Reading this I could not help but think of compliance and treatment safety for self-managed dosing.

It's evident, for example, that drugs such as Paracetamol (Tylenol for you Americans) should be dosed by body weight in children. To make life simpler for parents, they are given age and/or weight brackets, sometimes along with upper thresholds (e.g. mg/day).

This of course means that lighter children are comparatively over-dosed and heavier children under-dosed compared to a median.

The problem is - I think this works pretty well as a safeguard against dangerous over-dosing (i.e. liver toxicity etc.).

Now how would we turn that advice into a gradual dosing recommendation? We can use mg/kg body weight as is done e.g. in antibiotics. But that carries the potentially fatal risk of miscalculation, and some parents might intentionally overdose over a wrong risk perception.

What we would need is something like an exponential risk curve, indicating a "safe zone" and a "danger zone" while highlighting some critical threshold. This again would need to be age/weight-specific.

Do we think parents would be deterred from giving a kid too high of a paracetamol dose? I'm not so sure, especially over time.

So in the end, I think that in some cases (especially with self-administered dosing) round numbers and sharp thresholds may work well to mitigate fatal risks, even while increasing nonfatal risks.

> paradoxical risk, where successful treatments unexpectedly lower the risk of higher-risk patients to below that of untreated lower-risk patients.

This seems perhaps tautological whenever the treatment intensity is binary, and it's an effective treatment. Someone at the threshold that receives treatment would necessarily do better than someone at the threshold not receiving the treatment.

It's a pretty good argument against any binary treatments, or at least to set the threshold low enough that improvement with treatment at the threshold is minimal.

This is helpful in any number of fields with metrics-driven responses.