New opiate and crack-cocaine users: characteristics and trends 25 
 
estimated percentage of the total incidence captured by the observed incidence. In other words, 
our lag-to-treatment distribution suggests that of the 8,960 individuals who began use in 2005, 
85 per cent will have come to treatment by 2014; so by adding the other 15 per cent on (1,523), 
we reach our estimated total incidence for that year: 10,483.  
The second model uses the same principles but instead of looking only at the lag-to-treatment 
distribution for the 2005 cohort (i.e. the top row of Table 13), it incorporates available lag-to-
treatment data from all new presentations between 2005 and 2014 (i.e. all rows in Table 13). 
This is done by calculating the total number of individuals within the sample who have a lag-to-
treatment of a year or less, the total number with a lag of 1-2 years and so on. By comparing 
these numbers with the total number of individuals within the sample who could have come to 
treatment with that length of lag or less, it is possible to produce a 10-year lag-to treatment 
distribution, which is similar to Table 11 except uses data from the whole sample. (The 
mathematical calculations for this are set out in the appendix of Hickman et al., 2001). As before 
we then index the trend to the older cohort to model the tail of the distribution and use the 
results to calculate incidence in an identical way to the first model. The results are shown in 
Table 14 below, which is a slimmed-down version of Table 13, showing the only column that 
has changed (the one headed `percentage of total incidence accounted for by observed’) and 
the impact this has on resulting incidence (in the final column.)  One of the important differences 
between the methods is that method 2, which incorporates all the data from the 2005-14 sample 
has a much shorter lag to treatment overall, which suggests that lag-times have generally 
reduced since 2005. 
Table 14: Results of model two 
Year of first use Observed 
Percentage of 
total incidence 
accounted for by 
observed 
Estimated 
number yet to 
come to 
treatment 
Estimated total 
incidence 
2005 8,960 97% 286 9,246 
2006 8,495 96% 332 8,826 
2007 8,084 95% 447 8,531 
2008 7,252 92% 615 7,867 
2009 6,290 88% 823 7,113 
2010 4,739 82% 1,010 5,749 
2011 3,744 74% 1,301 5,045 
2012 3,036 62% 1,849 4,886 
2013 2,225 44% 2,868 5,092 
 
The incidence estimates from the two models are shown in Figure 9.