# Easy answer…to an easy question

I previous posts I have mentioned that I was going to try and look at forecasting the volume of treatments of admitted patients carried out in English hospitals.  The graphs below show first the national volume of treatments, across all hospitals. (FCE stands for finished consultant episode, the unit treatments are counted in).  The second graph shows a zoom in of the results of the forecasting methods.  If you are wondering, yes methods 3 and 5 have produced almost exactly the same result.

It would seem from this graph that method 2 is the most accurate. Method 1 was never going to be any good: it was really just me checking I was using Stata correctly to create the new forecast data.  Methods x-y are all based on econometric estimators.  Although they appear to all present the same results at a national level, at the level of individual hospitals their accuracy does vary slightly.

The statistics used for more accurately measuring the forecasts at the level of each hospital (which is what I care about) are based on the average difference between the forecast value and the actual value.  Expressed as a percentage the econometric methods had an average error of between 0.5% and 0.7%.  This is not not too shabby.

Method 2, which says the growth rate will be the same as in the last year observed proves to be the most accurate at the level of individual hospitals, with a mean error of 0.01%: the most successful by a long way!

The reason why this task an “easy question” is because while the data are complicated – many observations across multiple hospitals – forecasting two data points when the data do not vary a great deal from year to year means that any reasonable method is never going to be significantly wrong.  What I might do next is look at some hospitals in more detail, possibly those with the worst forecast, and see if there is anything they have in common.

It would also be interesting to try forecasting over a longer period of time.  Another option is to download the monthly version of this activity data and use that, which would mean twelve times more detail! I could also use Monte Carlo simulation (doing the forecast lots of times) to get a distribution of results, rather than just a single point estimate for each year.