text: cent (25,000/150,000).14 It is then possible to model how many of the original population of 
  crime-involved OCUs would be likely to test positive in any given year. For example, if there 
  were 150,000 crime-involved OCUs in 2008, the chances of one of that group having a first test 
  in 2013, providing they remained a crime-involved OCU throughout the period 2004–2013 is 
  given by: 
  
  (1*–*probability of arrest)^8 = chance of not getting caught between 2004 and 2012 
  
  Multiplied by: 
  
  Probability that they do get arrested in 2013 
  
  This can then be calculated for a range of plausible values for the initial number of OCUs, and 
  hence range of arrest rates, to give a range of plausible values for the number of new testers in 
  2013 who were actually longer-term users. The results of this modelling suggest that we would 
  expect about 2,400–7,000 new positive tests from individuals who are actually longer-term 
  OCUs.15 So the fact we only see 4,281 in the real data suggests that genuinely new initiates 
  may be a minority within this figure, as many (probably most) will be from the original cohort. 