text: However, caution needs to be exercised. Not only will this trend be affected by the changing 
  level of DIP coverage but also DIP only started in 2004 so every new individual who tests 
  positive in that year is effectively ‘new’. This means that because the probability of arrest, for 
  any offence committed, is less than one (i.e. not everyone gets caught), it is likely that there will 
  be a natural downward bias in the trend for positive first tests. To see this, imagine a population 
  of 100 OCUs who commit one crime each year. If the probability of arrest is 20 per cent, 20 
  individuals will show up in the DIP data as ‘first positive tests’ in the first year. In the second 
  year, 16 will show up from the original cohort (80 x 20%), alongside 20 per cent of any new 
  crime-involved OCUs joining the population that year.12 
  
  So the sharply falling trend cannot simply be interpreted as a sharp fall in the number of 
  genuinely new crime-involved OCUs, as the figures will also be capturing declining numbers of 
  the original cohort. Looking at the fourth row in Table 5 we can see that it is only in 2012 that the 
  total number of unique individuals testing positive exceeds 100,000. Given that available 
  estimates suggest the total number of OCUs in the mid-2000s was around 300,000 (Hay et al., 
  2013), it is clear that plenty of the pre-existing population probably appear as ‘new’ positive 
  testers right the way through the series.13 