Life Expectancy and Convexity

LIFE EXPECTANCY AND CONVEXITY

Whenever you question some aspects of medicine—or unconditional technological “progress”—you are invariably and promptly provided the sophistry that “we tend to live longer” than past generations. Note that some make the even sillier argument that a propensity to natural things implies favoring a return to a day of “brutish and short” lives, not realizing it is the exact same argument as saying that eating fresh, noncanned foods implies rejecting civilization, the rule of law, and humanism. So there are a lot of nuances in this life expectancy argument.

Life expectancy has increased (conditional on no nuclear war) because of the combination of many factors: sanitation, penicillin, a drop in crime, life-saving surgery, and of course, some medical practitioners operating in severe life-threatening situations. If we live longer, it is thanks to medicine’s benefits in cases that are lethal, in which the condition is severe—where he regards the potential benefit as large relative to treatment harm—the convex cases. So it is a serious error to infer that if we live longer because of medicine, that all medical treatments make us live longer.

Further, to account for the effect of “progress,” we need to deduct of course, from the gains in medical treatment, the costs of the diseases of civilization (Taleb’s list mixes claims about cardiovascular disease, cancer, and dental cavities with jokes about economic theories and lounge music); advances in lung cancer treatment need to be offset by the effect of smoking. From the research papers, one can estimate that medical practice may have contributed a small number of years to the increase, but again, this depends greatly on the gravity of the disease (cancer doctors certainly provide a positive contribution in advanced—and curable—cases, while interventionistic personal doctors, patently, provide a negative one). We need to take into account the unfortunate fact that iatrogenics, hence medicine, reduces life expectancy in a set—and easy to map—number of cases, the concave ones. We have a few pieces of data from the small number of hospital strikes during which only a small number of operations are conducted (for the most urgent cases), and elective surgery is postponed. Taleb interprets reports of mortality during these strikes as evidence of possible overtreatment. Short-term mortality during a strike is not, by itself, a measure of life expectancy or the long-term effects of postponed treatment. Further, which is significant, many of the elective surgeries are subsequently canceled upon the return to normalcy—evidence of the denigration of Mother Nature’s work by some doctors.

Another fooled-by-randomness-style mistake is to think that because life expectancy at birth used to be thirty until the last century, that people lived just thirty years. The distribution was massively skewed, with the bulk of the deaths coming from birth and childhood mortality. Conditional life expectancy was high—just consider that ancestral men tended to die of trauma.1 Perhaps legal enforcement contributed more than doctors to the increase in length of life—so the gains in life expectancy are more societal than from the result of scientific advance.

As a case study, Taleb criticises annual mammography for women over forty, claiming that treatment prompted by screening can offset its benefits. The excerpt does not supply the evidence needed to establish that claim about overall mortality. The concern he raises is overdiagnosis and overtreatment: detecting a tumour that would never have caused harm can lead to treatment with harms of its own. Whether a screening programme’s benefits outweigh those harms requires assessment of the particular population and programme. We have built up so much paranoia against cancer, looking at the chain backward, an error of logic called affirming the consequent. If all of those dying prematurely from cancer had a malignant tumor, that does not mean that all malignant tumors lead to death from cancer. Most equally intelligent persons do not infer from the fact that all Cretans are liars that all liars are Cretan, or from the condition that all bankers are corrupt that all corrupt people are bankers. That reversal of an implication is invalid; it is not modus ponens, the valid inference from a conditional and its antecedent. Taleb’s broader evolutionary argument is that an overreaction can sometimes favour survival even when the underlying inference is unreliable.2

Misunderstanding of the problems with mammograms has led to overreactions on the part of politicians (another reason to have a society immune from the stupidity of lawmakers by decentralization of important decisions). One politician of the primitive kind, Hillary Clinton, went so far as to claim that critics of the usefulness of mammograms were killing women.

We can generalize the mammogram problem to unconditional laboratory tests, finding deviations from the norm, and acting to “cure” them.