Of all the magnificent sleights of hand attributed to statistical science, few come close to matching the formula by which NHS funds are allocated to primary care trusts (PCTs).

Most people probably assume that the money is simply divided up between PCTs on a pro-rata basis, taking into account the population they serve. But this is very far from being the case. Some PCTs are much more equal than others: Hull, for example, gets 50 per cent more per head to provide healthcare than does the neighbouring PCT, East Riding. Islington sloshes with money; but PCTs in middle-class areas such as Guildford have to get by on much less.

The allocation formula in its various forms has been responsible for creating these inequalities. If you live somewhere nice, the underlying principle is that you need less money for healthcare. That may be why, when the shoe pinches, it is the PCTs and hospital trusts in the South and South West of England which tend to suffer the biggest deficits, simply because they get the least money.

Mervyn Stone, Emeritus Professor of Statistics at University College London and a long-time critic of the way the process works, has produced a new report for the think-tank Civitas, published yesterday, that exposes the many layers of confusion around the latest version of the formula, launched in 2008.

At the time, I wrote that only the brave or foolhardy venture into some areas of NHS management (BMJ, 2009;338:b77). Resource allocation is certainly one. The principle is fairly uncontroversial: to divide up the £80 billion or so spent by PCTs in order to assure equal opportunity of access to healthcare for people of equal risk, and to help reduce avoidable health inequalities.

But trying to make it work is another matter. Three different formulae have been tried since the idea was first introduced by John Major's Government, and all have been heavily criticised. In 2006, responding to the criticism, a new version was commissioned by the Government’s Advisory Committee on Resource Allocation (ACRA). It was supposed to be much better: more technically robust and more transparent.

However, ACRA admitted when it was launched that there was no way of meeting both of the objectives listed above within a single formula. The reason, paraphrased by Professor Stone, is that it is not technically possible to determine the cost of reducing health inequalities between PCTs in a way that could be used to inform allocations.

For the Government, the new formula raised other problems. It took account of age – an important determinant of health demand – but the consequence of doing this was to reduce the proportion of funding that went to deprived areas or those with a large ethnic minorities. If implemented, says Professor Sheena Asthana of the University of Plymouth, an expert on health inequalities, it would have led to a major redistribution of resources.

ACRA clearly felt uneasy about this, and suggested there was a case for diverting some money back towards these areas of deprivation and large ethnic minorities. But it lacked a mechanism for doing this fairly.

So it devised a formula that gave more money to areas where healthy life expectancy was lower, but left it to ministers to decide how much of the budget should be distributed acording to this formula – suggesting as illustrations 10 per cent, 15 per cent, or 20 per cent.

Ministers chose 13 per cent. That meant that £10 billion a year was top-sliced from the budget and distributed according to the ACRA inequality formula, and the rest according to the health needs formula. This is in spite of much evidence showing that healthcare spending has a limited effect on health inequalities.

At a meeting of the Rural Services All-Party Parliamentary Group in February, Professor Asthana asked (p13 of Mervyn Stone’s report) why the academic evidence had been ignored. The effect of the ministers’ decision was to restore PCT allocations to exactly where they had been under the earlier, discredited formula, she said.

 “The value judgement has been made to maintain the status quo despite the fact that the status quo was deeply problematic in terms of achieving the objectives of equal access for equal means” was the way she put it.

In a letter to shadow health secretary Andrew Lansley, health minister  Ben Bradshaw rather gave the game away. He said that the 13 per cent figure “keeps the distribution of funding between the most and the least deprived areas in line with the previous formula”.

So why go to the trouble of devising a new formula only to override it so as to achieve the same distribution of money as the old formula did? For Professor Stone, politics is the only possible reason.

Why, it may be asked, was the Rural Services APPG interested in this arcane issue? Because the old formula disadvantaged rural areas, and the hope was that the new one would redress the balance. But in spite of all the effort and the elaborate statistical and econometric modelling, at the end of the process nothing changed.

And why was the chairman of the hearing, Graham Stuart MP, so interested? Because, as he told a witness, he was then the Conservative MP for Beverley and Holderness, in  the East Riding PCT area. East Riding, as he pointed out, is far less well-provided than neighbouring Hull. (Mr Stuart is standing again in the current election.)

While East Riding PCT had a deficit, Hull PCT was in surplus: hardly surprising, in view of the relative levels of funding. Famously, Hull PCT  planned in December 2008  to spend £400,000 of this surplus on a yacht, to provide unemployed 17-19 year olds with something to do. The plan caused outrage, but nobody pointed out its connection to the very odd way in which the NHS distributes its money.

Here’s a picture of the yacht, just to make the good people of the East Riding grind their teeth.

 
                                 
 
A final word: Professor Stone was hoping on April 20 to attend a seminar at which Professor Steve Morris of UCL, the author of the "new" allocation model, was due to speak. But the seminar was cancelled at the very last moment. Professor Morris had been told not to speak - presumably, yet another victim of the electoral purdah which has sealed so many mouths during this campaign. Or at least that is Professor Stone's interpretation.