Fun with numbers: NHS Stop Smoking Services

From The Metro:

Help offered by the NHS to people wanting to give up smoking may have saved 70,000 lives over the last 10 years, it has been claimed (1). Researchers at the Department of Health based the figure on the two million successful quit attempts (2) recorded since the introduction of NHS Stop Smoking Services. Reformed smokers are considered to have quit if they have kept away from cigarettes for a month.(3)

... Studies have shown that ... 60% of current smokers have made a serious attempt to kick the habit in the past five years (4).
-------------------------
Ho hum, something tells me the figures are wildly exaggerated. There are two ways of looking at this: a) Just take the figures in the article at face value, which suggest that three-fifths of those that the NHS have "helped" to quit in the last ten years would have died by now, or b) Look at relative life expectancy tables and so on, which suggest that the NHS would have to have "helped" three times as many smokers to quit as actually did so.

Method a), taking the article at face value:

(1) Note the use of the words "may" and "has been claimed", which is press release-speak for "we are parroting questionable figures".

(2) OK, maybe there were "two million successful quit attempts", but "attempting" and "succeeding" are two quite different concepts...

(3) To consider everybody who "kept away from cigarettes for a month" as a "successful quit attempt" is pathetic, as the relapse rates are enormous...

(4) ... there's a good clue here. If on average a quarter of adults in England smoke, that's ten million. If 60% of them, i.e. six million, have made (say) two "attempts" in the last five years, that's a total of twelve million attempts. And how many gave up? If there are 1.4 million fewer smokers than five years ago (from the article, smokers as a % of adult population down from 28% to 21% over ten years, so divide that by two to get the five year decrease), about half of whom may simply have died or be young people who were never seriously addicted anyway, then maybe 700,000 stopped smoking as a result of quitting; each actual quit must follow an "attempt"; so out of twelve million "attempts" one-in-seventeen was successful.

So, out of the two million NHS-assisted "attempts", only about 118,000 will have led to somebody stopping smoking permanently, so to claim that 70,000 of them (59% or three-fifths) would otherwise have died in the last ten years is laughable.
--------------------------------------------------
Method b) is to look at life expectancy tables.

A thirty year old in England had a remaining life expectancy of 55 years in the middle of the ten year period (from Table 18). Let's assume it is true that smokers live ten years less than non-smokers, so an average thirty year-old smoker has a life expectancy of 50 years (2% chance of dying each year) and a thirty year-old non-smoker has a life expectancy of 60 years (1.7% chance of dying each year), so if you smoke, your chance of dying goes up by 0.3% (in absolute terms).*

Assuming the same number of quitters each year and a cumulative figure for "lives saved", we can break that 70,000 down into 1,273 in the first year; 2,546 in the second year (being 1,273 "saved" in the first year plus another 1,273 "saved" in the second year) and so on (tip: 1+2+3+...+10 = 55 and 1,272 x 55 = 70,000).

If the chance of dying in any year goes down by 0.3% as a result of giving up, then the number of lives saved in Year 1 (1,273) = the number of people who quit ("Q") x 0.3%. Turning that round, Q = 1,273 ÷ 0.003 = 424,333 people, i.e. 424,333 people would have to quit in Year One (and each subsequent year) and that would "save" 424,333 x 0.3% lives in Year One (being 1,273, the figure derived by dividing 70,000 by 55); 2,546 in Year Two and so on. Over ten years that would be 4.2 million quitters.

While it is true that 2.8 million people appear to have stopped smoking over ten years (ten million x 28% minus 21%), let's say half of them died or were young people who were never seriously addicted anyway (as above), so that's 1.4 million quitters. So for the "70,000" figure to be true, the NHS Stop Smoking Service would have to claim credit for getting 4.2 million people to have stopped smoking, as against the 1.4 million who actually did, i.e. three times as many.

Just sayin', is all.
--------------------------------
* The even more scientific approach says that if a thirty year smoker old has a remaining life expectancy of 50 years, after 50 years half will have died. Assuming the same survival rate every year, 98.6% of that cohort survive each subsequent year (=0.986^50=0.5) and with a 60 year life expectancy, the survival rate is 98.9% (=0.989^60 = 0.5), which also gives an 0.3% better survival rate for non-smokers.