Statistical Advice: Scottish Safety Camera Programme

The Scottish Safety Camera Programme has, since 2010, produced an annual bulletin ‘Key Scottish Safety Camera Programme Statistics’ summarising and analysing the data from the more than 400 camera sites in Scotland. This has generally compared the numbers of accidents and casualties in a three-year baseline period with the most recent three-year period post-installation.

So far these comparisons have not made any allowance for trend or regression to the mean. It has been of some concern that the methodology may be open to criticism as the results do not provide a reliable estimate of the effect of the cameras.

National data from Reported Road Casualties Scotland 2011 show that over the decade 2001 – 2011 the number of fatal and serious collisions fell by 4% per year and the number of all injury collisions fell by around 3% per year, on average. There seems no reason to doubt that the same trend would have occurred at camera sites. Therefore any estimate of the effect of cameras should take account of trend.

When the decision to install a camera is based on a high number of collisions in the preceding period (typically three years), and this same period is used to provide the “before” data in a before-after comparison, there is the danger of regression to the mean, as has been amply demonstrated in previous studies. Ideally the baseline period should be a three-year period that follows the making of the decision as then the period would provide a true, unbiased estimate of the before camera collision rate. This happens only rarely in practice.

If regression to the mean cannot be ignored, then it is necessary to allow for it. The commonly accepted way to do this is through the Empirical Bayes method, as was employed on a subset of the data in the DfT 4-year evaluation report. This requires an independently developed predictive accident model which, using data on the flow, length and design of the site, predicts the expected number of accidents. This prediction is then combined in a weighted average with the observed number of accidents in the baseline period to give an unbiased estimate of the true accident rate. This adjusted value can then be used in place of the observed value in a before-after comparison to estimate the effect of the cameras in reducing accidents.

This report recommends therefore that in future both trend and regression to the mean should be allowed for in the comparison of accident numbers in baseline and after periods at Scottish safety camera sites.