# Methods for quantifying the uncertainty in NHS reference costs

NHS reference costs are used to calculate how much providers of health services should be paid for performing operations, running clinics, delivering chemotherapy, and many other things. They are calculated by all of the different providers allocating the costs they incurred to the different activity they performed. These are then averaged across all the providers.

NHS reference costs are frequently used when estimating how cost-effective different treatments would be in the NHS.

When economic models are developed for estimating cost-effectiveness, a key part of the process is to quantify the amount of uncertainty in the different parameters, including the costs of procedures. There are three key sources of uncertainty to consider:

• Sampling uncertainty – Some procedures are not performed very frequently, so if there were additional procedures within the same year, our estimate for the average in that year may move.
• Heterogeneity – The cost of performing a procedure may vary systematically according to characteristics of the patient or the organisation. In the published reference costs, the heterogeneity due to organisations can be seen in the organisation level data, which can show significant variability in the average costs (see Figure 1).
• Changing costs over time – The cost of performing a procedure may change over time. The cost of a procedure in the financial year 2014-15 may be estimated with great precision, but this might not be a good estimate of the cost of the same procedure in 2015-16 (even after adjusting for inflation).

A common approach is to estimate the standard error from the lower and upper quartile unit costs from the different organisations.

Let $n_t$ denote the number of organisations providing unit cost estimates. Let $c_{0.25}$ and $c_{0.75}$ denote the lower and upper quartile unit costs.

$SE(c) \approx \frac{c_{0.75}-c_{0.25}}{(Z_{0.75}-Z_{0.25})\sqrt{n_t}}$

My thoughts on this approach, and some alternatives, to follow…