A huge percentage of the job of a pharmacist is to keep track of potential negative interactions between different drugs, of which there are an incomprehensible number. I don’t think linearity is a reasonable assumption here, the interaction terms between multiple interventions should be though of as, on average, big. Augmentation and synergistic effects exist, but are in general risky and quite hard to find. Even the effects of one drug are not linear, there are significant nonlinearities in dosage effects for most drugs.
i’m not really making any strong linearity assumptions, only local linearity. this doesn’t seem that different from ML, where hyperparameters can sometimes interact heavily nonlinearly, but often they don’t. i also don’t think the quadratic assumption is crazy; we assume that loss land scapes are locally quadratic all the time, even though they are obviously highly nonconvex and it’s still a very useful intuition pump.
also, my understanding is most of the really bad interactions are pretty well known, so the probability of having a really weird surprising interaction that nobody has ever catalogued is small.
I think our mental models here might be different enough that it’s hard for me to understand what you’re saying here. By nonlinearity here I mean that, in addition to nonlinear interactions between drugs, there are interacting systems, equilibration mechanisms, etc., to the point that I think intuitions about ML systems basically shouldn’t transfer at all. But then I know your intuitions about ML are better than mine, so it’s hard to be sure of that.
Re: interactions specifically, this definitely isn’t true in polypharmacy situations. We know most of the bad drug pairs in the normal population, and because doctors are wary of prescribing many different medications, this means we rarely encounter new bad interactions in the normal population. But there are drug combinations that only become dangerous in triples (search terms: the Triple Whammy, a combination of 3 drug classes, any 2 of which are generally safe but which cause kidney failure in combination, this interaction was discovered in 2000 but the drugs became available in like 1980), there are interactions which are only dangerous in the context of certain mutations (for example there are ultrametabolizers who simply can’t use prodrugs like codeine).
Interactions like this are rare right now largely because doctors are wary of prescribing too many drugs at once, but polypharmacy is becoming more common and more bad interactions are emerging as a result, basically just for combinatorial reasons. It’s definitely possible for combinations of drugs to be prescribed safely and for them to just not interact, but if we push this further, I suspect there are very few combinations of, say, 10 drugs that are simultaneously safe for most people (even if we ignore cholinergic response).
A huge percentage of the job of a pharmacist is to keep track of potential negative interactions between different drugs, of which there are an incomprehensible number. I don’t think linearity is a reasonable assumption here, the interaction terms between multiple interventions should be though of as, on average, big. Augmentation and synergistic effects exist, but are in general risky and quite hard to find. Even the effects of one drug are not linear, there are significant nonlinearities in dosage effects for most drugs.
i’m not really making any strong linearity assumptions, only local linearity. this doesn’t seem that different from ML, where hyperparameters can sometimes interact heavily nonlinearly, but often they don’t. i also don’t think the quadratic assumption is crazy; we assume that loss land scapes are locally quadratic all the time, even though they are obviously highly nonconvex and it’s still a very useful intuition pump.
also, my understanding is most of the really bad interactions are pretty well known, so the probability of having a really weird surprising interaction that nobody has ever catalogued is small.
I think our mental models here might be different enough that it’s hard for me to understand what you’re saying here. By nonlinearity here I mean that, in addition to nonlinear interactions between drugs, there are interacting systems, equilibration mechanisms, etc., to the point that I think intuitions about ML systems basically shouldn’t transfer at all. But then I know your intuitions about ML are better than mine, so it’s hard to be sure of that.
Re: interactions specifically, this definitely isn’t true in polypharmacy situations. We know most of the bad drug pairs in the normal population, and because doctors are wary of prescribing many different medications, this means we rarely encounter new bad interactions in the normal population. But there are drug combinations that only become dangerous in triples (search terms: the Triple Whammy, a combination of 3 drug classes, any 2 of which are generally safe but which cause kidney failure in combination, this interaction was discovered in 2000 but the drugs became available in like 1980), there are interactions which are only dangerous in the context of certain mutations (for example there are ultrametabolizers who simply can’t use prodrugs like codeine).
Interactions like this are rare right now largely because doctors are wary of prescribing too many drugs at once, but polypharmacy is becoming more common and more bad interactions are emerging as a result, basically just for combinatorial reasons. It’s definitely possible for combinations of drugs to be prescribed safely and for them to just not interact, but if we push this further, I suspect there are very few combinations of, say, 10 drugs that are simultaneously safe for most people (even if we ignore cholinergic response).