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Capture-recapture estimates of problem drug use and the use of simulation based confidence intervals in a stratified analysis
  1. Islay Gemmell1,
  2. Tim Millar1,
  3. Gordon Hay2
  1. 1National Drug Evidence Centre, University of Manchester, MHSS NHS Trust, Manchester, UK
  2. 2Centre for Drug Misuse Research, University of Glasgow, Glasgow, UK
  1. Correspondence to:
 Tim Millar
 National Drug Evidence Centre, C/O Evidence for Population Health Unit, Stopford Building, University of Manchester, Manchester M13 9PT, UK; tim.millarman.ac.uk

Abstract

Study objective: To establish the prevalence of problem drug use in the 10 local authorities within the Metropolitan County of Greater Manchester between April 2000 and March 2001.

Setting and participants: Problem drug users aged 16–54 resident within Greater Manchester who attended community based statutory drug treatment agencies, were in contact with general practitioners, were assessed by arrest referral workers, were in contact with the probation service, or arrested under the Misuse of Drugs Act for offences involving possession of opioids, cocaine, or benzodiazepines.

Design: Multi-sample stratified capture-recapture analysis. Patterns of overlaps between data sources were modelled in a log-linear regression to estimate the hidden number of drug users within each of 60 area, age group, and gender strata. Simulation methods were used to generate 95% confidence intervals for the sums of the stratified estimates.

Main results: The total number of problem drug users in Greater Manchester was estimated to be 19 255 giving a prevalence of problem drug use of 13.7 (95% CI 13.4 to 15.7) per 1000 population aged 16–54. The ratio of men to women was 3.5:1. The distribution of problem drug users varied across three age groups (16–24, 25–34, and 35–54) and varied between the 10 areas.

Conclusions: Areas in close geographical proximity display different patterns of drug use in terms of prevalence rates and age and gender patterns. This has important implications, both for future planning of service provision and for the way in which the impact of drug misuse interventions are evaluated.

  • capture-recapture
  • prevalence
  • problem drug use

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Accurate and timely estimates of prevalence of drug misuse are important for planning service provision for drug users at the local level. However, because a proportion of the drug using population are not in contact with services at any one point or period of time, prevalence of problem drug use has to be estimated indirectly. This paper describes the application of capture-recapture methods to provide estimates of prevalence of problem drug use in Greater Manchester. This is an urban area in the north west of England with a population (aged 16–54) of around 1.4 million, comprising 10 local government authorities with the City of Manchester LA at its centre. Each local authority is responsible for responding to problem drug use in its own area.

Capture-recapture methods were developed over a century ago to estimate the size of animal or fish populations1,2 and the method was first applied to human populations in case ascertainment studies during the 1940s.3–5 The application of capture-recapture methods in epidemiological studies was developed mainly through the work of Wittes.6 Hook and Regal7,8 and the International Working group for Disease Monitoring and Forecasting9,10 provide an extensive description of the methodology used in applying multi-sample capture-recapture techniques in epidemiology.

Within the UK, multi-sample capture-recapture has been applied to estimate the prevalence of problem drug in the north west of England,11 London,12 Liverpool,13 Glasgow,14 Dundee,15 the north east of Scotland,16 and, in one of few studies involving rural areas alone, Cheshire.17

Outside the UK, the European Monitoring Centre on Drugs and Drug Addiction (EMCDDA) funded a study, using three sample capture re-capture methods, to estimate the prevalence of opioid misuse within six European cities for the age group 15–54.18 Other studies within Europe have estimated the prevalence of drug misuse in Amsterdam,19 Barcelona,20 and Berlin,21 while further afield, capture recapture methods have been used to estimate the prevalence of drug misuse in Michigan,22 Los Angeles,23 Bangkok,24 and Australia.25

METHODS

Unnamed identifier information on problem drug users resident in Greater Manchester during April 2000 to March 2001 was obtained from five sources: drug treatment services, general practitioners, the arrest referral system, Greater Manchester Police, and the probation service. With the exception of the probation sample, only cases involving the known use of opioids, crack, cocaine, or benzodiazepines by persons aged 16–54 were eligible for inclusion. This definition is comparable with other studies of problem drug use and covers the definitions used by the data sources.

The treatment sample included persons in contact with statutory, community based, drug treatment services in the Greater Manchester area. It was derived by combining information from a national census of persons receiving drug misuse treatment with information from drug misuse database (DMD)26 and the new national drug treatment monitoring system (NDTMS).27 Cases reported by statutory specialist treatment services were considered separately from those reported by GPs.

Arrestees who acknowledged a drug problem and who agreed to be assessed when interviewed by an arrest referral worker were included in the arrest referral sample and details of these people were obtained from the Greater Manchester arrest referral initiative (GMARI).

The police arrest sample included arrests for possession of heroin, methadone, other opioids, cocaine, crack, or benzodiazepines extracted from the Greater Manchester Police database of arrests under the Misuse of Drugs Act (1971).

Greater Manchester Probation service undertakes assessment of offenders using the assessment, case recording and evaluation system,28 which records the severity of an offenders drug problem and the degree to which the drug problem is related to offending. The severity of a drug problem is classified on a four point scale relating to “none”, “mild”, “moderate”, and “severe”. Offenders whose drug problem was assessed as “moderate” or “severe” were included in our sample.

People from each sample were matched according to their unique identifiers (initials, date of birth, gender) within each area and identifiers were encrypted before matching. Four samples were used in the initial analysis: statutory treatment services, arrest referral, police, and probation. The GP data source was not used in the initial analysis as the number of cases from this source were very small in most areas. The data were stratified by age group (16–24, 25–34, and 35–54) and gender and were aggregated into contingency tables describing the overlaps of individuals among sources within each stratum for each area.

All ethical safeguards were met and ethical approval for the use of NHS data in this study was granted by the North West Multi-Centre Research Ethics Committee.

ANALYSIS

The analysis of each contingency table entailed firstly fitting a log-linear model that assumed independence between samples. Interaction terms were subsequently applied and models containing one interaction were compared with the independence model using the log-likelihood ratio test.29 A significant change in deviance implied that the model containing the interaction provided a better fit to the data than the independence model. Competing models with the same degrees of freedom were compared using the AIC (akaike information criteria)7,30 and the BIC (Bayesian information criteria).7,31 Where an interaction model provided a better fit than the independence model, subsequent interaction models were applied and the simplest model was selected on the basis that it had the lowest AIC and/or BIC value and was not significantly improved by adding a further interaction. The final model provided an estimate of the number of people who did not appear in any of the samples. Confidence intervals for the estimate for each stratum were calculated using the likelihood interval method32 and the estimate of the total number of unknown problem drug users within each area was obtained by summing the stratified age-gender estimates. The GP dataset was substituted for the probation dataset in the City of Manchester to enable suitable models to be obtained for all six age-gender strata.

For each stratum in each of the 10 areas we derived an estimate of the unknown population x together with an upper and lower confidence limits, ciu and cil. The sum of these estimates provided an estimate of the unknown number of problem drug users in each area. However, a confidence interval derived from summing the upper and lower bounds of the 10 95% confidence intervals does not provide a 95% confidence interval for the summed estimate. We therefore used simulation methods to generate confidence intervals for the summed estimates. Assuming a log-normal distribution for x, the estimate of the unknown population, then μ = ln(x) is the mean of this distribution and the standard deviation σ of the distribution can be estimated as.

Embedded Image

The simulation procedure involved generating, for each strata, 10 000 random deviates from a log-normal distribution with mean μ and variance σ2. Confidence intervals for the sum of the strata were calculated by summing the six log-normal distributions and deriving the 2.5 and 97.5 centiles for the summed distribution. The log-normal distributions were generated using Minitab.

RESULTS

Table 1 shows the number of problem drug users identified from each source. The total number of known drug users in Greater Manchester from the contingency table that accounts for the overlap between sources was 8359.

Table 1

 Number of problem drug users identified from each source

Table 2 describes the log-linear models that were applied to each stratum in each area. For six of the strata, models containing three interactions provided the best fit to the observed data. Four models contained two interactions and for 29 strata, models with one interaction provided the best fit to the data. For 17 strata there was no improvement to the model by adding an interaction and the independence model was used, however for four strata no suitable model could be found. For these strata, the combined males and females estimate for that age group was used to calculate an overall estimate for the area. Further model checks entailed comparing the sum of the age strata estimates with the model estimates for men and women and comparing the sum of the gender strata with the model estimates for each age group. A p value of <0.05 indicates that the selected model is not a good fit of the observed data, in only one of the strata did we have to use a poorly fitting model.

The models for female problem drug users contained fewer interactions than those for males. This may be attributable to smaller numbers in this group or because female drug users are a more homogenous group, or both. The most common interactions were between the arrest referral and probation data sources and the arrest referral and treatment data sources. This may be because clients who were included in the arrest referral data source were more likely to be referred for treatment and to be identified to the probation service, because of the nature of the arrest referral system.

The capture recapture analysis suggests that during the period April 2000 to March 2001 there were 19 255 (95%CI 18 731 to 21 853) problem drug users in Greater Manchester, a prevalence rate of 13.7 (95%CI 13.4 to15.7) per 1000 population in the 16–54 age group (table 3). Around 43% of the problem drug users within Greater Manchester appeared in at least one of our samples.

Table 2

 (A) Results of log-linear modelling (men)

Table 2

 (B) Results of log-linear modelling (women)

Table 3

 Estimates of the number of problem drug users by local authority

The estimates indicate considerable variation in the gender distribution of problem drug users between areas. For Greater Manchester as a whole, we estimate that 78% of drug users are male, with a range by area from 66% in Trafford to 85% in Salford. The age distribution of problem drug users also varies throughout the region. The local authorities of Bury, City of Manchester, and Stockport have a lower proportion of young users than most other areas while Tameside, Trafford, Bolton, and Wigan have a relatively high proportion of young users (figs 1 and 2).

Figure 1

 Prevalence of problem drug use by gender.

Figure 2

 Prevalence of problem drug use by age group.

In this analysis we have used 60 stratified estimates of problem drug use to estimate the number of problem drug users in Greater Manchester, to overcome problems of heterogeneity and to enable age and gender patterns to be described. The confidence intervals used for the 10 area estimates (table 3) are based on the 2.5 and 97.5 centiles of the sum of six simulated log-normal distributions whose mean and variance were derived from the stratified capture re-capture estimates and the likelihood interval. Table 4 provides a comparison between the area estimates obtained from unstratified models with their associated likelihood confidence intervals and the estimates obtained from the sum of the stratified estimates with their associated simulated confidence intervals. The difference between the lower and upper bounds and the estimate are similar for the sum of stratified models and the sum of the unstratified area models indicating no loss of precision through the use of simulated confidence intervals.

Table 4

 Comparison of likelihood and bootstrap estimate and confidence intervals

The models used in the un-stratified analyses were more likely to contain interaction terms than the stratum models, possibly reflecting heterogeneity within the samples, and two of the models (Bury and Salford) were a poor fit to the data. Furthermore, the best fitting model for the un-stratified Greater Manchester area contained five interaction terms and was still not a good fit to the data. The simulation method enables confidence intervals to be obtained for the prevalence of problem drug use in Greater Manchester derived from the sum of stratified prevalence estimates.

DISCUSSION

This study suggests that that there were 19 255 problem drug users (PDUs) in Greater Manchester during 2000/01 giving a prevalence rate of 13.7 (95%CI 13.4 to 15.7) per 1000 population in the 16–54 age range. The greatest number of problem drug users was observed in the City of Manchester (6037 PDUs), a prevalence rate of 23.9 (95%CI 21.3 to 28.4) per 1000 population aged 15–54, this area accounted for almost a third (31%) of the county’s PDUs but less than a fifth (18%) of the Greater Manchester population aged 16–54. Although there was clearly a concentration of drug problems in the City of Manchester, most (69%) of the county’s PDUs lived in the surrounding areas. Within Greater Manchester male PDUs outnumbered females by a factor of 3.5:1 and prevalence was highest in the 25–34 age group. The stratified analysis showed variations in the age and gender distribution of PDUs across the 10 areas.

The rates observed here are slightly lower, but within the range, of those observed for other, predominantly urban, European areas, however other studies have used different age groups, time periods, and case definitions so direct comparison is hindered. Within the age group 15–55, the prevalence of PDUs in Dundee was estimated at 29 per 1000 population between 1990 and 199415 and at 20 per 1000 in Aberdeen in 1997 for the age group 15–54.16 In London, Hickman12 showed levels of problem drug use of over 30 per 1000 population aged 15–49 between 1992 and 1995. Brugha17 estimated a prevalence of two opioid users per 1000 population in Cheshire within the age group 15–55 in 1993 while Comiskey33 estimated that there were 21 opioid users per 1000 population aged 15–54 in Dublin in 1996. Benyon11 showed rates of 34 per 1000 in Liverpool Health Authority, 37 per 1000 in Manchester Health Authority, and 18 per 1000 in Bolton Local Authority in 1997 for 15–44 the age group.

Key points

  • Within a large urban conurbation, different patterns of drug use in terms of age group and gender patterns exist between areas, indicating different stages of growth in the prevalence of drug problems.

  • Simulation can be used to provide reliable confidence intervals for the sum of stratified prevalence estimates.

  • Stratified prevalence estimates can provide policy makers with essential information for future planning of service provision.

The 1997 prevalence rate estimated for Manchester Health Authority (co-terminus with the local authority in 1997) is higher than that observed here, however it is based on an estimate and population figures for the 15–44 year age range, rather than 16–54. Because the number of PDUs aged 15 or 45–54 is likely to be very small, a crude adjustment for the purposes of comparison is unlikely to introduce major error. Scaling the 1997 estimate for the 16–54 local authority population, gives a rate of 31.0 (95% CI 26.2 to 37.1) per 1000. Applying the same adjustment to the 1997 estimate for Bolton local authority gives an adjusted prevalence rate of 13.8 (95% CI 12.1 to 15.7) per 1000 population aged 16–54. Combining the results from the two studies might suggest that the prevalence of problem drug use has declined in the City of Manchester and increased in Bolton.

In this analysis we have stratified our estimates by age and gender. This approach has many advantages, it enables more detailed comparison of prevalence patterns across areas and can help indicate how patterns of drug use may be changing over time. Within Greater Manchester, our analysis indicates, that the “epidemic” was initially concentrated in the geographical centre of the region, the City of Manchester. Over time, the number of young (new) users has declined in this area the epidemic has diffused out to more outlying areas, in particular to Bolton, where there are mainly young (new) users. Age and gender stratification is also useful for policy makers who may be able to target resources more effectively at certain sub-groups within local government areas. Furthermore, stratifying the analysis may improve the validity of total area estimates by reducing heterogeneity within the samples. Stratification also identified different interactions within area, age, and gender strata. This may reflect different patterns of service provision between areas, particularly with respect to joint working between health and criminal justice as well as differences in which interventions access their target (age and gender) population.

Simulation methods were used to provide reliable confidence intervals for the sum of the stratified estimates for each area. This procedure was implemented using Minitab and the 95% limits obtained from the log-normal distribution provided a close approximation to the likelihood based confidence intervals for each stratum. As far as we are aware this is the first application of these methods within capture-recapture analysis of problem drug use and, as shown here, this method can provide researchers with a relatively simple method of combining stratified estimates to generate total area estimates with valid and reliable confidence limits. However, a refinement to the simulation method may be obtained through the use of the multinomial distribution, as applied in this study to derive the likelihood interval CIs and as used by Cormack.32

As in other studies a potential limitation of this study is the issue of case definition. Within the police sample we identified people arrested for possession of opioids, crack, cocaine, or benzodiazepines but had no information as to whether these people were actual problem drug users, however we attempted as far as possible to limit the sample to users by including possession offences only. During data extraction it was apparent that most of these people were arrested for possession of relatively small amounts of illegal drugs that are likely to indicate personal use. Within the probation data source, severity of problem levels of drug were categorised as “none”, “mild”, “moderate”, and “severe” and the relatedness of drug use to offending was categorised in a similar way but the exact drugs used were not recorded. To identify “problem” drug users we selected those people whose drug problem was recorded as, “moderate” or “severe”. Hence case definitions are as similar as was possible but would be improved if all data sources used in the analysis recorded individual drug use.

This research has established prevalence estimates for problem drug use, based on capture-recapture methods applied at the local strategic level, for the 10 local authorities within Greater Manchester and showed how simulated confidence intervals can be used in a summed stratified analysis. The findings presented here show that areas in close geographical proximity display different patterns of drug use in terms of age group and gender patterns, indicating different stages of growth in the prevalence of drug problems. This has important implications, both for future planning of service provision and for the way in which the impact of drug misuse interventions are evaluated.34 Although direct capture-recapture prevalence estimates are available for relatively few areas in England and Wales, datasets suitable for this purpose are likely to exist in most areas. Further studies of this nature would provide policy makers with essential information and enable further exploration of the methodological developments described in this paper.

Acknowledgments

This research could not have been undertaken without the help of the following individuals and organisations, who provided access to data: Claire Brown-Allan (Greater Manchester Police), Libby Brundrett (Greater Manchester Police), Sandra McFarlane (Greater Manchester Probation Service), Andrew Jones, Helen Morey, and Petra Meier (Drug Misuse Research Unit).

REFERENCES

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Footnotes

  • Funding: this study was funded by the Home Office Drugs and Alcohol Research Unit.

  • Conflicts of interest: none declared.

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