# Number of lives saved must be adjusted for those who cannot be saved, etc. (wonkish)

by Carl V Phillips

There is always some interest in quantifying how many people could be saved by THR, and it flared up this week thanks to estimates by Robert West (his paper; his press comments). As a result, Brad Rodu and I were discussing the challenge of correctly accounting for smokers who could not be saved by quitting (in any manner) because the disease by which smoking is going to kill them is already established. (Recall that CDC is apparently planning to try to trick people into believing that such diseases among vapers were caused by vaping itself, rather than because their learning about THR came a year or two too late — thanks in part to the CDC.)  Quitting is not the same as never having smoked, and THR switching is not the same as having always used the low-risk alternative.

The required adjustment for the number of people who cannot be saved is not huge, but it is also not zero, and it is a mistake to pretend that it is. The following back-of-the-envelope that I came up with is obviously not exact, but it is better than the (woefully common) approach of saying “we don’t know where the number is really 5 or 10, so let’s just call it 0.”  I am putting it here for comment and discussion, and because experience gives me the sinking feeling that my quick-cut will remain the best available calculation of the figure for a long time.

[Update: Brief very simple summary for those who do not want to read this whole thing, and that might prime the mind to understand what follows: For some people who currently smoke, it is too late to save themselves by quitting, so we cannot claim they can be saved by THR. I estimate how many. I then point out that any simple statement along the lines of “N people per year would be saved if…” is probably wrong.]

The text in bullet points is part of the calculation itself. The plain paragraphs are further analysis or explanation.

• Take as the population in question those smokers who are fated to die from smoking if something does not intervene. For verbal parsimony, label these people “fated”.

Conveniently, the present calculation — done as a percentage of that total — does not depend on agreeing about how large that population is, or what portion of total smokers they constitute.

• Ignore deaths that are hastened by smoking by hours or days.  More generally, ignore YPLL and just count deaths as the events.

Anyone who thinks seriously about “dying from smoking” statistics quickly realizes that serious analysis of them forces you to make all kinds of simplifications, and make guesses about what the “official” statistics really mean. Most such calculations demand these particular simplifications because it is probably the case that almost everyone with a long smoking history who eventually dies from a deteriorating “natural cause” dies a bit earlier because of the lung and CV weakening from smoking. This illustrates that the usual statistics are almost impossible to use in serious analysis because it is never clear how many years (or days) of potential life lost are necessary before someone makes the dichotomous move from “did not die of smoking” to “died of smoking”. Indeed, the people putting out the statistics probably have no clue about the answer, and most would not even understand the question. So for present purposes, I stick with the (perhaps false) simplification that each of the N people who are counted as dying from smoking do so many years before they otherwise would have.

• Of the fated, some have already smoked the cigarette that pushed them over the edge so that smoking will kill them even if they quit now. Call this group “doomed”.
• It is possible to estimate how many of the fated are doomed, and thus adjust the potential deaths-from-smoking saved by quitting/switching. Note, however, that the result of this calculation is based on the average smoker (or equivalently: randomly selected smokers or all smokers) — if you want to calculate the effects of those who have actually switched, it becomes a lot more complicated (discussed bel0w).

Note that these points are the ones at the core of the calculations I used in this paper.

• Assume the fated will smoke for an average of 50 years without intervention.
• Half of the fated will die from CVD.
• Half of the elevated CVD risk disappears almost immediately upon quitting smoking, and the other half returns to (almost) baseline over two years.
• This averages to one-quarter of the fated having one year of being doomed, yielding .25*(1/50) or about one half of one percent of the fated already being doomed from CVD.

This is the good news — there is almost always still time to escape fatal CVD if you quit now.

• The other half of the fated will die mostly from cancer and long-term lung disease.
• These risks take an average of ten years, or a bit more, to return to baseline after quitting.  (Lung cancer is longer than that, and COPD never fully reverses, but other of these risks disappear more quickly.)
• That yields .5*(5/50), or about 5% (probably a bit more) of those the fated who are already doomed from those diseases.

Bad news for smokers, but good news for the aforementioned CDC propaganda efforts. (Protip: quit sooner rather than waiting!)

• When considering switching rather than quitting to abstinence, any synergistic effects from using the alternative product and being a recent ex-smoker need to be considered. These are probably quite small (down in the rounding error range) but presumably do push up the total a bit. That is, a few more are already doomed if the alternative is switching as compared to abstinence.

Note that this factor should not be confused with the risk, if any, of just using the alternative product instead of ever smoking. It is not unreasonable to assume that the wash-out period for CVD risk is increased, at least by a bit, by continuing to use nicotine. A bit of such delay is not completely trivial; recall that the good news about CVD risk was all about how rapidly it disappeared. Also, if the alternative has lung involvement (i.e., e-cigarettes or other inhalers), it could push incipient lung-based dooming over the edge. Again, we do not know this to be the case, but we cannot rule it out.

Important practical note: this does not mean that switching is an inferior alternative to quitting to abstinence. If the switching could happen today whereas the quitting to abstinence would not happen until next week (or more likely, long after that), the chance of smoking that dooming cigarette during that week is almost certainly greater than the synergy effect. See my above-linked paper for more on that theme.

• Adding up these risks yields something in the mid-single-digit percentage range for fated smokers who are already doomed.
• Any estimate of how many current smokers could be saved by THR — or by quitting via any other means — needs to be adjusted downward by this factor.

Notice the overtly stated lack of precision in that final estimate.  Roughly speaking, we can say “5% or a bit more”, but experience shows that when you put out a number like that, people mistake it for being precise. I would guess that it is probably good within a factor of two. That is, if someone insisted that the real number was 11% or that it was 3%, I would not say I was sure they were wrong. If they said 20% or 1% I would say that was unsupportable.

So, circling back to what West said, he basically claimed that 90% of fated smokers would be saved if they all switched to e-cigarettes. This has been criticized because it was interpreted as suggesting that e-cigarettes are 10% as harmful as smoking, which is a huge overestimate based on all we know. However, if he were quietly accounting for 5% or more being already doomed, then the implicit estimated risk from e-cigarettes is down at 5% or a bit less. Still high, but not outside the plausible range. Of course, I don’t know if that was what he was doing.

Also, it gets rather more complicated. Saying it would save 90% of the currently fated if they all switched is fine (modulo disagreement about the exact number). But consider West’s formulation, “For every million smokers who switched to an e-cigarette we could expect a reduction of more than 6000 premature deaths in the UK each year”. There are two problems with this.

First, the millions smokers who actually switch will not be average (i.e., random) smokers. The data on this is pretty lousy, but it appears that in the USA (he was focused on the UK), the first wave of switchers were predominantly in their 30s and 40s, and many believed themselves unable to quit smoking after many other failed quit attempts. This put them at higher than average risk of being fated (if they really never would have quit otherwise) but a lower than average risk of being doomed (they were still young). This would mean that a calculation based on the average smoker quitting would substantially underestimate the benefits for this population (even apart from disagreements about the number for the average smoker).

After that first wave, switching appears to have skewed young; younger switchers were more likely to quit via other means before they were doomed, but are almost certainly not already doomed. These have opposite effects, so the net direction of bias compared to average smoker is ambiguous. Obviously some older smokers switched too, so there was a doomed subpopulation among switchers, but they appear to be significantly underrepresented compared to random selection.

Second, the “each year” is clearly not right. If a random million smokers switched right now, there would be some lives saved next year, but the number saved per year would increase over time, as the dates passed when more of the non-doomed fated reached the age they would have died from smoking. It would then pass a peak after most of that population passed the age at which they would have died from smoking, and drop down to zero late in the century. You could convert this to a scalar with something like “the average saved each year over the next 30 [or 20 or 40] years”, but it is clearly not an annual constant and there is no obvious right way to annualize it because of thin right tail makes it sensitive to the arbitrary choice of the annualization period.

[Update: It occurred to me that this was a classic “the units don’t match” problem — at least in spirit if not quite literally. For a change that is measured in one-off units of “X people change from state Y to state Z, once (and forevermore)”, with no time unit in the denominator, it is very unlikely that the outcome can be properly measured in a unit that has years in the denominator (i.e., lives saved per year). Measuring the absolute change in total people who would ever die from smoking would work.]

The problem here, of course, is that the easiest way for any of us to think about this is to start with what will happen under the status quo, pretending that it is in demographic equilibrium, even though we know it is not: Smoking currently skews older, increasing the doomed portion as a portion of current smokers, and the rate of uptake is steadily dropping. This is then compared to a steady state in which a portion of the current population switches and (roughly) the same proportion of would-be smokers takes up the alternative in the future to maintain the new relative rates. And finally, the statistics reported are what would occur after the initial washing-out period, when a new equilibrium emerged in this fictional population equilibrium scenario.

It is complicated. I realize that people want a simple scalar. But there must be some way to present a simplified scalar without embedding it in phrasing that is out-and-out wrong.

Thoughts?

### 15 responses to “Number of lives saved must be adjusted for those who cannot be saved, etc. (wonkish)”

1. Thought: almost any number that can be agreed upon is better than no number, as it will be In the 90% or better range. Wickholm in 2005 put an ST number cancer incedence at 7 per 200k users. That is roughly 35 per million. Compared to West’s 7000 or the newer official stats from Sweden of 12000 per million cigarette smokers.

2. Detlev

Fine piece. But a lot of assumptions. Wouldn’t it be easier and certainly more precise to go with a ‘years of live saved’ version? There is ample information about the expected lifespan of smokers, never-smokers and quitters (who really should be called stayers, perseverers).

Furthermore what I always find lacking is the ‘quality of life’ part. I know I have a bigger chance of dying 10 years earlier. Then again in my family dementia eats up the latter 20 years anyway so what’s the loss?

• Carl V Phillips

Thanks. YPLL is always a better measure, of course, since there is not really such thing as lives saved. As illustrated by the foray into trying to get my head around such numbers — briefly discussed in the post — there are a lot of hidden conditions that I am pretty sure the people at CDC “calculating” those numbers do not even think seriously about. It would be more precise in the sense that if you are measuring a phenomenon that is not really well-defined, you cannot really claim to be precise. However, once you define what the dichotomous measure really is, it is not clear you could measure YPLL more precisely. Indeed, it would definitely be harder because it is a much more complicated statistic. The most obvious way to calculate it is to attribute a death to smoking (as the first fuzzy statistic requires) and then try to figure out life expectancy in its absence. Just comparing lifespans would indeed give you a very rough cut at it, and is relatively easy, but it is way too rough: differences among those populations that are not caused by the smoking are huge. While you can at least pretend to adjust for some of that in an epidemiology study of a particular disease outcome (though that is generally done badly) the statistics that give you an easy cut at unadjusted life expectancy do not tend to have very rich information on confounders.

As for assumptions, I disagree: I technically don’t make any of what would normally be called assumptions, though I casually use that word a few times. I make a lot of estimates that the calculation hinges on, but any such calculation needs to. I obviously think these are pretty good or I would not try this (or put in a lot more caveats). But if someone thinks they are wrong, they can easily swap them out for a preferred figure. Assumptions usually refers to something that is more about the mechanisms of the analysis than the input numbers, as in “assume people have full information and are rational” or “assume that the point estimates of deaths from smoking in study X are exactly right”. The latter is one of many assumptions that go into the “official” body count statistics that are probably wrong. Quite often (as in this case) assumptions are unstated and so deeply buried in the guts of the calculation that the observer cannot figure out how to adjust for their falsity. If you do not like any of my estimates, the adjustment is easy. If you do not like the assumption that putting in particular covariates into a model eliminates confounding you are pretty much stuck.

This is why expert best-estimates are generally more useful than these fancy black-box numbers that get thrown around. When you start looking at the origins of those “precise” numbers (they report the deaths from smoking with two, sometimes three, sig figs, and yet they cannot even define what they mean!) it is almost parody, with countless entries and calculations and adjustments that would only matter if you could get precision up to one part in a thousand, alongside hidden assumptions that affect the result by a factor of two.

Quality of life matters, of course. A lot. That does not mean you cannot calculate survival without reference to quality, or make use of that statistic, which is what I and West were doing in the present case. When someone starts making policy pronouncements and general overviews, they are obligated to consider QoL (but never do). But someone still needs to calculate survival statistics.

• Detlev

Carl, I sense a bit of defensiveness on your part towards my reply. That is not at all nessesary, any mix-ups in assumptions and estimates and the like are mainly originating in me not being a native english speaker (I’m dutch). I am glad someone (i.e. you) is doing the work I can’t do.

• Carl V Phillips

Oh, no problem. I was not in any way offended (nor would I be if someone said “you are out-and-out wrong and here is why…” — that is how science works), and I was not being defensive. I just took the opportunity to partially explain why I did not work in YPLL even though it is a better unit. The belabored contrast between “estimate” and “assumption” was more a response to a problem in the world, rather than anything you said: There are lots of calculations out there that are dressed up as precise, and thus are naively interpreted as being so, even though they are so laden with dubious hidden assumptions that they are actually worse than a best expert estimate even though they get treated as if they were better.

3. You and Brad Rodu were working out the thing that’s been bugging me for a couple days. Vis: even assuming every smoker switched to e-cigs, what is the expected decline in disease rate? Knowing that certain precursors are likely already established it can’t be zero.
Second idea along with that. Study time for e-cig harm. Even a well designed longitudinal study would likely have difficulty controlling for the precursor phenomena. This likely leads to spin “E-cigarettes not the panacea promised, user disease rate still high.”
Thanks for putting your epidemiological expertise on these ideas Carl. Much appreciated.

• Carl V Phillips

Yeah, exactly. That is why basically all we know about the effects of smoke-free nicotine come from studies of lifetime snus users, which we then assume are a good estimate of the benefits of switching, and then further assume e-cigarettes are about the same. There are good reasons for accepting both of those assumptions, of course, but they are most definitely assumptions.

In theory it is possible to compared people who quit to abstinence to people who quit via THR, and thereby assess any increase in risk compared to the former caused by the latter. But the reality is if those in the different groups differ just a tiny bit — one of them, say, having smoked an average of a few cigarettes more per week, or eating a couple fewer servings of vegetables a week — the effect of that will swamp the signal you are looking for. Our data is never good enough to adjust for confounding that perfectly.

4. Chris Price

It seems to me that the value of West’s recent statement is that it is the first time that an establishment tobacco control figure has given any number at all for the potential mortality expected from ecigs per million users per year, compared to the same for smoking – at least in terms of annual figures that people can get their teeth into. Britton’s numbers were probably too big and too theoretical to get much reaction; nobody seems to have commented on those to any degree ( the ‘5 million’ number).

I believe that West’s mortality projections represent a theoretical model: at some point in the future, when potential smokers initiate with ecigs instead of cigarettes, and are never exposed to cigarette smoke, then the mortality rate will be 330 per million annually, at most.

To get a *real* figure – what’s going to happen next year, and in 2024 for example, then things get incredibly complicated. It is likely that, as you say, few can actually work that out and even fewer are allowed to publish an honest version of it. Perhaps the best way to express such figures is graphically. You could present a graph with year, smoking prevalence and vaping prevalence represented. The number of lives ending more than 5 years prematurely would fall over time as more smokers switched over to vaping.

The calculations required to produce such a graph would be beyond almost everyone and the assumptions that would have to be made would be equally problematic. Hardly anyone would agree the graph looked right even though it would take hundreds of hours to tweak.

In the end, West’s purely theoretical figures are useful because they are simple. If a million people initiate with vaping and never smoke, at most 330 per million per year are likely to die (early) as a result. It would probably have helped if he’d specified exactly what he meant, though perhaps he assumed it was obvious.

Producing a ‘real-world’ version of it even for a single country seems an almost impossibly difficult task – as you show – and might generate more criticism than plaudits anyway. Oh, and let’s complicate matters by choosing a place with about 8 million ST users and an unknown number of vapers, just to make sure that plenty of aspirins are needed for the calcs :)

5. I smoked for 38 years, and have used ecigs for less than two. I feel better and believe it has helped me in many obvious ways. But I accept that the damage from those 38 years is probably more profound than what I can see or feel. My reason for fighting for THR is for younger people — smokers and those who still haven’t begun smoking. If vaping makes it through this battle relatively intact, what will the death rate be in twenty or thirty years? That’s certainly what PH people should be thinking about — since they’re so determined to protect the children.

Do they sincerely believe their current anti-smoking campaigns combined with public bans and higher taxes will reduce smoking as a health threat so well that ecigs could cause more harm than good? Or do they just hate anything that bears a passing resemblance to smoking? Are they — especially the FDA right now — even able to honestly ask themselves those questions?

• Carl V Phillips

They exist so completely in an echo chamber that, yes, they manage to believe things that are contrary to all the evidence. It is really pathetic.

Two years with no apparent crisis means you have already reduced your chance of being among the doomed by well over 1/3, and counting. Best of luck with the continued “and counting”.

6. Thank you for the post. I wrote a similar calculation, in YPLL, here (the post is in spanish) http://www.e-volutas.com/2014/03/lavarse-las-manos.html

7. A bit late in the coming but anyway. The calculations and reasoning above does include saving. It however does not (partly) take in to account extension and improvement. A Health economy friend of mine always comes back to a weird currency that they use in their work. (Hope translation is understandable). It is called “considerably quality adjusted extra year of life”. Ought not switching today compared to cessation next year be a very compelling argument in our favor based on the extention and improvement parameters? Just a thought.

• Carl V Phillips

If I am understanding, you are arguing that the improved quality of life should also be counted as a benefit of something. That is certainly true for decision-making — all the costs and benefits should be counted. However, that does not mean it is not a legitimate question to just ask how many premature deaths will be averted. That is part of “all costs and benefits” so you need it. It is just important to not confuse it with all costs and benefits, as the “public health” people tend to do.

• 100% agreement if it were a 1 question discussion.
My point though, that I bang my head against every available brick wall (lots of them, you are a very welcome exception:) is we might consider trying to create sufficient a bombmat of positive likely outcomes and total benefits so as to make any one single scare tactic completely irrelevant and inconsequential in the greater whole scheme of things. To use a silly analogy from a known NY zealot: let’s solve obesity in the USA by banning super size soda in Manhattan. It will only work if we argue all, alternatives, all benefits, all risk reductions in a cohesive coordinated manner. They have more money so we have to have a better play book. (You come across as being brutally scientifically honest – I used to work with techie and engineering megapros. It turned out to be mainly a job of translating their gobbledygook to marketing gobbledygook and finally to the trickiest ones of all economics gobbledygook and awfully difficult legalese).

If this posting comes across as offensive I deeply apologize. It is actually meant as a compliment. I cannot imagine a better stick (pencil) than yours, to bash certain others over the head with. I just wish we could find a really good spin doctor to maximize effect of your excellent output. Br befrits

• Carl V Phillips

Definitely no offense. I consider those characteristics you cite to be features, not bugs :-)

I think I know what you are saying, and am pretty much in the same place. I agree that it is useful to have simple messages like the “we could save X lives” discussed here. I noted this was wonkish and was intended to help technically improve the science about such statements (and I have not followed-up with an update based on discussion — thanks for the reminder). It was not an attempt to question the value of such statements for getting the basic message across. Also along those lines, I have on my to-do list to update the estimates of the comparative risks of different product categories, this time not hesitating to note that it is plausible that smoke-free tobacco products provide a net benefit.