Excess excess costs of smoking

Remember that $1.9 billion dollar smoking cost figure that started floating around a few months ago?

I've just received by OIA the documentation on it (linked to below). Here's how I think it works. If I understand the number correctly, it's nonsense.

Somebody at MoH stratified their health data (NHI and resident 2007-8) by gender, income, age, ethnic group and smoking status. They then found that smokers had higher health costs, adjusting for each of the control variables. Add up those excess costs and you get $1.9 billion.

Now, why is this nonsense?

Suppose a 50 year old smoker costs more than a 50 year old non-smoker, correcting for everything else, and a 70 year old smoker costs more than a 70 year old non-smoker. But there are many fewer smokers around in the 70 and up group than there are non-smokers.

Let's take a simple example with completely made-up numbers. Suppose that all non-smokers live for three periods: young, middle and old. At age young, they cost the health system $200 each. At age middle, they cost the health system $500. At age old, they cost the health system $2000. All smokers live through periods young and middle but have only a 20% chance of reaching age old because, well, cigarettes kill people. At age young, smokers cost the health system $250 each. At age middle, they cost the health system $1000 each. At age old, they cost $4000. If we take a snapshot in any year, we'll see 1000 young, half of whom are smokers; 1000 middle, half of whom are smokers; 600 old, 100 of whom are smokers.

Let's now add up the excess costs of smoking, as best I understand the MoH method. We have 500 young smokers, each adding excess costs of $50: $25,000. We have 500 middle smokers, each adding excess costs of $500: $250,000. We have 100 elderly smokers, each with excess costs of $2000: $200,000. Total excess costs of smoking: $475,000.

But we have 400 smokers who fail to reach age old and consequently fail to impose any costs on the health system. If they had only the health costs of non-smokers, they would have cost the health system $800,000. The total lifetime health costs of the non-smokers is $2700; the total lifetime health costs of the smokers, on average, is $2050.

So we found by the MoH method (as best I understand it) that smokers impose massive costs on the health system: $475,000. But if we instead take a life cycle approach, we find instead that smokers save the health system a tidy $325,000.

My numbers are entirely made up, but I don't think I've been particularly aggressive in my assumptions. Young smokers don't cost the health system a whole lot more than non-smokers: smoking has large cumulative effects, but it takes a while to cumulate. But I still have them costing 1.25 times what non-smokers cost. At middle and old age, I have them imposing double the cost of non-smokers. But because smokers die earlier, and because even non-smoking old folks cost the health system a lot of money, they wound up saving the health system money. Some non-crazy numbers wound up reversing the fiscal effects of smokers on the health system if we consider a life-cycle rather than a snapshot "excess cost" approach. Careful readers will of course note that this is basically an application of the Simpson's Paradox: even if each cohort of smokers costs more than each cohort of non-smokers, because fewer smokers show up in the more expensive older cohort, the average cost of smokers winds up being lower than the average cost of non-smokers.

I'd be mildly surprised if a proper re-doing of the MoH figures found a reversal of the Vote.Health fiscal effects: I doubt mortality is quite as bad as I've put it above. But I wouldn't be at all surprised if fixing only this bit shaved a billion dollars off their figures. Again, if I'm understanding this correctly, counting the health care costs of a smoker dying at 63 of lung cancer against the health care costs of a non-smoker at 63, but taking no account of that that smoker then doesn't go on to impose other health care costs while dying of congestive heart failure at age 76, essentially assumes that the smoker could have gone on living forever without health care costs absent the smoking. But everybody dies of something, and lots of those somethings are pretty costly.

A few other rather important considerations:

• They've stratified their sample by a few covariates, but if smoking correlates with other risk-taking behaviours, then smoking costs may well be conflated with other risk-taking costs.
• In considering only Vote.Health, they've left aside that smokers, by dying early, cost the superannuation system a whole lot less as well: they pay into the system but draw far less from the system.
• We also need to account for that cigarette excise taxes are paid upfront while health care costs are far in the future. We can kinda view the young smoker as paying an annuity to the government to cover excess health costs 30 or 40 years in the future. Even if we find that that smoker paid in exactly as much as he later cost the health system, the time value of money means that the fiscal costs to the government are strongly negative.

I've put up the OIA document at Scribd. It's less than transparent about the full method used, but the above gives my best understanding of what they've done. I've also emailed the MoH contact listed as responsible; he's checking with the stats folks to see whether my interpretation of things is right. I'd be pretty surprised if the stats guy who came up with the number in the first place had any intention that it get out without a whole lot of further work; I'd also be surprised if the more zealous folks who really wanted big numbers over on the tobacco control side of MoH cared much about having a sound number or whether the number had gone through a proper quality assurance process. They needed a big number to help push the huge increase in tobacco excise taxes: the clean up work can always come later.

Shame on whoever at MoH let this politically convenient number out without proper quality assurance. And shame on everyone who repeated the number without thinking for a moment just how MoH managed to add well over a billion dollars to the prior estimate.

Update: Recall of course that even the anti-tobacco lobby's numbers show that smokers' excise tax payments far exceed the costs to the health system.