Limitations of the HRG tariff: the national average

Abstract

Every year NHS trusts calculate the apparent average cost of each health resource group (HRG), which is then averaged again over all trusts to give a national average cost. Apparently no regard is given to the average cost from previous years. It may be a useful exercise to determine how stable these calculated national average costs are over time. To do this we must first determine how ‘accurate’ the average cost will be at trust level. While there are a considerable number of perceived factors leading to variation in costs between trusts, it may be useful to focus on one often overlooked factor—variation in the calculated average due to the sample size. Figure 1 presents the results of a computer simulation of the range in calculated average cost, which could arise at a single trust for a single HRG where the cost of each individual patient is unique. In the simulation each patient could stay between 12 hours and 9.6 days at £200 per day and had a diagnosis/ procedure phase at the beginning of the admission lasting from 90 minutes to 6.6 hours at £300 per hour. In both cases the distributions were skewed to reflect the situation commonly seen in NHS cost data. All random variations were added together to give the cost per patient and this was then averaged over different numbers of patients admitted to our hypothetical HRG. As can be seen it takes around 1000 patients at a single hospital for that hospital to get a tight estimate of the true average cost for a single HRG. For a sample size of under 100 patients it can also be seen that the likelihood of high variation in the average significantly increases. Would it come as a surprise to note that the vast bulk of HRG have fewer than 10 admissions per trust? Should we be surprised that there is high variation in the apparent average price for each HRG submitted by different trusts? This unavoidable source of variation is high. Having demonstrated that sample size is a very important source of cost variation at local level, we now need to look at the national average cost. To demonstrate the uncertainty in the national average the average costs for HRG V3.5 have been followed from 2002/03 to 2005/06. Some HRG from 2002/03 (V3.1) were carried through to V3.5 and these have been incorporated into the time series. Earlier years have been adjusted for inflation and other costing changes and the ‘long-term’ average cost for each HRG has been calculated along with the standard deviation associated with that average cost. The calculated standard deviation has been divided by the average price to give a measure of variation as a proportion (%) of the price and this is plotted in Figure 2 as a function of the national activity (FCE) for each HRG. Emergency, elective overnight and day case are all shown together as there appears to be no intrinsic difference between the different admission types. The scatter around the trend line is mainly due to the magnitude of the cost and the number of trusts submitting a cost for each HRG. The trend line (in red) describing the standard deviation (%) associated with the national average price Figure 1. Maximum and minimum calculated average cost 3000