However, it's worth looking at this statement in a little more depth to understand what's really going on. At first reading, one might assume that suicide is becoming more common, particularly in young people. This isn't the case, however.
A recent paper looking at trends in suicide rates from 1861-2007 (Thomas, K., & Gunnell, D. (2010). Suicide in England and Wales 1861-2007: a time-trends analysis [In Press - DOI: 10.1093/ije/dyq094]. International Journal of Epidemiology) would indicate that suicide rates in all groups are the lowest they have been for over a hundred years.
Data published by the Department of Health confirms that the suicide rates in all age groups are generally trending downwards, and have been for the last 15 years or so. So why are more people dying by suicide than on the roads?
The simple answer is that over time, the rate of decrease in road deaths is greater than the rate of decrease in suicides. Cars are getting safer, speed cameras might be affecting driving behaviours in high-risk areas, public-health messages on drink-driving might be having an effect, etc. This can be seen in the figure below which uses data from the WHO Health For All (HFA) database; a great (and free) source of population data for European Countries.
The rates are very similar if you correct for changes in population over time (the data are available from National Statistics).
It's a similar situation to deaths from many cancers, which are often reported to be going up. They are going up relative to other causes of death not because they are becoming more common but because fewer people are dying of other causes. A hundred years ago, people were dying of diptheria, typhoid, tuberculosis, and a host of diseases that have been 'tamed' with the advent of vaccinations and modern therapies. If these diseases don't kill you, then you stand a good chance of living long enough to die of cancer.
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