In Defence of Liberty

Driven by data; ridden with liberty.

Statistics and Lampposts XXVII: Bivariate Analysis and A&E

As part of their document about pressures on the National Health Service, the Vote Leave campaign have suggested that continuing migration will induce much higher Accident & Emergency attendances [1].

In ‘Paving the road from Ankara’: the EU, immigration and the NHS, the document states:

The graph shows the relationship between cumulative increases in net migration and attendances at accident and emergency in England.


Great job with Excel there. (Source: Vote Leave)

As the graph shows, there is a very strong correlation (>0.9) between cumulative net migration and A&E attendances. As a result, it is possible to project the impact on A&E attendances of rising EU net migration until 2030.

It is always “possible” to project one variable on the basis of a relationship with another, but that does not mean it is robust, particularly if one factor has been over-emphasised and other factors have been ignored.

A&E attendance since 2003

From 2003-04 to 2014-15, A&E attendance in NHS England has grown from 16.5m to 22.4m, an increase of 35%. According to the ONS, over that same period, the population in England has increased by 9% [2].

The per-capita attendances has increased from 0.331 to 0.412, or a growth of 24%. (Note that, for the sake of simplicity in the calculation, I am placing the 2003-04 A&E attendance against the 2003 mid-year population estimate).

The Vote Leave bivariate analysis presumes that net migration is the only factor involved in growing A&E attendance, when it uses the correlation between those two variables to extrapolate into the future. Their analysis implies that each marginal migrant increases A&E attendance by 2.4 visits per year. This is certainly an odd conclusion.

However, not all A&E attendances are equivalent. If we consider only Type 1 attendances, in major health centres, then attendances have gone from 12.7m in 2003 to 14.6m in 2014, or an increase of 15%.

The per capita attendance has only increased from 0.254 to 0.269, or a 6% increase. This is entirely in line with an ageing population.

“The range of new services available”

As Ian Blunt of the Nuffield Trust writes [3]:

However, more careful inspection of the data revealed that this rise was almost exclusively acting on minor A&Es (for example, urgent care centres, minor injury units and walk-in centres). Although attendances at major A&E departments had also been increasing, this was at a much lower level (just 13 per cent between 2003/04 and 2012/13) was entirely in line with what would be expected based on population ageing growth see Appendix B). Much of the increase in attendances at minor A&E units is likely to be related to the range of new services available (Rosen, 2014). It is also worth nothing that some of the increase is thought to be an artefact of better recording and changes to the labelling of existing services, rather than ‘new’ service use.


The increase in attendance has been particularly severe for older people. (Source: Nuffield Trust)

Given the various factors at work affecting attendance at A&Es, it seems disingenuous to suggest that only one factor — net migration into the UK from the EU — is the only one of true concern.

Relying on a single variable for forecasting without testing its robustness is also not advisable.


[1] Vote Leave, 2016. ‘Paving the road to Ankara’: the EU, immigration and the NHS. Available from:’Paving_the_road_from_Ankara’_the_EU__immigration_and_the_NHS.pdf?1463745000 [Accessed: 23rd May 2016]

[2] ONS, 2015. English population mid-year estimate. Available from: [Accessed: 23rd May 2016]

[3] Blunt, I., 2014. Focus on: A&E Attendances. Nuffield Trust. Available from: [Accessed: 23rd May 2016]



This entry was posted on June 8, 2016 by in Statistics and tagged , , , .
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