New opiate and crack-cocaine users: characteristics and trends 23 
 
cocaine. From this information it is possible to create a distribution, for all presentations, of the 
lag-time between initiation and their first presentation at treatment. This might show – for 
example – that only ten per cent of all individuals presenting to treatment do so in the first year 
of use, but that 25 per cent present within two years, and so on. This means that for each year, 
we can estimate the number of individuals who have begun an opiate-crack career but who 
have yet to come to treatment. Adding these to the numbers who began in that year and have 
come to treatment gives our total incidence estimate for each year. 
The first model uses NDTMS data for the cohort starting use in 2005 (n=8,960), the lag-time 
distribution for those initiating use in 2005 and presenting to treatment between 2005 and 
201418 is shown below. 
Table 11: Time-to-treatment distribution for those initiating use in 2005 and presenting to 
treatment between 2005 and 2014.19 
Lag time to 
treatment (years) 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 
Percentage 15% 17% 17% 14% 10% 9% 6% 5% 4% 4% 
Cumulative 
percentage 15% 31% 49% 62% 73% 82% 88% 92% 96% 100% 
 
Table 11 shows that 15 per cent of the individuals who started use in 2005 and had presented 
for treatment by 2014, presented within one year of initiation. A further 17 per cent presented 
between one and two years after initiation, prior to coming to treatment, meaning that overall 31 
per cent of the sample said they came to treatment within two years of first using opiates/crack. 
(The fact this is not 32% is simply due to rounding). 
As a basis for the total lag-to-treatment distribution, the main limitation with the above analysis 
is that it assumes all individuals coming to treatment do so within ten years. Examining data 
from earlier cohorts suggests this is inaccurate, as a small proportion of OCUs will continue to 
use these drugs for a long time, sometimes two decades or more, before seeking treatment, 
and some never will. However, we cannot use an earlier cohort for the distribution because this 
is equivalent to using out-of-date data. The average lag-to-treatment is likely to have reduced 
over time given the expansion of treatment places and the influence of DIP. Using old data will 
miss this and bias the estimates. Even using the 2005 cohort’s distribution contains the 
assumption that the time-to-treatment lag has not altered significantly between 2005 and 
2013/14. So, to try and obtain the most accurate model, we used the figures from the 2005 
cohort for the first ten years, as above, on the basis that this covers the majority of individuals 
and for that we want the most up-to-date data possible whilst maintaining a long enough time 
period. We then index the trend at that point to an older cohort, and use data from that cohort to 
model the ‘tail’ of the distribution – i.e. those who take longer than ten years to reach 
treatment.20 The result is a 20-year lag-to-treatment distribution, shown in Table 12 below. 
 
18  Data for 2014 was available until October 2014. This was converted to annual figures by multiplying up by 1.2 to account for 
the missing months in a linear fashion. 
19  The percentages from this table can be calculated from the numbers in Table 13. 
20  In reality there is always a trade-off in this methodology between the up-to-dateness of the cohort used to measure the lag-
to-treatment and the number of years of lag measured, i.e. we could use a more recent cohort, say 2008. But that would 
mean excluding all those who take longer than seven years to come to treatment, an even larger proportion. We are 
indebted to Tim Millar for providing the dataset used to model the ‘tail’ of the distribution. It contained a longer time series of