«For use by NatioNal Drug aNalysis laboratories Photo credits: UNODC Photo Library Laboratory and Scientific Section United nationS office on drUgS ...»
Representative Drug Sampling
For use by NatioNal Drug aNalysis laboratories
UNODC Photo Library
Laboratory and Scientific Section
United nationS office on drUgS and crime
Guidelines on Representative
in cooperation with the
Drugs Working Group
European Network of Forensic Science Institutes
New York, 2009
UNITED NATIONS PUBLICATIONSales No. E.09.XI.13 ISBN 978-92-1-148241-6 This publication has not been formally edited.
Acknowledgements The present guidelines on representative drug sampling were developed by the Drugs Working Group (WG) of the European Network of Forensic Science Institutes (ENFSI).
They represent the result of an extensive consultation process among European drugs experts over the course of the years 2001-2003.
The Laboratory and Scientific Section of the United Nations Office on Drugs and Crime is grateful about the agreement reached in 2007 with the ENFSI Drugs WG to publish these guidelines substantially unchanged* with the aim of making them available to a wider, international audience.
The list of contributors to the original ENFSI publication is included on page iv.
UNODC’s Laboratory and Scientific Section also wishes to acknowledge the contributions of Dr. Reinoud Stoel, Netherlands Forensic Institute, to the validation of the tables and software.
* Changes have been made in chapter 1 (introduction) to adapt it for international use. The ENFSI foreword was replaced by the above acknowledgements. Tables and software were validated and relevant corrections made. An application for estimating tablet numbers was included in the software. The rest of the guidelines remained substantially unchanged.
iii List of contributors Sergio Schiavone (Chairman of the Sampling Subgroup of the ENFSI WG Drugs) Raggruppamento Carabinieri Investigazioni Scientifiche, Reparto di Roma, Sezione di Chimica Via Aurelia 511, 00165 Roma, Italia Phone 0039-06-66394656, Fax 0039-06-66394748, E-mail: firstname.lastname@example.org Martine Perrin Institut de Recherche Criminelle de la Gendarmerie Nationale, Department Toxicologie 1, Boulevard Theophile Sueur, F-93111, Rosny Sous Bois Cedex, France Phone 0033-1-49355079, Fax 0033-1-49355027, E-mail: email@example.com Hugh Coyle (also macro development) Forensic Science Laboratory Department of Justice, Equality and Law Reform, Garda Headquarters, Phoenix Park, Dublin 8, Ireland E-mail: HJCoyle@fsl.gov.ie Henk Huizer Netherlands Forensic Institute Volmerlaan 17, 2288 GD Rijswijk, Netherlands (till Oct 15th, 2004) E-mail: firstname.lastname@example.org Annabel Bolck Netherlands Forensic Institute Volmerlaan 17, 2288 GD Rijswijk, Netherlands (till Oct 15th, 2004) E-mail: email@example.com Bruno Cardinetti Raggruppamento Carabinieri Investigazioni Scientifiche, Reparto di Roma, Sezione di Balistica Via Aurelia 511, 00165 Roma, Italia Phone 0039-06-66394668, Fax 0039-06-66394748, E-mail: firstname.lastname@example.org
TLC Thin-layer Chromatography PCWG Police Co-operation Working Group SWGDRUG Scientific Working Group on Drugs UNDCP United Nations Drug Control Programme (a predecessor of UNODC) UNODC United Nations Office on Drugs and Crime
1. Introduction The present guidelines describe a number of sampling methods, from arbitrary methods to methods with a statistical background. They focus on sampling in cases where large numbers of relatively homogeneous material are available. They do not deal with so-called tactical sampling, which may be applied for house-searches or in clandestine laboratory investigations. These cases are characterized by different materials, sometimes in different amounts, different packages and/or sometimes with different suspects; these cases are considered as so specific and so dependent on the situation (also in legal aspects) that a guideline would be inadequate in many cases. Thus, the present guidelines contain a number of sampling strategies for cases with large numbers of items of relatively homogeneous material. However, from the descriptions of the sampling methods, it is not automatically clear which strategy should be preferred (or would be optimum). This is mainly due to the fact that it is not possible to define a sampling strategy, if the requirements have not been defined. This is the main reason why it was decided to refrain from giving advice at local, regional or national level.
In guidelines for wider application, such as the present guidelines, the advice cannot be as fine-tuned as it can be in a specific agreement between prosecutor, police, and chemist and laboratory management at local, national or regional level.
However, some aspects of sampling for international cases are discussed in chapter 6 and in annex II. Here, the advantages and disadvantages of various methods, also in relation with sampling practice, are brought up. It seems that a Bayesian approach is a reasonable one in many cases, but its complexity might be a major drawback, especially for court. Fortunately, the hypergeometric and Bayesian approaches appear to show more or less the same results in cases where no prior probability is used.
Since sampling is often carried out by police and customs, the guidelines refrain from giving advice where the number of samples must be calculated for each separate case; this would be confusing and bother law enforcement personnel with computers or lists with Bayesian and hypergeometric tables. Therefore the final sampling advice just mentions the (minimum) number of samples to be taken (5, 8 or 11, the number of samples being dependent on the circumstances). The forensic laboratory 2 Guidelines on Representative Drug Sampling can then, if necessary, perform the final evaluation and probability calculations.
The collection of items under discussion. A population may be real or hypothetical; finite or infinite; homogeneous or heterogeneous. For the purposes of this booklet, the term population will refer to a real, finite homogeneous population unless otherwise specified.
(b) The arithmetic mean of a sample. This is an estimate of µ calculated from a sample of the population. It is denoted by X.
Unless otherwise stated, the term “mean” will refer to the arithmetic mean of a sample as described in 6 (b).
This is a measure of the variation in the values of a set of measurements. The
standard deviation can refer to either:
(a) The standard deviation of a population. This is the true standard deviation calculated from the entire population. It is denoted by σ. Or (b) The standard deviation of a sample. This is an estimate of σ calculated from a sample of the population. It is denoted by s.
Unless otherwise stated, the term “standard deviation” will refer to the standard deviation of a sample as described in 7 (b).
Qcorr = correction factor in weight estimation
3. Representative sampling techniques A representative sampling procedure can be performed on a population of units with sufficient similar external characteristics (e.g. size, colour). The decision on how to perform it is left to the discretion of the examiner.
An example about what is meant by similar external characteristics is very important. Considering a group of heroin street doses, which are packed in similar packaging, we can apply a sampling rule to this population. So, if there are 100 street doses with different groups of external characteristics, these 100 street doses have to be separated into as many groups as dissimilarities. Each group will be considered as a whole population and will be sampled alone. In some rare cases, although the external characteristics look the same, upon opening the units (sampling), huge differences in the powder appearance among the units may be seen. In this case, the sampling procedure should be stopped according to the above mentioned criteria. In general this happens when the external characteristics of the packages are ignored.
The theoretical way to select a truly random, unbiased representative sample from a population is to individually number each item in the population and then use a random number generator to choose which item to select. This is not possible in practice, especially for large populations containing many thousands of units.
When preparing samples, it is essential that two principles are maintained:
" The properties of the sample are a true reflection of the properties of the population from which the samples were taken.
" Each unit in the population has an equal chance of being selected.
In reality, it is more difficult to adhere to these principles than it first seems.
As was mentioned before, the decision in selecting the samples is left to the discretion of the examiner because, when the population is high, it is impossible to number all the units and use a protocol based on a random selection of numbers. So, considering a subjective choice, it happens that sometimes the expert tends to choose similar sized units, instead of running a real random sampling.
The practical solution for random sampling is quite easy: after having observed that the external characteristics are the same, all the units can be put in a “black 8 Guidelines on Representative Drug Sampling box” (plastic bag or something similar) and a sample can be chosen randomly.
This kind of solution can be applied to practical cases such as seizures of a thousand heroin street doses in similar external packages or a thousand tablets.
In this case this “black box” sampling method can be applied to eliminate (or at least reduce to a minimum) any bias that may be introduced by the person selecting the samples. When we refer to a “black box” method we mean any method that will prevent the sampler from consciously selecting a specific item from the population. These methods are not standardized yet and we can refer to the example given above.
4. Arbitrary sampling The following are various arbitrary sampling methods. They are often used in practice and work well in many situations. However, they have no statistical foundation and may lead to a very large sample in case of large seizures. Not all existing sampling procedures are given; some laboratories use variations of these.
The methods discussed in this chapter provide statistically founded ways to determine the sample size. The first two methods concern a frequentist approach, while the third method describes a Bayesian approach.
The assumption behind a frequentist approach is that a fixed but unknown proportion of the seizure contains drugs. The proportion of drugs in a sample (= the sampled units) can estimate this seizure proportion. The proportion of drugs in the sample will, however, vary over different samples. Therefore, the frequentist methods provide a confidence, (1 −α)100% (for instance 95% if α is selected to be 0.05), that with a given sample proportion the seizure proportion is at least k100% (for instance 90% if k is selected to be 0.9). In other words, one would be correct about a seizure containing at least 90% drugs in 95 out of 100 cases.
The assumption behind a Bayesian approach is that the sample proportion is known and fixed. This proportion is used to calculate probabilities on certain values of the unknown seizure proportion that at that point is still assumed variable. With this approach it is possible to incorporate some knowledge about the seizure that you may possibly have. The seizure proportion is not known but often some ideas about this proportion exist. For instance, if all plants in a hemp nursery appear similar they probably are all hemp plants. It is also possible that there is no clue about the amount and type of drugs in a seizure.
These various forms of prior information will result in different mathematical models to estimate a desired sample size in the Bayesian approach.
This is the hypergeometric distribution. The first (and mostly used) frequentist method is based on this distribution.
In sampling drug units, the numbers of positives, N1, and negatives, N − N1 are unknown. To determine these numbers exactly the whole seizure has to be analysed. If some uncertainty is allowed, the hypergeometric distribution can be used to calculate a sample size of n units that have to be analysed such that at least K ( = kN ) units are positive with (1 −α)100% confidence. For instance, calculate n such that with 95% confidence at least 90% of the pills contains illegal drugs. These choices of the numbers for α and k depend on laboratory guidelines, costs, legal requirements and so on.
If the choices about α and k are made and if an assumption is made about the number of positives to be expected in the sample (usually x), the sample size n can be solved from the above formula. Take for the cumulative probability P ( X ≥ x ) = (1- α) and for N1 = K. Table 1 provides the required sample sizes for some standard choices of α and k with different population sizes, if all sampled units are believed to be positive. Table 2 provides the same information if 1 or 2 of the sampled units are expected to be negative (contain no drugs). Sample sizes can also be calculated with a macro in software such as Excel®, as available via the ENFSI website (www.enfsi.eu under Documents Publications).
Table 1. Hypergeometric distribution
Note: Required sample size to guarantee with 95% or 99% confidence that the seizure contains at least a proportion of k drugs, if it is expected that all sampled units contain drugs.
Example 1 Suppose that a population contains 100 packages. To guarantee with 95% confidence that at least 90% of the packages contains illegal drugs, a sample of 23 packages has to be drawn and all of these packages have to contain illegal drugs (see table 1).