text: Modelling methodology 
  
  This brief section outlines the modelling process behind the conclusion in section one, which 
  states that we might expect somewhere between 2,400 and 7,000 individuals from the original 
  cohort of users in 2004 to be captured within the 2013 figure of new DIP arrestees (who test 
  positive for opiates-only or who are positive-for-both). 
  
  We begin by putting in a plausible range of crime-involved OCUs through the period. This 
  combines the total OCU estimates published by Hay et al., (ranging from around 320,000 OCUs 
  down to around 295,000 in recent years) with available estimates of the percentage who are 
  likely to be committing acquisitive crime. The latter was found to be almost exactly 50% in the 
  NTORS study (Gossop et al., 2003). As such, a range of between 170,000 and 100,000 crime- 
  involved OCUs is likely to include all plausible values (see first row of table below). 
  
  We then calculate the rate at which that population is likely to be arrested and test positive by 
  using the number of individuals testing positive from 2008 (25,433), when DIP was fully up and 
  running. This gives the second row of the table. Combining the values in the first two rows and 
  applying the probability formula given in the main body of the text gives the third row: the 
  probability of first positive DIP test in 2013. Note that this assumes all these individuals continue 
  to offend through the period, which may not be the case, hence final results are probably an 
  upper bound. The final row simply multiples the figure in the first row by the figure in the third to 
  give our estimate of the original cohort who might appear in the 2013 DIP figures as new. 