New opiate and crack-cocaine users: characteristics and trends 16 
 
Figure 7: Trends in total positive tests divided between those that are the individual’s first 
positive test and those that are subsequent positive tests. 
 
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 
 
12  Note that this assumes individuals do not become more likely to be arrested once they have already been arrested once, 
which may not be true if, for example, they became a known ‘face’ amongst the police. 
13  We certainly would not expect the whole of the 330,000 original population to appear in the data, given that: 1) Evidence 
suggests up to half finance their drug use without resorting to acquisitive crime (Morgan, 2014); 2) Some of the crime-