains a delicate skill. You can have too few features to make accurate predictions. You can have too many features, making it hard to find consistent patterns. You might be in a situation where you have completely uninformative features. We don’t have particularly effective methods to deal with missing data, and missing data plagues many prediction problems about people.
Most worrisomely, the predictions trained on statistical counts have limited temporal validity, as the population of people changes faster than the statistical prediction rules can be updated. Statistical prediction relies on past counts being reasonable predictions of the future. We have plenty of experience that tells us this is often not a safe assumption.
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Data scientists and software engineers at technology companies refer to this degradation as staleness [...] and constantly retrain their prediction systems to prevent predictions from becoming less accurate. Not all fields are as diligent about the maintenance of their prediction systems. Medical risk assessments may remain static for decades, although they become ineffective within a matter of years.
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Moreover, statistical rules need to be targeted at interventions with simple outcomes. Trying to shoehorn every decision into a simple statistical decision narrows the possibilities of the world we inhabit. The Meehlian actuarial game transforms the world into machine language. This is explicitly part of the problem setup, which demands machine-readable rules, data, and outcomes. The game is rigged because we organized the problem to be mechanical. Once the problem is mechanical, it can be solved by a machine. However, if machines can’t function, they have no role in decision making. We can only compare human to machine decisions on the problems where we level the playing field for the machine.
Nonetheless, one of the primary impulses of the modern state is to translate human experience into data readable by machines. Bureaucracies render humanity in a simplified state in order to make decisions about it. And, as explicated by Farrell and Fourcade [2023], our massive technology companies aid, abet, and profit from helping with such rendering. These systems remove the discretion of people in the decision making chain. These people, be they your primary care physician or a trial judge, often consider benefits not captured in actuarial evaluations.
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