Tuesday 11 September 2012

Risk in black and white terms

Risk is just another word for chance. It's the probability or likelihood of a bad thing happening. In the real world, risk is always fluid, always changing, because there are an enormous number of factors involved in risks.

It is more risky to drive at 70mph than at 40mph. However, if you drive at 40mph in a 20mph zone, that is more risky than driving at 70mph on an empty motorway. But it is still more risky to drive at 70 mph than 40mph (imagine how risky it'd be to drive at 70mph in a 20mph zone!).  

If you drive around a corner and crash into a tree, your speed does not cause the accident, although you may have avoided it were you driving slower. The tree does not cause the accident, although if it hadn't been there, you wouldn't have hit it. The corner does not cause the accident, although if it hadn't been there, you probably wouldn't have hit the tree.... There are lots of factors that affect the risk, i.e. the probability of the accident occuring, none of which are solely to blame.

Breastfeeding - or the lack thereof - does not give a child a disease or prevent a child from getting a disease. It reduces/increases the risk.  No more, no less.

Simply put:

Most babies will get some minor diseases. Most breastfed babies get colds, most formula fed babies get colds.  
Most babies will not get major diseases. Very few babies get necrotizing enterocolitis, however they are fed.

Nevertheless, if a baby is breastfed, they are less likely to get both minor and major diseases, and the symptoms of these diseases are more likely to be milder than in a formula fed baby.

It doesn't matter if you personally know 100 breastfed babies who always have colds, and 100 formula fed ones who are never ill. The formula fed ones are nevertheless at greater risk of getting colds (by virtue of being formula fed) than the breastfed ones, even if other risk factors or plain luck affected the end results.

Imagine there are 2 bags – one red, one blue. Each bag has a certain number of black stones and a certain number of white stones in it. Horace chooses the red bag, and Boris chooses the blue bag. The aim of the game is to draw out a white stone. Each round, more stones are added, and they try again.

The blue bag holds 49 white stones and 1 black stone. When Boris picks a stone randomly, he is most likely to get a white stone, but may be unlucky and get the black one.

The red bag holds 39 white stones and 11 black ones. Horace is also more likely to pick a white stone than a black one, but that doesn't chance the fact that the risk of him picking a black stone from his bag is greater than Boris's risk.

Round 2: One player gets another 10 white stones and 40 black ones, the other gets 40 white and 10 black.

If Horace gets more white stones than black this round, he ends up with 79 white stones and 21 black stones, while Boris would end up with 59 white and 41 black. Horace now has a better chance of success than Boris.

This does not mean it is just as safe to chose the red bag as the blue bag. This means that Boris was unlucky in this round. As shown in the table below, while it is possible for someone with the red bag to have more white stones than someone with the blue bag in round 2, that is despite their poor start, and doesn't change the fact that they still have 10 more black stones than they would have done had they had the blue bag in the first place.



Round 1
Round 2

Initial stones
10 black/40white
40 black/10white
Blue bag
1 black, 49 white
11 black, 89 white
41 black, 59 white
Red bag
11 black, 39 white
21 black, 79 white
51 black, 49 white
Probability of getting a black stone
Blue: 2%

Red: 22%
Blue: 11%

Red: 21%
Blue: 41%

Red: 51%


It doesn't matter how many other stones are added to the bags – the blue bag will always be the safest choice to have made in that initial round. And since having a blue bag does not increase your chances of getting more black stones at a later date, it is impossible for it to be 'just as good' to have taken the red bag.

If you have a genetic propensity to SICK (Some Illness - Could Kill), and your children have a 98% chance of getting it anyway, that chance is still increased by formula feeding/reduced by breastfeeding. In the simile above, that's as if you start off by adding an extra 98 black stones and two white in your bag – it being a blue or red one still makes a difference to the probability.

It isn't your fault, and you are not to blame if you didn't know that the red bag was more risky than the blue bag, or if you did not have the option of picking the blue bag. No more than a family history of SICK is your fault. And, I'm sorry, but one day, a black stone will come out of every bag. And none of us can ever know which round of the game added that particular stone to our bag. All we can do is reduce risks whenever we can, and accept them when we can't. You can never, ever say with 100% certainty that 'formula feeding didn't do me any harm' (or indeed any other thing you do that may increase risks of illness in later life), unless you are permanently in perfect heath until you die from something that couldn't possibly be related to it (like getting hit by a bus). Even if you live in perfect health until you are 100, and then draw that metaphorical black stone from a bag containing millions of stones – it would have been more likely to have been white, had you started with 1 black stone instead of 11.

Which sounds really depressing, until you look at it from the other angle: look at the table above. If you had the red bag, and got lucky in round 2 – your risk has decreased from 22% to 21%! No matter how many black stones there are in your bag, there are other ways to add white ones, and improve your chances. Formula feeding your infant increases the risk. But you can reduce the risk in so many other ways – how you feed your infant matters, but you have the power to minimise the impact in real terms by what you choose to do next.






Note: I am aware that I have referred here to breastfeeding reducing risks as well as formula use increasing them. I know that this is rather frowned upon, as it does not use the biological norm of breastfeeding as a starting point, as lactivists generally prefer. This is important in cases where the risks of formula are being played down, and formula is being treated as the norm. This doesn't really transfer well to the metaphor I'm using today, so I am using both phrases. It would be as absurd to suggest that breastfeeding has no benefits when compared to formula feeding, as it is to suggest that while breastfeeding has benefits over formula feeding, there are no risks to formula feeding.

4 comments:

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    1. Couldn't find the edit button, so deleted and reposted.

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  2. Apparently I need to point out that the risks of the black/white stone game are not equivalent to the risks of formula/breast feeding an infant. The difference in risk is far less than 20%. I simply couldn't use numbers big enough to demonstrate this in a simple analogy.

    Last year the stat was publicised that 900 lives in the USA would be saved if 90% of babies were breastfed. So that'd be 900/311,591,917 apparently. Yep. Tiny percentage. Most babies, as I said, will be fine. 900 really won't be, though.

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