Tuesday, 27 September 2011

Bowel Cancer Statistics - a funnel plot

I'm grateful to David Spiegelhalter of Understanding Uncertainty for the suggestion that I should display these data in a funnel plot.  (Click on the plot for a full-screen version.)

For a given population size, and assuming that the death rate is uniform across each authority, an authority has the same probability of falling outside the funnel lines whatever its size - the funnel is narrower at the right-hand end of the plot where the authority sizes are larger and the standard deviation of the distribution is smaller relative to its mean.

Under the uniform distribution assumption, the probability of a point falling above the upper dotted line is 2.5%, as is the probability of a point falling below the lower dotted line.  There are 378 points, so typically nine or ten of them would be above and below the dotted lines.  For the dashed line, the probabilities are 0.2646%, which I chose so that one point would typically be above and below the lines.

What stands out from the plot is that Glasgow City's poor result is fantastically unlikely to be random.  There may be a meaningful pattern too in the figures for North Lanarkshire and Falkirk, which cover the area from Glasgow east-north-east to the Firth of Forth above Edinburgh.

Only Westminster falls below the lower dashed line.  Since we expect one point there at random, this is perhaps not worthy of much attention.  However, there are a lot of points - 21 - below the 2.5% line, most of them in south-east England (one of them - Stirling - is in Scotland).

I suspect that there are genuine regional variations in outcome, Glasgow aside.  But the data need looking at over regions larger than most local authorities.

(Wales, which is presented as a single, very large, region is a long way off the right-hand end of my plot.  But it falls comfortably within the funnel.)

[This post is a follow-on to my previous analysis of the same data]

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