Count me confused. I listen to the “studies” that various physicians authored, stuff like “a daily cup of coffee cuts cancer risk by 20%”, or “a daily glass of red wine cuts heart attack risk by 40%”, eating green vegetables reduces cancer rate by 10%".
My question: if I drink coffee, green tea, red wine, etc., do these benefits add up?
And, if you eat ALL of these “healthy” substances, do you actually become immne to cancer, heart disease, diabetes, etc.?
This is a wonderful question. One difficulty comes because adding variables complicates any study. I’ve seen studies where they measured two items and the added benefit. Remember, the added benefit of the two could even be more than the cumulative simple addition of the benefits. Two things that had a 10% difference individually might have a 25% when combined.
When you look at an ingredients label on food, the items listed are part of a GRAS list. GRAS stands for generally regarded as safe. The possible combinations of items make it impractical to study in combination as to whether they are always safe.
Obviously all the good things can’t add up or some people would live forever.
I have seen it mooted the opposite way.
For example, smoking may increase the risk of certain diseases such as emphysema by X, but smoking whilst also being asthmatic increases the risk by multiples X x A = INCREASED RISK, instead of it being X + A.
Assuming that is true, then I would expect that benefits may also multiply up - what works one way, surely works the other?
No, it means in one or more studies people who drink a daily cup of coffee had an average lower incidence of cancer compared to people who didn’t of 20%, or even worse one particular subset of people in a study had that high a risk reduction.
Or, in the case of journalists reporting it might mean someone tried a chemical that also occurs in broccoli on cancer cells in a petri dish and ballparked a 10% risk reduction when badgered for a number for real world effect.
All of us will die eventually and some of us from things our diets make us, on average, less susceptible to.
Cumulative? Possibly. Additive? No.
As they are mostly imaginary numbers, addition of them is quite possible. But you have to keep them separated from the real part.
Of course not.
It is certainly possible that the benefits combine. However, even in an ideal case, they would combine multiplicatively, not additively.
Meaning, if a daily glass of red wine cuts the risk by 40%, and eating green vegetables cuts the risk by an additional 20%, then if you do both, your risk goes down by 52% (.40 + .20 * (1.00 - .40) = 0.52), not 60%. This means that, even theoretically, you can never get your rate down to 0%.
And note that you can totally erase any of the benefit of these things by adding in risk factors, like being overweight.
This is pretty seriously non-obvious. Can you justify it?
Sounds like it might go like this:
Daily glass of red wine cuts risk by 40% (i.e. reduces risk to 60% of control group)
Eating green vegetables cuts risk by 20% (i.e. reduces risk to 80% of control group)
IF these are statistically independent, then:
Daily glass of red wine AND Eating green vegetables = 1 * .6 <wine> * .8 <veggies> = .48 = 48%. So, doing both reduces your risk to 48% of what it would have been otherwise, i.e. it reduces your risk by 1-.48 = .52 = 52%
What we don’t know if they are truly independent though (i.e. if doing them both magnifies each other’s effect due to super-heath or if they don’t fully complement each other because each improves health through the same biological manner (e.g. in the same way that if you smoke both cigarettes and cigars, you don’t necessarily get TWO separate “you smoke” risk factors multiplied in))
I totally agree with this, but in general, you assume dependence unless proven otherwise. That’s the bit I have a problem with.
Sorry. That’s what I meant by “in an ideal case” - meaning, assuming that both foods decrease your risk by independent mechanisms.
Which is the big uncertainty. E.g. if a little wine improves your health by cleaning your arteries, and eating veggies improves your health by cleaning your arteries, you are probably going to only get the benefit of one, in the same sense that changing your car’s oil every 1500 miles instead of every 3000 miles isn’t likely to give you a double maintenance effect and greatly prolong the life of the car. Maybe it’ll get you another year of life, but maybe not.
Part of the problem when combining items is that they may actually REDUCE the effects. For example, iron in spinach is made less available by Vitamin C. So… while they might be healthy independently, the vitamin C reduces a health benefit of the spinach.
On reflection, this is assuming something much stronger than simple independence. If A is the event that you get some disease and B is the event that you receive/give yourself some treatment of interest, then what’s being claimed is that P(A|B) = 60% * P(A|B[sup]c[/sup]). What you’re claiming is that if B and C are two treatments of interest with P(A|B) = 60% * P(A|B[sup]c[/sup]) and P(A|C) = 80% * P(A|C[sup]c[/sup]), then independence of B and C implies that P(A|B, C) = 48% * P(A|B[sup]c[/sup], C[sup]c[/sup]). This is simply not true for pretty much any distribution over A, B and C that you didn’t get by working out the numbers so that it does hold.
(You can look here for a more detailed explanation of where these numbers in the studies come from.)
ETA: This does work out if A, B and C are independent, but that’s not really an interesting case.
Actually, Vitamin C has been shown to increase the bioavailability of non-heme iron, not decrease it:
Oops… thanks for the correction. It looks like oxalate/oxalic acid is what’s believe to reduce absorption and C does assist.
And it has a phase angle that is vanishingly close to ±π/2.
Stranger
Well, the most obvious thing is that if you were to do 3 things that reduced your risk of something by 40%, you’d have a -20% chance of getting it.