Wrong signs in the NHS allocation formula
Nigel Williams, 14 December 2013
A new report for Civitas by Professor Mervyn Stone is published online today. It calls for an answer. On 17th December 2013, the NHS England Board meets to review the policy of how to allocate funding. The implications are potentially serious. In 2008, Stafford General was petitioning its local Primary Care Trust, South Staffordshire, for more money to close the shortfall in staff levels.
Paragraph 1.236 of the Francis report reads:
A report dated 28 May 2008, prepared by Mr Griffiths of SSPCT, noted that the Trust requested an additional £775,000 funding for medical and nursing staffing and support. It was also reported that the Trust had identified a £2.5 million shortfall in the necessary funding to correct nursing capacity and skill mix issues. The Trust had stated that it could not afford more than £1.15 million out of its own resources. The report stated that the PCT supported the view that nursing levels should be increased but was not sympathetic to the request to fund the gap.
South Staffordshire PCT’s allocation was at the lower end of the per-person funding range, calculated using ancestors of the present formula. In 2009-10, South Staffordshire was allocated £1,351 per head by funding formula. If the hospital had approached North Staffordshire instead, there would have been £1,504 per head. Tower Hamlets received £1,852 per person. Those would be big differences in a situation of plenty, when we would just hope that the unspent resources would be frugally returned. When margins are tight to the point of frozen posts and suspected rationing, differences of that scale need to be openly justified. Staffordshire did not receive the lowest allocation. Other areas with lower capitation provoked no such scandal. Nevertheless, many of the safeguards that will help avoid future failings in care depend on getting enough money through NHS England’s system of allocation.
David Buck and Anna Dixon for the King’s Fund made the point that ‘Pace of Change’ requirements, that no provider should receive a substantial real-terms cut from what they had received in the year before, were making any complicated means of distributing money increasingly irrelevant. They make a strong case for removing much of the baggage from the calculation process; for getting back to a situation in which both the managers that account for the money and the public that provide it can tell why it is being given and what is meant to be done with it.
For over a decade, the misuse of multiple regression formulas for resource allocation has concerned Professor Stone and other statisticians who expect the formulae to be properly understood, especially by anyone using them to take decisions on behalf of others. A big problem is that, given a large set of data and a large number of explanatory variables, it is very easy to manufacture plausibly causal relationships that do not exist. An example is the penalty of £1,143 for ‘other conditions originating in the perinatal period’, specifically for the over-65s. It does not in itself prove that the allocation formula is wrong, but it does suggest that it is unlikely to match the true need for health care.
Buck and Dixon picked up on a paper Professor Stone wrote for Civitas early in 2013, that revealed the absence of logic in some striking features of the current formula. Today’s paper refines the earlier analysis and supplies a couple of corrections. It starts from the observation that several illnesses are associated in the funding model PBRA3with reductions in predictions of the required funding. Among other ailments, if a practice puts a patient in hospital for dementia, they can expect a reduction in funding in the next round. By returning to the algebra underlying regression, Professor Stone has set out what these negative coefficients really mean: on average, people with those ailments receive less funding than people without them but with the same referral history. The details are in the paper.
This paper is on the technical side even for Civitas’ Statistics Corner. However, any Civitas reader should be concerned with the sensible use of public funds. If policy makers are using machinery that requires explanation beyond general public understanding, that is itself a cause for concern. An obvious place for publication would be the Royal Statistical Society’s ‘Statistics in Society’, where it did not get past the single referee, who felt that it was no more than an exercise in explanation. Instead, it is offered here in the hope that others will join in to explain or simplify. RSS referees and authors of the funding formula that Professor Stone criticises are very welcome to contribute to the discussion.