Statistics and bacon

[wigginhall]

Not being a statistician, I need help with bacon.  Another report today that every slice of bacon or ham increases the risk of bowel cancer by 20%   Now this puzzles me, because if about 6% of people will develop bowel cancer, that 20% figure applies to the 6% who will get cancer.  This means a 1% rise, doesn't it?  Or does it mean that the 94% who won't get cancer, are more likely to?

If I have made a Horlicks of this, please tell me.

[bluehillside Retd.]

Wiggs,

Not being a statistician, I need help with bacon.  Another report today that every slice of bacon or ham increases the risk of bowel cancer by 20%   Now this puzzles me, because if about 6% of people will develop bowel cancer, that 20% figure applies to the 6% who will get cancer.  This means a 1% rise, doesn't it?  Or does it mean that the 94% who won't get cancer, are more likely to?

If I have made a Horlicks of this, please tell me.

Let me help you. If every slice increases the chance of bowel cancer by 20%, that means that five slices equals 100% so you're guaranteed to get it. That's why I've only ever eaten four slices of bacon. I'm taking no chances me.

Oh hang on though - do smokey bacon crisps count? Bugger....

[ProfessorDavey]

Not being a statistician, I need help with bacon.  Another report today that every slice of bacon or ham increases the risk of bowel cancer by 20%   Now this puzzles me, because if about 6% of people will develop bowel cancer, that 20% figure applies to the 6% who will get cancer.  This means a 1% rise, doesn't it?  Or does it mean that the 94% who won't get cancer, are more likely to?

If I have made a Horlicks of this, please tell me.

It would mean 20% greater than the existing risk. So if your existing risk was 5% the 20% increased risk would mean you final risk would be 6%.

These stats are pretty well meaningless unless you know the starting point risk. So if you had a one in ten thousand chance (0.01%) chance of getting a disease and doing something increased that risk by three fold (300% increase) then your final risk would still only be 3 in ten thousand (0.03%) so there isn't much point worrying as the likelihood of not getting the disease is pretty well indistinguishable (99.99% vs 99.97%).

If the starting point risk is 6%, well that's quite a different matter.

[wigginhall]

Well, I think 6% is the incidence often cited for bowel cancer, so the 20% rise figure is misleading.

Blue, damn, forgot about crisps.

[ProfessorDavey]

Well, I think 6% is the incidence often cited for bowel cancer, so the 20% rise figure is misleading.

Blue, damn, forgot about crisps.

I don't think it is misleading - it just means that the final risk is 20% higher than the initial (6%) risk, in other words 7.2%.

[Roses]

We never have a cooked breakfast so it is very rare for us to eat bacon.

[bluehillside Retd.]

Floo,

We never have a cooked breakfast so it is very rare for us to eat bacon.

Breakfast? You can have it for breakfast as well as for lunch and dinner (plus a late night snack of course)? Oh Lordy...!

[bluehillside Retd.]

Prof,

I don't think it is misleading - it just means that the final risk is 20% higher than the initial (6%) risk, in other words 7.2%.

Actually I think it can be presented very misleadingly. The press will often say something like "increases the risk by 20%" which at first pass can be misinterpreted as "increases the risk to 20%". Or worse, you might think that a background rate of, say, 5% would then be 25% for the bacon eaters. That's the trouble with headlines - short (but misleading) summaries fit the page better than longer (but accurate) ones.     

[Roses]

Floo,

Breakfast? You can have it for breakfast as well as for lunch and dinner (plus a late night snack of course)? Oh Lordy...!

We have had it occasionally if I have done a fry up for lunch, but I can't remember when we last had it. We never have snacks, and don't eat anything after 6pm.

[bluehillside Retd.]

And while we're on the subject of background risk, "Knife murders increases by 100%" is terrifying right, unless that is the rate has gone from 1:1,000,000 to 2:1,000,000 (ie, a 100% increase) in which case you're probably not going to change your behaviour much in response, albeit that it's still a tragedy for the two victims. 

[Nearly Sane]

I don't think it is misleading - it just means that the final risk is 20% higher than the initial (6%) risk, in other words 7.2%.

is it? Or is it an increase of .2% v the 94%?  Stats need context. Assuming the context is not a good position

[ProfessorDavey]

Prof,

Actually I think it can be presented very misleadingly. The press will often say something like "increases the risk by 20%" which at first pass can be misinterpreted as "increases the risk to 20%". Or worse, you might think that a background rate of, say, 5% would then be 25% for the bacon eaters. That's the trouble with headlines - short (but misleading) summaries fit the page better than longer (but accurate) ones.   

But that is about the presentation of the stats to sell papers rather than the stats themselves.

[ProfessorDavey]

is it? Or is it an increase of .2% v the 94%?  Stats need context. Assuming the context is not a good position

Eh - don't understand your maths.

Clearly if the risk is increased it relates to the original risk of something happening, not the non-risk of something not happening.

[bluehillside Retd.]

Prof,

But that is about the presentation of the stats to sell papers rather than the stats themselves.

I agree, but the point I think was that the presentation can be misleading even when the research paper being cited isn't. 

[ProfessorDavey]

Prof,

I agree, but the point I think was that the presentation can be misleading even when the research paper being cited isn't.

Which requires the media to be more responsible in their presentation - plus also a better informed, more numerate, reader/viewership to be able to see the wood for the trees.

[Nearly Sane]

Eh - don't understand your maths.

Clearly if the risk is increased it relates to the original risk of something happening, not the non-risk of something not happening.

is it clear? Because that's just your assumption.

[ProfessorDavey]

is it clear? Because that's just your assumption.

Yes it is clear - if it describes an 'increased risk' the baseline is clearly the initial risk.

Still don't understand your maths though

[bluehillside Retd.]

Prof,

Which requires the media to be more responsible in their presentation - plus also a better informed, more numerate, reader/viewership to be able to see the wood for the trees.

Yes indeed. How do we achieve all that though, especially in this age of citizen journalism where anything pretty much goes?

Just to develop the nonsense by the way, if the background risk of getting the cancer is 5%, that means the chances of not getting it must be 95%. So if the chances of getting it post full English breakfast go up by 20%, that must mean that the chances of not getting it also decrease by the same 20%, so instead of 95% it’s now 76%!

Yikes!   

[Nearly Sane]

Yes it is clear - if it describes an 'increased risk' the baseline is clearly the initial risk.

Still don't understand your maths though

you just worship at the goddess of assumption.

[ProfessorDavey]

There is a further complexity here, which is the proportion of people who do, and do not eat bacon (in this case).

Wiggs assumes the increase is over the starting point 6%, but this is the risk for the whole population - in other words those that do and those that do not eat bacon. The actual 20% increased risk is comparing those that do eat bacon with those that don't. In a world where most people do eat bacon then the risk of eating bacon is only a touch higher than the 6% of the whole population. The big difference would be a decreased risk (down to about 5% for those that don't eat bacon.

[ProfessorDavey]

you just worship at the goddess of assumption.

Sometime you simply have to assume that people are able to understand simple english - in other words that 'every slice of bacon or ham increases the risk of bowel cancer by 20%' means just that, an increased risk.

[bluehillside Retd.]

NS,

you just worship at the goddess of assumption.

Well, maybe he’d be in good company if he does:


Catholic Mariology

"The four dogmas of perpetual virginity, Mother of God, Immaculate Conception and Assumption form the basis of Mariology."

https://en.wikipedia.org/wiki/Catholic_Mariology

[Nearly Sane]

Sometime you simply have to assume that people are able to understand simple english - in other words that 'every slice of bacon or ham increases the risk of bowel cancer by 20%' means just that, an increased risk.

In the case of science reporting, your assumption just makes you assuming, and based on evidence against it.

[Nearly Sane]

NS,

Well, maybe he’d be in good company if he does:


Catholic Mariology

"The four dogmas of perpetual virginity, Mother of God, Immaculate Conception and Assumption form the basis of Mariology."

https://en.wikipedia.org/wiki/Catholic_Mariology

So they are a perpetual virgin?

[bluehillside Retd.]

Prof,

Sometime you simply have to assume that people are able to understand simple english - in other words that 'every slice of bacon or ham increases the risk of bowel cancer by 20%' means just that, an increased risk.

But look at the ambiguities in that "every"! Clearly it can't actually mean "every" or just one slice eaten by an otherwise lifelong vegetarian would have the same effect wouldn't it? So does it mean the 20% increase is for people who eat just one rasher every day? And if it does, does that mean that eating more than one rasher every day increases the risk even more? I think we should be told!