Thursday, 26 January 2017

An interesting medical scam

When I was writing the chapter about the pink alternative medicine clinic, I found myself challenged to come up with something so bizarre that it would be obvious it was a satire. Just so, I later discovered that bananas occasionally emit positrons. This means that the wobbly bananas I described are occasionally sending out electrons that are going backwards in time.

No doubt sooner or later someone in the alternative medicine world will conclude that sufficient exposure to wobbly bananas, preferably while lying naked on a couch, can make you younger. Of course you'd have to be properly quantumly entangled with the bananas.

However there are some forms of medical wackyology that are more cleverly dressed in the outer garments of science and can fool even quite intelligent people. I here present one such piece of tomfoolery for your education.

It works like this: the practitioner promises to improve the patient's health by re-balancing them. To do this he or she orders a very large number of blood tests. Then, if there are any blood tests that are abnormal the practitioner will offer to rectify this by prescribing some supplement or other.

Sounds reasonable, doesn't it? After all, if someone feels tired and their doctor finds out that they have a deficiency of (say) iron, they can fix it by prescribing iron tablets.

However, medicine is generally a bit more complicated than that. If someone is genuinely iron-deficient it is important to ask why, and to look for the cause. In this context, merely 're-balancing' could be dangerously negligent.

The real basis of the scam is actually mathematical. Consider a field full of women of the same age. Line them up according to height. Most of them will be somewhere around the average, but there will be a few really short ones and a few really tall ones. Even if we remove the ones who are tall or short because of some medical abnormality, there will still be a variation. Thus, healthy people can be tall or short, and a few will be extra tall or extra short without there being anything wrong with them.




(Image taken from this web site)

When the laboratory measures something in someone's blood, most of the time the result will be somewhere in the middle of the range, but some results will be outliers. This will happen fairly often even in perfectly healthy people. There is no absolute cut-off where something suddenly becomes abnormal. The laboratory somewhat arbitrarily defines the range as the middle 95% of values. This should not be referred to as 'the normal range,' rather, it is properly referred to as 'the laboratory reference range.'

It's the same thing with height. If a child is in the bottom 10% for height, you don't think much about it, especially if their parents are short too. If they are in the bottom 2% for height, you start wondering if there is a problem, and you look at the parents' heights and at the previous measurements of growth to see if there is a pattern suggesting disease or not.

In the same way, if a laboratory value is outside the laboratory reference range, you ask yourself if there is a pattern to it or not (such as, all the liver tests are out and the patient drinks too much, or, only one of them is out and the patient is a perfectly healthy teetotaller).

So now we come to the essence of the scam. One or two values being 'out' may or may not indicate a disease process. What is the probability that at least one value will be out in a perfectly healthy person?

Consider first the simpler case of tossing a coin. What is the probability that it will be heads? Fairly obviously 1 in 2, or half, or as normally expressed, a probability of 0.5.

What is the probability that it will be heads twice in two tosses? The answer is the probability that it will be heads the first time multiplied by the probability that it will be heads the second time: 0.5 x 0.5 = 0.25 (a quarter). Three times in three tosses? 0.5 x 0.5 x 0.5 = 0.125 (an eighth) - and so on. What is the probability that in three tosses of a coin at least one will be tails? 1 - 0.125 = 0.875 (seven-eighths).

To do our calculation we use the same process. The probability of a test being within the laboratory reference range is 0.95 (19 times out of 20). The probability of  two tests being within the reference range is 0.95 x 0.95 = 0.9025 (nearer 18 times out of 20). We multiply the probability together with itself the number of times there are tests. If there are 20 tests that is 0.95^20=0.36. This is the probability that all the tests will be 'normal' - just over a third. To get the probability of at least one test being 'out' we subtract this number from 1. So if we do 20 tests on a healthy person, the probability that at least one will be out of range is almost two-thirds (0.64).

For thirty tests the probability of at least one test being 'out' is 0.78, or more than three-quarters. So in such a case on average three out of four healthy people will be convinced they need 're-balancing' and will no doubt purchase whatever is recommended to do the re-balancing, plus of course the consultation fee. Of course this is unlikely to make any difference to anything so they'll be back for more until they decide to save their money and get on with the rest of their lives.

I'm not a cynic, I am simply reporting what I see. As the saying goes, 'you do the math.'

Monday, 23 January 2017

On not believing everything you read

[...] By which it appears how cautious men ought to be of taking things upon trust from vulgar opinion, and that we are to judge by the eye of reason, and not from common report. - Montaigne, from Of Cannibals.

Don't believe anything as certain unless you have verified it for yourself. As to things spiritual, they require verifying ceaselessly.

Monday, 16 January 2017

A Mermaid in the Bath is available in India

A Mermaid in the Bath is now available in India. Go to my Amazon links page for where to order around the world.

Friday, 6 January 2017

Archimedes' bath and the Dogon method of divination

How to let the creative mind play its part in solving problems


Many years ago I was much influenced by one of those little talks Radio 3 (the Third Programme in those days) used to sandwich into the intervals in live broadcast concerts. It was about the divination method of the Dogon tribe of Mali in West Africa. (My memory of details may be a little inaccurate after all this time, but the principle holds good.)

Apparently they have two gods, Nommo and the Fox. Nommo represents order and the beginnings of things, and is fixed and rather crystalline. The Fox represents disorder and change. A person with a question will draw a diagram in the dust near the road, the diagram being a box divided horizontally into upper and lower sections, representing respectively the world at large and one's immediate neighbourhood or household. The box is also divided into three vertically, representing respectively Nommo, the questioner's own place in the world, and the Fox. One might think of this division as representing past, present and future, but that perhaps is more our own way of thinking in linear time. Thus we have six cells each representing a part of our world.

The person asking the question will place various sticks and pebbles in the various cells, representing aspects of the problem or people involved in the problem. The interpretation of the diagram to anyone else will not be obvious because the enquirer doesn't want everyone to know his or her business. He or she will then also place some pieces of meat around the diagram, and go home and stop thinking about it, confident in the knowledge that the question will now be answered.

In the night the foxes will come, eat the meat and in the process scatter the sticks and pebbles around. The enquirer returns in the morning and interprets the diagram. A crude example might be, should I make the journey to the distant village or not? If the pebble representing the enquirer has moved from the lower middle cell to the upper right cell, the answer is obviously 'yes.' However the interpretation will usually be subtler than that.

The point of this process is that the enquirer has gone through an intellectual process of wrestling with and defining the problem in clear enough terms that the question can be expressed using the diagram. Then the intellectual mind rests, because at this stage reason would otherwise produce an unending stream of 'yes, but' contradictions.

Meanwhile the creative part of the mind works quietly on the problem, hence our modern advice to 'sleep on it.' The solution is allowed to emerge during the interpretation of the oracle.

Similarly, Archimedes wrestled with the problem of how to determine the composition of the king's crown without breaking it. He had done all the intellectual groundwork. The creative part of his mind presented him with the solution while he was relaxing in the bath.