The Abuse of Regression in the National Health Service Allocation Formulae: Response to the Department of Health’s 2007 ‘Resource Allocation Research Paper’

Abstract

Summary. Weighted capitation formulae for the allocation of funds to England's regional health authorities go back decades. In 2006, a paper in the Journal of the Royal Statistical Society, Series A, criticized the formula that has been used, with little change, from 2003 to 2009. The Department of Health has responded tangentially in a report from a team of academics whose remit was to revise the formula for its continued use beyond 2009. The Series A critique is here renewed and strengthened by analysis of the role of some elementary statistical tools in the construction of the latest formula. The conclusion is that, if the force of the extended critique is accepted, other approaches will have to be considered.

Beyond Subjective and Objective in Statistics

“…Will the authors please explain how their checklist could have helped in achieving consensus about arguments when simply responding to their perceived flaws failed to do so? In the case of a recently used National Health Service funding formula, what could a checklist have usefully added to fully documented exposure of the formula's reliance on spurious tests of model specification (Galbraith and Stone, 2011) or to exposure of the ignorance of regression to the mean on the part of stout defenders of the formula (Williams and Stone, 2013)? The same question can be posed for the recently proposed police funding formula given that exposing the glaring irrationality of fixing resource allocations by the weights of the standardized cost variables in the first principal component has failed to elicit any response from the Home Office.…”

Getting to grips with England's formula for local authority support

“…The derivation relied on statistically significant t-values and non-significant values of RESET (an exotic specification test of candidate models). When it adopted these enduring formulae, was SWG aware that such statistical tools are open to abuse of the sort recently documented in Galbraith and Stone (2011)? Was it not concerned that there is no theoretical framework to justify such purely empirical formulae-which is a relevant vacuity when a financial instrument is formulated by fitting a dependent variable by an expression that leaves a large amount of variation unexplained.…”

“…When experts disagree, how much trust should be placed in a formula when judgements of different relevant professional disciplines differ widely on the very question of trust? A recent paper (Galbraith and Stone, 2011) shows just how wide that gap can be in the case of a National Health Service (NHS) formula that allocates tens of billions of pounds sterling. Together, Stone (2005) and Stone (2009) cover the NHS case, the present subject (rather lightly) and some other examples of malfeasance.…”

Assessing Relative Spending Needs of Devolved Government: The Case of Healthcare Spending in the UK

“…Unavoidable excess costs are calculated by considering differences in wage, land and building costs relative to the national average. The healthcare allocation formulae have been criticised on a variety of grounds, including the statistical methods used, the appropriateness of the 'utilisation method', and data selection (STONE and GALBRAITH, 2006;GALBRAITH and STONE, 2011), leading to assertions that the formulae produce results which are arbitrary and unfair. Nonetheless, utilisation-based capitation formulae remain the preferred mechanism of the NHS in England, Scotland and NI to allocate healthcare resources.…”