# Review of the EU, NAFTA and CODEX Procedures for MRLs Calculation

***José Domingo Salazar***[^1]

***European Crop Protection Association***

***10^th^ July 2007***

> **Summary.** This document provides a review of the regulatory
> procedures in use or proposed in the EU, NAFTA and CODEX for the
> calculation of the *maximum residue levels* (MRLs) based on residue
> values obtained from supervised field trials. Some theoretical and
> practical issues with these procedures are highlighted. We conclude
> that both the EU and the NAFTA procedures are scientifically based,
> reliable and may be made to produce similar results (if EU MRL classes
> are not used). A recent proposal for the calculation of CODEX MRLs
> based on the binomial distribution is also discussed. Recommendations
> for improvement and harmonization of the existing methods as well as
> open issues are included at the end of this report.

## Introduction

In recent years, the degree of mathematical sophistication in the
regulations of residues of crop protection products (CPPs) in foodstuffs
has grown considerably (see references \[1\] and \[2\]). This has been
stimulated by increased public attention to food safety and by a desired
for harmonization to facilitate international trade. As a result, more
advanced statistical and mathematical methods have been introduced for
the analysis of residue data.

In this report, we review in some detail the EU, NAFTA and CODEX
procedures in use or proposed for the calculation of the *maximum
residue levels* (MRLs) and discuss their strengths and weaknesses. We
also compare their results and provide some recommendations about their
application.

## Nature of the Residue Data

The CPP residue populations are usually left-censored (i.e. truncated at
the limit of detection (LOD) or the limit of quantification (LOQ)
levels), right skewed (i.e. asymmetric, having a long right tail) and
contain outliers (extreme values that appear discrepant from the rest);
see Figure 1.

![](media/image1.wmf){width="3.7604166666666665in"
height="2.8361111111111112in"}

Figure 1. Diagrammatical depiction of a typical residue sample
population.

The censored values represent loss of information and can seriously
affect the calculation of certain statistical measures like the mean and
the standard deviation. The long right tail of the dataset leads to the
appearance of residue values seven or eight times the size of the mean
value. This complicates the classification of any of these extreme
values as outliers.

There is great diversity in the appearance of residue datasets. Some
seem to follow a normal distribution (also called a bell-shaped or
Gaussian distribution, see Figure 2). Others seem to follow a lognormal
distribution (the logarithm of the residue values would follow the
normal distribution), which is a right skewed distribution as depicted
in Figure 1. Others still seem even more right skewed than the lognormal
distribution and finally some residue datasets are so erratic that they
do not appear to follow any known distribution at all.

## EU Calculation

The EU gives detailed statistical guidelines for calculating MRLs (see
\[1\]) which specify the use of two methods. Method I proceeds as if the
samples are derived from a normal distribution and sets the MRL at the
right-side end-value of the 95 % confidence interval of the 95^th^
percentile. That is, the MRL is set so 95 % of the time, the 95^th^
percentile of the assumed underlying normal distribution is lower than
the MRL (see Figure 2). Both the confidence interval and the percentile
are computed using the formulas corresponding to the normal
distribution.

![](media/image2.png){width="3.9097222222222223in" height="2.925in"}

Figure 2. In method I, a normal distribution is assumed.

Method II does not assume that the residue data follow any particular
distribution. Instead, the 75^th^ percentile of the sample is computed
and then doubled. The percentile is computed using the Weibull
procedure, which consistently (and for small datasets, considerably)
overestimates the percentile values (see \[3\]), representing a somewhat
artificial worse case scenario. The Weibull procedure requires
increasingly larger datasets to estimate higher percentiles and that may
explain why the EU does not require the computation of the 95^th^
percentile by this procedure and instead chooses to require the 75^th^
percentile and then double it.

It is important to point out that the "PERCENTILE" function available in
Excel is not appropriate for computing the percentiles mentioned in
Method I or Method II. For Method I, the appropriate methodology derived
from the normal distribution should be used as explained in \[1\]. For
Method II, a special Excel add-in should be produced, which implements
the Weibull method as described in \[1\].

Unfortunately, the EU regulations do not provide guidance for when to
use Method I or Method II or for what to do when the MRLs produced by
the two methods differ. It simply says that the next step consists in
the rounding of the MRL value to one of 16 discrete MRL classes listed
in \[1\].

The EU guidelines require the substitution of non-detected residues by
LODs/LOQs values. This give a much exaggerated worst-case scenario and
it is clearly undesirable from a statistical point of view because it
skews the residue distributions, inflates the estimator of the mean and
decreases the estimators of the variability \[4\]. On the other hand,
the guidelines allow for the removal of suspected outliers by using the
Dixon's Q-test, which assumes normality of the residue population. The
guidelines warned very appropriately against the use of Dixon's Q-test
for non-normal residue distributions.

Of the two methods included the guidelines, Method I is expected to be
more sensitive to the substitution of non-detects and the removal of
outliers, due to the fact that it is based on a normality assumption.
Method II should be less sensitive (for a small proportion of
non-detects), because it does not make any distributional assumption.

## NAFTA Proposed Calculation

Recently, a new method for MRL calculations has been proposed for the
NAFTA area, where MRLs are called "tolerances" \[2, 5\]. During the
development process, the regulators considered a number of possible
calculation methods and selected some of them for use. A flowchart was
produced, which indicates under what circumstances each method must be
used (see Appendix).

The first part of the procedure requires "filling in" the values of the
non-detects (NDs, which stands here for LODs and LOQs) by assuming that
the samples have been produced from a lognormal distribution. The
lognormality of the resulting dataset is checked both by the use of the
Shapiro-Francia test as well by a visual inspection. If the dataset is
considered not to be lognormal, then the "California method" is
suggested, which sets the tolerance value three standard deviations
above the sample mean (for a normal distribution, this would be roughly
equivalent to setting the MRL at the 99.9^th^ percentile).

If the dataset is deemed lognormal, then up to three different
statistical measurements may be required:

-   the 95% upper confidence limit on the 95^th^ percentile;

-   the 99^th^ percentile estimate and

-   the product of 3.9 times the upper prediction limit of the median
    (this quantity is referred to as "UPLMedian95" in the flowchart).

All these measures are calculated following the rules of the lognormal
distribution; so although the first measure looks very similar to the
one used in the EU Method I, it is likely to produce a higher result.
The third measure is produced under the additional assumption that the
*coefficient of variation* CV (the ratio of the standard deviation to
the mean) has a value of one.

For large datasets (more than 15 data points), the minimum of the first
two measures is taken forward (these two measurements are referred
collectively as the "95/99 rule" in the flowchart). For smaller
datasets, the minimum of all three measures is required. Whichever
option is taken, the result must be rounded.

There is no allowance in the NAFTA procedure for the removal of
suspected outliers by any statistical method.

## The Binomial Method

Recently, a deterministic method for the computation of CODEX MRLs has
been proposed \[6, 7\], which is claimed to produce similar MRLs to
those already approved by CODEX. The method is based on computation of
percentiles according to a certain "binomial procedure" and the
subsequent estimation of MRLs based on a particular collection of
residue data.

The computation of percentiles using the "binomial procedure" seems to
lack theoretical justification. It does not correspond to any previous
modelling use of the binomial distribution or any known mechanism for
the computation of percentiles.

The NAFTA statistical team lead by Mr David Miller at the USA
Environmental Protection Agency (EPA) has performed extensive
simulations to determine the accuracy of this binomial method \[5\]. It
was found to overestimate the percentiles for normal and lognormal
distributions.

Even if an alternative procedure for the computation of the percentiles
were to be devised, issues may remain with the dependence of the
binomial method on a particular residue database. Very little
information has been provided about this dataset, and it is an open
question how relevant it may be as a model for all residue populations,
regardless of pesticide, GAP or crop.

## Discussion

A number of comments may be made at this stage about the EU and NAFTA
MRL calculation procedures. Each procedure combines more than one
method, which seems sensible given the diversity in behaviours exhibited
by residue datasets.

The EU combines two methods: Method II is a distribution-free method but
Method I assumes that the residue samples are derived from a normal
distribution. Given the right skewed nature of most residue
distributions, it would seem more sensible to apply Method I to the
log-transformed residue values instead of to the residue values
themselves (as is done for some of the methods in the NAFTA
calculation). The log-transformation would tend to "normalize" the
residue samples, allowing a more reliable estimate of the mean and the
standard deviation.

The log-transformation of the residues would also facilitate the use of
the Dixon's Q-test for the removal of suspected outliers. In practice,
it is very unlikely that this test would be applicable to real residue
distribution directly but it may be applicable to their
log-transformations. Nevertheless, given the right skewed nature of
residue distributions, a negative outcome for this test is expected
almost every time.

However, the EU calculation's main drawback seems to be its lack of
guidance for which method to use in each circumstance; this leaves the
residue expert with considerable uncertainty.

The NAFTA method on the other hand seems, at first sight, much more
prescriptive. However, it is heavily influenced by the expectation that
the residue samples would follow a lognormal distribution closely, not
only that they will be right skewed[^2]. As a result, the NAFTA
procedure suffers from a certain circular logic. If non-detects are
present, it is requested that they should be substituted or "filled in"
by values extracted from a lognormal distribution (no attempt is made to
decide if the residue values above the LOD level follow a lognormal
distribution or not prior to the fill-in procedure). Then the newly
computed values are added to the existing ones and the whole dataset is
checked for lognormality. Even if the "extended" dataset failed the
lognormality test, the residue values introduced following the
lognormality assumption are to be used in the subsequent computations.

Another objection that could be made to the NAFTA procedure is that the
check on the size of the residue datasets is done at the bottom of the
flowchart, although this factor is likely to influence significantly
both the LODs filling as well as the checks on lognormality.

From a practical point of view, perhaps the main drawback of the NAFTA
procedure is its considerable statistical sophistication, which made it
hard to use for exposure specialists without a sizable statistical
background. This is particularly the case in relation to the checking of
the lognormality assumption. The NAFTA regulators have provided two
spreadsheets that implement their tolerance calculation: one for filling
in the LODs and another one for the actual tolerance calculation.
According to the stated rules, the lognormality of the residue dataset
should be decided firstly by performing a Shapiro-Francia test.
Nevertheless, the regulators found the implementation of this test to be
too time consuming and decided on implementing instead an approximation
to it[^3]. Should this approximation reject the lognormality of the
dataset, the spreadsheet user is then expected to look at a probability
plot of the residue data and evaluate by himself or herself whether the
dataset is indeed lognormal or not.

This graphical step does not seem very satisfactory. Users of the
spreadsheet who may lack advanced statistical experience may feel
uncomfortable having to take this decision based on a visual inspection,
since even those with plenty of statistical experience may disagree
about the outcome. It would perhaps be more practical and objective to
rely on a robust lognormality test instead.

The NAFTA regulators claim that their procedure produces similar MRLs to
those already approved by CODEX. It was not possible to verify this
assertion independently at the time of writing this report. But previous
work done in Syngenta seems to indicate that the EU and the NAFTA
methods can be made to produce similar MRLs. As can be seen in Figure 3
(left panel), after taking the maximum of the two EU methods as the MRL
but not applying the Dixon's Q-test or the MRL classes, the two
procedures produce very similar results. This state of agreement is
degraded once the EU MRL classes are applied (Figure 3, right panel).

![](media/image3.png){width="4.769444444444445in" height="3.0375in"}

Figure 3. EU vs. NAFTA MRLs before and after rounding.

Indeed, the comparison between the two panels of figure 3 highlights the
fact that the use of the MRL classes as a rounding mechanism in the EU
regulations has the effect of distorting the calculations in the
direction of an exaggerated worst-case scenario and nullifying some of
the benefits obtained from the use of good statistical methods. These
MRL classes are not essential, and any extra margin of safety that they
may introduce is uneven and arbitrary. As shown by the NAFTA
regulations, it is perfectly possible to devise a simpler rounding
procedure.

## Conclusions

-   Both the EU and NAFTA MRL calculation procedures are scientifically
    based and provide reliable ways of dealing with the great diversity
    of residue dataset patterns.

-   Both methods produce similar results as long as the maximum of the
    two EU method estimates is taken as the MRL and the Dixon's Q-test
    and the MRL classes are not used. When the MRL classes are used, the
    EU procedure may produce higher MRLs.

-   Setting the LOD-residues at a fixed residue value and the use of MRL
    classes as required in the EU procedure are unnecessary steps which
    distort the statistical calculations.

-   The binomial procedure seems to lack theoretical justification.

## Opportunities for Improvement and Harmonization

-   EU procedure:

    -   better handling of LODs (perhaps in a similar way than NAFTA);

    -   assume lognormality instead of normality in method 1 (again,
        like NAFTA);

    -   remove the MRL classes and substitute them by a NAFTA-style
        rounding;

    -   most importantly, provide guidance about how the results from
        method 1 and 2 should be integrated.

-   NAFTA procedure:

    -   reduce complexity by using fewer statistical methods (the use of
        a distributional one and a non-distributional one as done in the
        EU seems sufficient);

    -   reduce reliance on the lognormality assumption;

    -   most importantly, move away from visual estimation which will
        always be subjective and requires considerable statistical
        experience.

## Open Issues

1.  **Very small datasets.**

> Under some circumstances, submissions may be accepted which contain
> results from only 4, and sometimes only 2, field trials. A specific
> policy should be developed for these very small datasets which would
> probably depend more on the knowledge of the residue experts than the
> use of statistical procedures.

2.  **Dealing with LODs/LOQs.**

> As mentioned above, the EU guidelines require the substitution of
> non-detected residues by LODs/LOQs values which is not recommendable
> from a statistical point of view. The NAFTA procedure is more
> enlightened and allows for the non-detects to be "filled in" by the
> values extracted from a lognormal distribution. This is a more
> realistic option but it has the obvious drawback of forcing these
> non-detected values to conform to a particular distribution.
>
> As can be seen in \[4\], it may not be necessary to give actual
> numerical values to these non-detects. There are reliable statistical
> methods that can use the information available in the values above the
> LOQ level plus the **proportion of non-detects** in the dataset to
> draw statistical inferences. Would it be possible to develop a MRL
> calculation procedure that would not require the imputation of
> numerical values for the non-detects?

## References

1.  Guidelines for the generation of data concerning residues as
    provided in Annex II, part A, section 6 and Annex III, part A,
    section 8 of Directive 91/414/EEC concerning the placing of plant
    protection products on the market. Commission of the European
    Communities.

-   Appendix D. *Comparability, extrapolation, group tolerances and data
    requirements.* Directorate General for Health and Consumer
    Protection (SANCO E.1). Doc. 7525/VI/95, revision 7, 12^th^ June
    2001.

-   Appendix I. *Calculation of Maximum Residue Levels and Safety
    Intervals e.g. Pre-harvest Intervals.* Directorate General for
    Agriculture (VI B II-1). Doc. 7039/VI/95 EN, 22^nd^ July 1997.

2.  *Guidance for setting pesticide maximum residue limits based on
    field trial data.* US EPA Office of Pesticide Programs and Health
    Canada PMRA, 28^th^ September 2005.

http://www.pmra-arla.gc.ca/english/pdf/pro/pro2005-04-e.pdf

3.  *Does calculation of the 95th percentile of microbiological results
    offer any advantage over percentage exceedence in determining
    compliance with bathing water quality standards?* P. R. Hunter.
    Letters in applied Microbiology 2002, vol. 34, 283-286.

4.  *Statistical Methods in Water Resources (chapter 13)*. D. R. Helsel
    and R. M. Hirsch. United States Geological Survey.
    <http://water.usgs.gov/pubs/twri/twri4a3/>

5.  *Statistical Basis of the NAFTA Method for Calculating Pesticide
    Maximum Residue Limits from Field Trial Data.* US EPA Office of
    Pesticide Programs and Health Canada PMRA.

6.  *Statistical Calculation of MRLs.* Denis Hamilton. 11^th^ IUPAC
    International Congress of Pesticide Chemistry, 6-11^th^ August 2006,
    Kobe, Japan. Abstract III-4-09B.

7.  *Pesticide Residues in Food 2006.* Joint FAO/WHO Meeting on
    Pesticide Residues, 3-12^th^ October 2006. FAO Plant Production and
    Protection Paper 187.

8.  *Environmental statistics and data analysis*. Wayne R. Ott. CRC
    Press, 1995.

9.  *An approximate Analysis of Variance Test for Normality*. S. S.
    Shapiro and R. S. Francia. Journal of the American Statistical
    Society 1972, vol. 67, no. 337, 215-216.

10. *The Probability Plot Correlation Coefficient Test for Normality*.
    James J. Filliben. Technometrics 1975, vol. 17, no. 1, 111-117.

11. *Normal Probability Plots and Test for Normality*. Thomas A. Ryan,
    Jr. and Brian L. Joiner. Statistics Department, The Pennsylvania
    State University, 1976.
    <http://www.minitab.com/resources/articles/normprob.aspx>

**Appendix**

NAFTA procedure flowchart.

![](media/image4.png){width="6.689583333333333in"
height="8.919444444444444in"}

## 

[^1]: Syngenta, Human Safety, Jealott's Hill International Research
    Centre, Bracknell, Berkshire RG42 6EY, United Kingdom. E-mail:
    domingo.salazar@syngenta.com

[^2]: This expectation is actually in accordance to "the theory of
    successive random dilutions", proposed by Wayne R. Ott, formerly at
    the US Environmental Protection Agency (EPA). This theory models the
    movement of pollutants in the environment as a mixing process and
    concludes that their concentration should follow a lognormal
    distribution \[8\]. Although some of the processes involved in the
    decline of the pesticide residues may be well modelled indeed as a
    "random dilution event", others like pesticide deposition and
    pesticide transport inside the plant may not be. Perhaps, how close
    the final residue distribution is to be lognormal is then a function
    of whether the dominant process in the decline of the residues of a
    particular pesticide is a random dilution or not.

[^3]: It seems to be some version of a probability plot correlation
    coefficient test (see \[9-11\]).