Occasional reflections on Life, the World, and Mathematics

Back when I was in ninth grade, we were given a worksheet where we were supposed to fill in the appropriate conjunction in sentences where it had been left out. One sentence was “The baseball game was tied 0 to 0, ——– the game was exciting.” Not having any interest in spectator sports, I guessed “but”, assuming that no score probably meant that nothing interesting had happened. This was marked wrong, because those who know the game know that no score means that lots of exciting things needed to happen to prevent scoring. Or something.

With that in mind, fill in the appropriate preposition in this sentence:

Death rates in children’s intensive care units are at an all-time low ————— increasing admissions, a report has shown.

If you chose despite you would agree with the BBC. But a good argument could be made that because of or following a period of. That is, if you think about it, it’s at least as plausible — I would say, more plausible — to expect increasing admissions to lead to lower death rates. The BBC is implicitly assuming that the ICU children are just as sick as ever, and more of them are being pushed into an overburdened system, so it seems like a miracle if the outcomes improve. Presumably someone has done something very right.

But in the absence of any reason to think that children are getting sicker, the change in numbers of admissions must mean a different selection criterion for admission to the ICU. The most likely change would be increasing willingness to admit less critically ill children to the ICU, which has the almost inevitable consequence of raising survival rates (even if the effect on the sickest children in the ICU is marginally negative).

When looking at anything other than whole-population death rates, you always have the problem of selection bias. This is a general complication that needs to be addressed when comparing medical statistics between different systems. For instance, an increase of end-of-life hospice care, it has been pointed out, has the effect of making hospital death rates look better. (Even for whole-population death rates you can have problems caused by migration, if people tend to move elsewhere when they are terminally ill. This has traditionally been a problem with Hispanic mortality rates in the US, for instance.)

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