After the flummery of the last two weeks, back to some solid epidemiology.
Age-period-cohort models are used to sort out whether an increase in disease incidence is due to a period effect or a cohort effect. A period effect will show itself as a sudden increase in incidence in all age bands; a cohort effect will only affect a particular age band, but throughout life, so as that cohort ages the peak in incidence will affect ever older age bands - 5 yr olds in 2005, 10 yr olds in 2010, 15 yr olds in 2015 and so on. Actually of course it is never as clear as that an period and cohort effects overlap.
The most famous example of a period effect was the increase in asthma mortality seen in the 1960s - mortality increased in all age bands over only a year or two. This was later seen as due to the introduction of a new treatment which though not obvious at the time increased mortality.
Cohort effects are less easy to exemplify but perhaps smoking will do - it became fashionable among the younger generation, who gradually aged.
If a disease is on the increase, knowing whether you are looking at a period effect or a cohort effect will help to rule in or rule out some potential causes of the increase.
So here is the worked example.
As always, note the data source: a service register. This affects ascertainment: people have to be on the register to receive special services for autism. The authors discuss the biasses which this may cause (e.g. pushier parents get on the register; poorer ones don't.)