Dual use and the arithmetic of combining relative risks

by Carl V Phillips

It was called to my attention that UCSF anti-scientist, Stanton Glantz, recently misinterpreted the implications of one of his junk science conclusions. Just running with the result from the original junk science (which I already debunked) for purposes of this post, Glantz make the amusing claim that because vaping increases heart attack risk by a RR=2 and smoking by a RR=3 (set aside that both these numbers are bullshit) then dual use must have a RR=5. WTAF?

First off, there is no apparent way to get to 5 except by pulling it out of the air. It is apparent that Glantz thinks he was adding the risks: 2+3=5. Except you cannot add risks that way. Every first-semester student knows the formula for adding risks, which is based on the excess risk. Personally I have always thought that having students memorize that as a formula, rather than making sure they inuit it, is a major pedagogic failure. But that aside, they do memorize the formula, which subtracts out the baseline portion of the RR then adds it back, as should be obvious: (RR1 – 1) + (RR2 – 1) + 1. So, the additive RR = 2-1 + 3-1 + 1 = 4. Think about it: If you “added” Glantz’s way then two risks that had RR=1.01 (a 1% increase in risk) would add to 2.02 (more than double). Or two exposures that reduced the risk by 10% (RR=0.9) would add to an increased risk, RR=1.8. Not exactly difficult to understand why this is wrong.

Additivity of risks is a reasonable assumption if the risk pathways from the exposures are very independent. The excess risk of death caused by both doing BASE jumping and smoking is basically just the excess risk of each added together. (A bit less because if one kills you, you are then not at risk of being killed by the other.) If the risks from the two exposures travel down the same causal pathways (or interact in various other ways), however, adding is clearly wrong. If vaping causes a risk (for heart attack in this example, though that does not matter), then smoking almost certainly causes the same risk via the same pathway. There is basically no aspect of the vaping exposure that is not also present with smoking (usually more so, of course). When this is the case, there are various possible interaction effects. One thing that is clear, however, is that simply adding the risks as if they did not interact is wrong.

The typical assumption built into epidemiology statistical models is that the risk multiply. This is not based on evidence this is true, but merely on the fact that it makes the math easier. The default models that most researchers tell their software to run, having little or no idea what is actually happening in the black box, build in this assumption. It is kind of roughly reasonable for some exposures, based on what we know. In the Glantz case, this would result in a claim of RR = 2 x 3 = 6, which is also not the same as 5.

So, for example, if a certain level of smoking causes lung cancer risk with RR=20, and a certain level of radon exposure causes RR=1.5, then if someone has them both, it is not unreasonable to guess that the combined effect causes RR=30. The impact on the body in terms of triggering a cancer and then preventing its growth from being stopped seems like it would work about like that. On the other hand, there are far more examples where the multiplicative assumption is obviously ridiculous. If BASE jumping once a week creates a weekly RR for death of 20, and rock climbing once a week has RR=2, doing each once a week obviously adds, as above, for RR=21, rather than multiplying to 40. (Aside: most causes of heart attack are probably subadditive, less than even this adding of the excess risks, as evidenced by dose-response curves that flatten out, as with smoking.)

But importantly, notice the “each once a week” caveat. That addresses the key error with the stupid “dual use” myths by specifying that the quantity of each activity was unaffected by doing the other. If, on the other hand, someone is an avid BASE jumper, doing it whenever he can get away, and he takes up rock climbing, the net effect is to reduce his risk. The less hazardous activity crowds out some of the more hazardous activity. This, of course, is what dual use of cigarettes and vapor products (or any other low-risk tobacco product) does. This is not complicated. Every commentator who responds to these dual use tropes — and I am not talking epidemiology methodologists, but every last average vaper with any numeracy whatsoever — points this out. Vaping also does not add to the risk of smoking because it almost always replaces some smoking rather than supplementing it. In this case, using Glantz’s fictitious numbers, it would mean the RR from dual use would fall somewhere between 2 and 3. Not added. Not multiplied. Not whatever the hell bungled arithmetic that Glantz did. Between.

As I said, everyone with a clue basically gets this, though it is worth going through the arithmetic to clarify that intuition. It is not clear whether Glantz really does not understand or is pretending he does not — as with Trump, either one is plausible for most of of his lies. Undoubtedly many of his minions and useful idiots actually believe it is right. The “dual use” trope gets traction from the fact that interaction effects from some drug combinations are worse than the risk of either drug alone. Many “overdose” deaths are not actually overdoses (the term that should be used for all drug deaths is “poisonings” to avoid that usually incorrect assumption), but rather accidental mixing of drugs that have synergistic depressant effects, often because a street drug was secretly adulterated with the other drug.

But as already noted, that is obviously not the case with different tobacco products, whose risks (if any) are via the same pathways. Even if total volume of consumption was unaffected by doing the other (as with “each once a week”) the risks would not multiply and would probably not even add. Since that is obviously not true — since in reality, consuming more of one tobacco product means consuming less of others — the suggestion is even more clearly wrong. In fact, using the term “dual use” to describe multiple tobacco products makes no more sense than saying that about someone who smokes sticks that came out of two different packs of Marlboros on the same day.

In the context of tobacco products, the phrase “dual use” is inherently a lie. It intentionally invokes the specter of different drugs (or other exposure combinations) that have synergistic negative effects. That is not remotely plausible in this case. It also intentionally implies additivity of the quantity of exposure (“doing all this, and adding in this other”) when it is actually almost all substitution, as with which pack you pull your cigarette from. To the extent that it increases total consumption of all products, this is a minor effect (a smoker who vapes not only as a partial substitute, but also occasionally when he would not have smoked even if he did not vape). This only matters to someone who does not care about risk, let alone people, and only cares about counting puffs.

There is a long list of words and phrases that when used by “public health” people should make you assume they whatever they are saying is a lie: “tobacco” (when used as if it were a meaningful exposure category), “addictive” (meaningless for drugs with little or know functionality impacts), “chemical” (a meaningful word, but invariably used because it sounds scary), and “carcinogen” (when used as a dichotomous characterization, without reference to the relevant dosage and risk). “Dual use” should be added to this list, in the same general space as “chemical”, another word that is inherently just a simple boring technical descriptor, but that is almost exclusively used to falsely imply negative effects.