One of the consequences, most probably intended by David ‘I want…the NHS to be a fantastic business for Britain’ Cameron, of the NHS reforms is a rise in the promotion of healthcare insurance. Against a background of a financially squeezed NHS, junk insurance mailshots have started rising like miasmic bubbles through the financial swamp, and now regularly surface in Dr No’s inbox and on his doormat, where they emit a foul and distasteful odour. The gist of the pitch is usually see a doctor of your choice today for only a few pence a day. Why indeed wait weeks to see one of those nasty mean health service docs when you can get an appointment right away with Dr Nice at Clinics-R-Us? Dr No’s answer is simple: he has already paid for his healthcare, through general taxation, so why on earth would he want to pay twice?

There are of course other reasons. Funding healthcare through general taxation is broadly progressive (those who can afford least pay least, while the richer pay more). It also completely removes the pre-existing condition problem, because, within necessary and sensible limits, tax funded NHS coverage is both comprehensive and universal. No NHS hospital says ‘sorry pal, no can do, because you forgot to tell us about X or Y’. Yet this is exactly what for-profit insurers will do here once they get hold of the market, if American healthcare insurance is anything to go by. If the thought of Very Willing Cowboys being encouraged to repair Dr No’s hernia has him calling for his brown trousers, then just the possibility of the insurance vultures getting their beaks in the healthcare market has him calling for his red shirt.

The reason Dr No calls for his red shirt is the toxic combination of profit and illness. Insurance companies exist with but one primary aim, to make money for shareholders, and from that it follows that they must maximise premiums and minimize claims. The bid to the former is evident in the miasmic emails and letters that surface ever more frequently in our inboxes and on our doormats, while the later is taken care of by one of the insurance industry’s most odious secrets, a practice known as rescission. Rescission is the dark art of shredding your policy, often on spurious grounds, the moment you make a significant claim. And the worst of it is: the greater your claim, the greater the likelihood your policy will be shredded.

Here’s how it works. The vast majority of healthcare policy holders make minimal claims. These are the geese that lay the golden eggs for the insurer. A smaller number make substantial claims, but the payouts are not so large that the insurer cannot recuperate the loss through premiums within a couple of years – and so the insurer wants – indeed needs – the punter to remain on its books. It is only when we get to the top of the claims pile that things start to go badly for the insurer, with payouts that can never be recovered in premiums. These are the punters who must be punted, because they threaten profit. And punted they get, at a staggering rate. In America, the global home of un-socialised insurance based healthcare, an eye-watering near one in two of the top one percent of biggest claims gets punted. Dr No will repeat that: *if you are in the top one percent of claims, you have a 50:50 chance of having your policy cancelled and your claim rejected.*

Naturally insurers are keen to hide this awkward fact, and hide it they do as best they can, by uttering blandishments and statistics that suggest all is well. Typically, insurers claim that ‘less than one-half of one percent’ of all punters have their policy shredded, and those that do are rejected on solid grounds of claimant fraud. That seems fair enough. No one wants to encourage fraudulent punters. But it seriously – very seriously – misrepresents the picture, should you just happen to make a high value claim.

To understand how that overall figure transforms into a one in two chance of rejection for the top one percent of claimants – who are there because they are the most ill, and so most in need – we need to delve briefly into business logic and then invoke a mathematical teaser known as the Monty Hall problem, fittingly enough named after an American game show presenter. Monty Hall is all about *conditional probability*.

The set up for rescission starts with the healthcare insurance application forms. These are designed to be so complex that only the superhuman can avoid introducing inadvertent errors, errors that the insurer will bank and use, for the unfortunate, as its ‘*sorry, pal, you’re on your own*’ get out clause. Once the punter is on the insurer’s books, the insurer wants the average punter to stay that way, another goose laying golden eggs. No fox will prowl their paddocks, for the vast majority pay more in premiums that they will ever cost in payouts. Even those who make more substantial claims will soon return to laying golden eggs, as their premiums pay back the claim payout. In all these cases, business logic dictates that the insurer wants to – must – retain the punter, such that, in effect, that the vast majority of punters face *no real risk of rescission*, because no sensible business is going to dump the geese that lay the golden eggs.

Now, this is where it gets interesting. If the claimed overall half of one percent risk of rescission does not apply to the vast majority of policy holders, where does that leave the small minority who do make profit-threatening claims? They end up, in effect, disproportionately carrying the half of one percent risk: that is, they are more likely to be dumped, because they have made an expensive claim. By the same bottom line logic, the higher the claim, the more likely are the insurers to want to get shot of them.

We can see what this means if we put some numbers to the logic. The general case we are considering here is what is the probability of X, given Y, or, in our specific case, being dumped, given a high value claim. Since we already know that the vast majority face no real risk of being dumped – quite the opposite, in fact – then the figures work out like this. Those in the top ten percent, who account for almost two thirds of all US health expenditure (63.6 percent, mean $23,992, 2008 figures) may be at risk of rescission, and if so, around one in twenty can expect to be dumped, because the half of one percent risk applies not to all, but to the top ten percent – the other 90 percent, recall, are being kept in the paddock so they can carry on laying golden eggs – so the sum (see below for a fuller explanation) becomes 0.5 percent/10 percent, that is to say 5 percent (0.5 is 5% of 10), or one in twenty. If insurers target rescission on the top one percent, who account for over twenty percent of all expenditure (21.8 percent, mean $90,061, 2009 figures), then the sum becomes 0.5 percent/1 percent, that is to say fifty percent, or one in two, at risk of being dumped.

Clearly, the scam only kicks in when most healthcare funding, including that for serious and chronic conditions, is provided by insurance. At present our private healthcare insurance industry is small, and covers mostly elective procedures and top ups – and, needless to say, they would never stoop to such low practices. But with the Prime Minister banging on about fantastic business, a financial squeeze, and the American corporates already circling, one can only wonder what is round the corner. That is why Dr No has got his read shirt on: just in case.

Footnote: The basis for these calculations lies in conditional probability: what is the chance of X, given Y. The easiest way to understand this, at least for Dr No’s mathematically fuddled brain, is to convert the percentages into absolute numbers. For the sake of convenience, let us say the insurer has 10,000 punters on its books. Half of one percent of 10,000 is 50 people. But those 50 people aren’t spread equally among the total 10,000; instead, they are focused on, let’s say, the top ten percent – the 1000 people – who make the biggest claims. So instead of being 50/10,000 (= half of one percent), it becomes 50/1000, which is five percent, or one in twenty of that top ten percent. Likewise, the top one percent becomes 50/100, that is 50%, or one in two.

The same process is at work in the Monty Hall problem. A contestant on a game show faces three doors. Behind two of the doors lie duds, while the third hides a prize. The contestant has to choose a door to open, and, clearly, has a one in three chance of getting the prize. He chooses door one. The presenter then opens one of the other doors, which he knows hides a dud, and asks the contestant if he wants to switch doors. Should he switch?

The counter-intuitive answer is definitely yes. While simple reasoning suggests that, facing two doors, he has a 50:50 chance of being right with either, in fact the probabilities are altered by the fact it is now a ‘what is the chance of X, given Y’ situation. When he made his first one in three choice, he had one in three chance of being right, which means (because probabilities must always add up to one), the ‘set’ of doors he didn’t choose had a 2/3 chance of hiding the prize. If you then remove one of those two doors from the choices (the ‘given Y’ – the opened door does not hide the prize), all the 2/3 probability ‘transfers’ (because the total must still remain one) to the remaining door…and so he wont always get the prize, but he will two times out of three…which is better than his original one in three chance.

Still not convinced? Try this website: Monty Knows.

Thanks For Sharing such a wonderful post with us