Research paperEstimating incidence of problem drug use using the Horwitz-Thompson estimator – A new approach applied to people who inject drugs in Oslo 1985–2008
Introduction
The trend in the number of new problem drug users per year (incidence) is the most important measure for studying the diffusion of problem drug use. This measure shows how the total and combined effects of protective and risk factors affect incidence trends. Drug policies and prevention measures may or may not affect such trends. The efforts to understand them will help determine how effective policies and prevention measures are, and how they could be modified or improved.
Estimating the trends in the number of new problem drug users is difficult. It requires systematic routine data collection that is not readily available, and calls for statistical models that are not easily accessible. In 2006 the International Journal of Drug Policy reprinted an article from 1974, which offered a method that could transform routine data collection into trends in incidence (Hunt, 2006). Hickman points out that much further progress could have been made in data collection and methodology if the method had been actively pursued, despite some problems with the proposed method (Hickman, 2006).
Since this time, some further work has been carried out and a review of methods is provided in Sánchez-Niubò, Mammone, and Scalia Tomba (2013). In the case of heroin use, estimation methods of incidence have been mainly based on data from treatment facilities. Lag correction methods (Hickman et al., 2001, Hunt, 2006, Nordt and Stohler, 2006, Sánchez-Niubò et al., 2007), log-linear models of quasi independence (Sánchez-Niubò et al., 2009) and back-calculation methods (De Angelis et al., 2004, Sánchez-Niubò et al., 2013a, Scalia Tomba et al., 2008) have been employed. Most results are based on the estimates of the distribution of time from onset of heroin use to first entry to treatment, often called the “lag time distribution”.
A weakness of methods based on data over successive years from first entrance to treatment, is that some problem drug users may never, or only after very long time, show up for treatment. Users may die or cease their use without entering treatment, or they may refuse treatment or simply choose not to seek treatment. These biases have been addressed in different ways. Incidence estimates have been restricted to the subsample that entered treatment during the observation period (so-called relative estimates), or assumptions have been made regarding the size of bias (Hickman et al., 2001). Also, assumptions regarding the risk of death or permanent cessation of heroin use before entering treatment for the first time, have been integrated into the estimation methods (De Angelis et al., 2004, Nordt and Stohler, 2009, Sánchez-Niubò et al., 2013a).
Newer approaches have been developed based on data for all persons in treatment, not just for those who enter for the first time (Nordt et al., 2009, Nordt and Stohler, 2008). Nordt and Stohler (2008) found that in Zurich it was sufficient to base heroin incidence estimation on data for the first use of heroin for all persons on a single day in treatment. In such methods, those who temporarily cease drug use would not be accounted for. Those not accounted for, may have a different distribution of onset than those not observed. Depending on the type of model and data employed, such factors will bias incidence estimates. Temporary inactive injectors were included in one study estimating an entry rate to intravenous drug use (the entry rate being the sum of new injectors and previous injectors who relapse after a period of non-injecting) and this approach may be useful in estimating trends in incidence (Amundsen, Bretteville-Jensen, & Kraus, 2011).
The aim of this study was to widen the palette of available methods and types of data used for incidence estimation of problem drug use over time, based on series of cross-sectional data, while taking into account that there are temporary inactive users. Our study sample exemplified people who inject drugs in Oslo.
Section snippets
Data
Semi-annual, cross-sectional surveys of people who inject drugs (PWID) picking up needles and syringes from a needle and syringe program facility in Oslo were conducted from 1993 to the present (Bretteville-Jensen & Skretting, 2010). Surveys were anonymous. Precautions were taken to prevent individuals from being interviewed twice during the same two-day, semi-annual interview session. The number of persons interviewed each year is shown in Table 1, distributed by age and year of survey. The
Results
Our method yielded estimates of incidence over time with confidence intervals, based on likely assumptions regarding drug use progression and the probability of being included in a sample.
For Oslo the incidence of injecting drug use significantly decreased from 365 (CI 328–402) in 1985 to 164 (CI 140–187) in 2008. There was no significant decrease in incidence from 1985 to 1992 (see Fig. 3). The average decrease per year from 1985 to 2008, based on the trend depicted by a linear regression
Discussion
Our method yielded incidence estimates for problem drug use over time, addressing periods of inactivity. Applied to PWID in Oslo, we found a robust downward trend. In addition, the method was less data intensive than previous methods.
The downward trend in incidence of PWID in Oslo was not surprising, but not obvious either.
Our method addressed temporary inactive injectors. The sensitivity analysis showed that the largest deviation from the basic assumptions was evident when temporary cessation
Acknowledgements
We would like to thank Albert Sánchez-Niubò for his useful comments on the final manuscript. The work was funded by SIRUS.
Conflicts of interest: The authors declare that there are no conflicts of interest.
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