Estimation techniques

In order to estimate the extent of the more severe patterns of drug use at the local and national level, The Rapid Assessment and Response Guide on Inject-ing Drug Use (RAR) (WHO 1998a) suggests the followInject-ing estimation tech-niques:

- case-finding and enumeration - multiplier techniques

- nomination techniques

- capture-recapture techniques

Whilst with the multiplier and nomination techniques basically all consumers can be considered, i.e., hidden populations as well, case-finding and capture-recapture methods are limited to those drug consumers who are already known to the addiction care, welfare and health authorities or the law. The following ex-planations essentially follow the Rapid Assessment and Response Guide on Injecting Drug Use (WHO 1998a):

Case-finding and simple enumeration

Using the techniques of case-finding and simple enumeration, the size of the

"visible" population of drug addicts can be estimated. (i.e. clients of treatment and care services, as emergency case in hospitals or by the police). It is possible to draw conclusions as to the size of the overall population (including the hidden population) using this technique.

By listing all the clients of treatment and care establishments (case-finding), the prevalence of known drug abusers during a definite period of time can be deter-mined. In order that the survey is as complete as possible, the cases must be re-corded by using a combination of various information sources (case-finding in various services and agencies), whereby various points are of significance:

- Coverage: Owing to inefficiencies in the basic reporting systems it is unlikely that the coverage of the known population will be complete.

- Feasibility: Information sources and screening strategies may need to be as-sessed beforehand in order to test if they can (or are willing) to provide the data required by the study.

- Case Definition: In order to obtain reliable and comparable data, clear case definition and comparability across agencies are required.

- Double counting: When different sources are combined there is a risk of over-estimating the number of cases. By assigning "unique identifiers" to the cases in a standardised way across all sources, it is possible to identify the cases and the duplicate cases can be removed.

- Confidentiality: It is necessary to ensure that the identities of the drug abusers are not disclosed to others. Therefore the "identifiers" should not allow the identity of the individual drug abuser to be inferred.

Multiplier techniques

The estimation of the total number of a population using multiplier techniques is based on informed assumptions on the proportion of the cases in the population being examined which undergoes a certain experience during a definite time pe-riod (e.g. overdose, death, arrest). The multiplier and the benchmark provide numbers for the events that are known to occur.

Procedure:

- Select a benchmark where data is available

- Select a multiplier using data from research studies

- Calculate the number of cases by multiplying the benchmark by the multiplier.

Example:

A benchmark might be the total number of deaths in a region which are attributed to drug abuse during the year in question, say 50. The multiplier in this case is the assumed mortality rate of drug abusers, say 1%. Applying the benchmark-multiplier calculation to these figures, the size of the population would be: 50 x 100 = 5,000.

When estimating the entire population multipliers and benchmarks should be used if possible from various data sources. This results in a range of estimates of the total number of drug users which provides an approximation of the actual number.

Advantage: Once the necessary statistical data are obtained, the calculation pro-cedure is very simple.

Disadvantage: The number of people in need of treatment within specific popula-tion sub-groups (e.g. age, gender) cannot be estimated.

Nomination techniques

With nomination techniques, the estimation of the entire population is based on information which individuals in a sample provide about their acquaintances.

Prevalence is estimated by using the benchmark-multiplier approach. In contrast to the multiplier technique, the multiplier with the nomination technique is based on information which can be gained from the informants who are interviewed.

Example: A sample of drug abusers is asked whether they or their friends (who are drug abusers too) have had any contact with a drug treatment agency in the

past six months. The ratio ”did have contact” / ”no contact” is compared to the number of persons known to the agencies. The total number can be extrapolated.

Capture-recapture techniques

One of the most important methods of estimating the size of the drug abusing population is the capture-recapture method. The size of a population is estimated from the number of members of this population who appear in multiple samples taken from the same population.

Capture-recapture refers to a technique developed at the beginning of the twen-tieth century in biostatistics to estimate the size of wild animal populations. It in-volves capturing a random sample of animals who are then marked and returned to their habitat. Subsequently a second sample is recaptured and the number of marked animals from the first sample is observed. The ratio of marked animals in the recaptured sample to the recaptured sample size is assumed to be the same as the ratio of the first captured sample to the total population.

When estimating the drug abusing population, existing records from two or more sources are utilised. Possible sources of information are police records for pos-session of narcotics or court convictions, hospital emergency room admissions or admissions to drug abuse treatment agencies. The overlap of cases between the data sources is then measured.

Example: In a given area or region two separate listings of drug abusers are available. The first list (sample 1) consists of overdose cases appearing in hos-pital emergency rooms and the second list (sample 2) consists of drug-related ar-rest cases. With two lists there are four possible locations for any given individ-ual: on list 1 and not on list 2, on list 2 and not on list 1, on list 1 and on list 2 and finally on neither list 1 or list 2. The following contingency table presents the range of possible locations.

List 2 (sample 2):

Drug related arrest cases

Yes No

List 1 (sample 1): Yes f11 f12 Overdose Cases

No f21 f 22

The only unknown cell of the table is f22. From the number of cases in the first three cells f22 can be estimated and subsequently the total number of drug abusers (P).

f12 * f21 (f11+f12) * (f11+f21)

F22 = _____________

P = ______________________________

f11 f11

For effective two-sample capture-recapture studies the following points are im-portant:

- The two samples are independent of each other.

- There is an equal likelihood of each member of the population being sampled on each occasion.

- The population is stable during the sampling period.

- Both samples must cover different aspects of drug consumption (e.g. health-related and legal system, etc.).

- The homogeneity and the representativeness of the samples in terms of the population must be considered.

- The direction in which biases might occur must be considered (e.g. if samples are not independent the estimation will over-estimate the true population).

- Both the time period and the graphical area must be limited.

- The definition of the target population must be equivalent in all samples (in relation to geographical area, time period, drug use, etc.).

- Unique identifiers must be attached to each case (e.g. date of birth, mother’s birthday and first name, gender, etc.). The larger the number of unique identi-fiers, the greater the precision in matching.

- The resulting estimate should be compared with other prevalence estimation.

There is no restriction on the number of samples that may be used in the calcula-tion of estimates. The more samples included in the calculacalcula-tion the more precise the estimate. The requirement of independence can be ignored with three or more samples since more sophisticated statistical methods using log-linear modelling are used for the estimation.

Improving comparability

The EMCDDA Projects CT.97.EP.04⁹³ and CT.96,EP.07⁹⁴ have the aim of im-proving the comparability of estimations of the extent of the problematic drug

93European Monitoring Centre for Drugs and Drug Addiction (EMCDDA). Study to Obtain Comparable National Estimates of Problem Drug Use Prevalence for all EU Member Stages. Lisbon: EMCDDA, October 1999.

consumption at national and local level. The EMCDDA has made available on its homepage the final report of the project, guidelines for using the estimation tech-niques in the EU as well as a help desk which supports local prevalence estima-tion studies:

http://www.emcdda.org/activities/epidem_comparability_estimates.shtml