Here is a good example of using routine statistics.
Co-proxamol is a pill containing paracetamol and an opiate. It is both dangerous and unnecessary: dangerous because the opiate stops your breathing in the mildest of overdoses; unnecessary because there are plenty of other mild analgesics.
Between 2005 and 2007 co-proxamol was withdrawn from use in the UK. This paper documents the results. Crucially, patients did not turn to other drugs to commit suicide; there was no increase in death from drug overdose. (This paper can't tell us whether depressed people turned to other methods such as hanging or jumping, but we know that the national trend for suicide is downwards.)
As with a number of papers I've blogged recently, the statistical methods are tricky but the graph speaks clearly.