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The Collapse of the Probability Function

Posted by Dr No on 28 August 2009

roulette.jpgOne of the more striking changes in medicine in recent years has been the increasing use of - and reliance on - numbers. Now, cosying up to numbers is all very well, as long as you understand them. Most doctors do not.

Sure, most doctors can add two plus two and get four. Getting the decimal point in the right place can be a bit trickier (and accounts for a lot of drug errors). But when it comes to statistics – most doctors haven’t got a clue.

Take probability. Now this seems pretty straight forward: it is a number that expresses the chance that something might happen. So we say that there is a one in ten, or ten percent, chance that something might happen. That means that on one in ten occasions that thing will happen.

Doctors increasingly use probability to decide how to treat their patients. They have sexed it up a bit (by calling it evidence based medicine) but the underlying process is all about probability.

This might just be fine and dandy for public health doctors like Sir Liar Liar Pants-on-Fire Donaldsong, but for jobbing doctors treating individual patients it contains a fundamental flaw. That flaw is that what applies to groups (populations) does not apply to individuals.

Consider cardiovascular risk – that is, the risk of something serious going wrong with your ticker. The risk is increased if certain conditions are met – for example you have high blood pressure, high cholesterol, or are diabetic. Researchers can, and have, calculated what the risks are, depending on what conditions are met. The results are included at the back of the BNF (British National Formulary – the doctor’s prescribing bible) as a series of pretty coloured graphs. Doctors increasingly rely on these graphs to decide whether to prescribe or not.

Now, the problem is this. What validly applies to groups cannot and does not apply to individuals. We can say that on average the parents living in Acacia Avenue have 1.7 children – but that does nothing to tell us how many children Mr and Mrs Jones at Number 10 Acacia Avenue have. They certainly don’t have 1.7 children (if they did social services should probably be involved). They could have none or ten or any number for that matter – we simply just don’t know.

And so it is with cardiovascular risk. The BNF graph may show that you have a 10% chance of a cardiovascular “event” (doctors, like weather forecasters, who also deal in probabilities, like the “E” word) in the next ten years. What does that mean?

For you, almost nothing. A doctor might look into the waiting room for his or her high blood pressure clinic, and be able to say, quite validly, that of the ten people sitting there, one will almost certainly have a heart attack in the next ten years.

But when he or she calls them individually in to his consulting room, the numbers break down. There is no way the doctor can tell whether the patient sitting in front of them is the one who will have the heart attack. To say they have a 10 % chance is meaningless: they can’t have a 10% heart attack, they either have one or they don’t. And nine out of the ten will not.

It is like roulette. Whatever your chances of wining or losing, when the ball finally comes to rest you will have either won or lost.

Throwing numbers around always sounds scientific and serious. The sleight of hand being practised here is the application of valid group (population) statistics to an individual. It simply doesn’t work. It is what we might call the collapse of the probability function.


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