Efficacy
and Equivalence of Phytosanitary Measures
A discussion and reference paper prepared
for the
IPPC Expert Working Group on the Efficacy
of Phytosanitary Measures
Imperial College, UK 2-4
July 2002
Ricardo
Sgrillo
Cocoa Research Center (CEPLAC/CEPEC)
Rod. Ilehus-Itabuna, km 22
45650-000 Ilheus, BA, Brazil
ricardo.sgrillo@terra.com.br
This paper represents the views of
the author and not necessarily those of his country and/or organization.
1.
Introduction
The World Trade Organization
Agreement on the Application of Sanitary and Phytosanitary Measures (the
SPS Agreement) emphasizes the importance of a sound technical basis for
measures affecting trade. In spite of the recognition of this concept in
the SPS Agreement, very little has been done regarding the development
and application of analytical methods to establish quantitative parameters
for phytosanitary measures based on fundamental mathematical concepts and
statistical analyses.
The increasing development
and application of international standards associated with the SPS Agreement
and increasing pressure by trading partners for greater transparency and
recognition of equivalence has led to a shift in the paradigm of past approaches.
This has resulted in greater interest and need for appropriate quantitative
methods to measure, assess, and justify risk management decisions.
The main quantitative
application widely used by the phytosanitary community in the past
is the probit 9 approach, as it was proposed more than 60 years ago as
the basis for measuring the efficacy of treatments for fruit flies (–Baker,
1939).The general rationale behind
the probit 9 approach is very simple and straightforward: if you
kill a very high percentage (99.9968 %) of the pest population then
you will decrease the chance of pest establishment to zero (or very close
to zero). This rationale assumes a worst case scenario and results
in a high-kill treatment requirement that may not be technically justified
based on pest prevalence.
The probit 9 approach
has been criticized, in particular because: "While probit 9 was clearly
designed to reduce the prevalence of pests by a predictable amount, it
does not account for other variables contributing to pest risk. Natural
survival rates, the likelihood of infestation, and the colonization potential
of the pest are a few of the more important risk based considerations that
are ignored by a direct estimation of mortality such as probit 9. Process
parameters such as pre-shipment cultural practice, packing and shipping
procedures, and distribution times or areas, are not considered when mortality
is the sole criterion for determining quarantine security (Liquido
et al. 1997)
In
recent years, the evolution of phytosanitary approaches to measuring the
efficacy of measures has led to the recognition of another rationale: if
you decrease the number of fertile pest individuals in a commodity to a
pre-established number assessed through risk analysis, then you will decrease
the risk of establishment of this pest to an acceptable level. A considerable
effort and significant progress has been made through the application of
this rationale to understanding options for achieving a desired level of
quarantine security. This has opened the door for expanding the understanding
and use of many importantconcepts
for risk management, including:
Pest
Free Areas (places and sites of production)
- a risk management option based upon a sound pest risk assessment coupled
with satisfactory evidence of effective, on-going surveillance and exclusion
measures to maintain such areas pest free. (Liquido et al. 1997)
Systems
Approaches - consecutive
phytosanitary measures are used to decrease the number of fertile pest
individuals in a commodity.
Alternative
Treatment Efficacy - where the percentage
of the population of the pest that has to be killed is variable, depending
mainly on the initial infestation level and on the characteristics of the
pest and of the commodity.
Maximum Pest Limits
(especially for fruit flies) has developed as "the maximum number of immature
fruit flies that may be present in consignments imported during a specific
time to a specific location" (see Bartlett et al. 1996 and Liquido et al.
1995 for a deeper discussion on these concepts).
These initiatives
demonstrate a trend toward exploring and applying more systematic approaches
to evaluating (and justifying) the efficacy of phytosanitary measures.
Yet a common understanding of the range of possible quantitative methodologies
and the development and routine use of appropriate methodologies to evaluate
and compare the efficacy of phytosanitary measures is far from being well-
developed in the phytosanitary community.
While considerable
progress has been made and guidance developed to measure the risk associated
with a specific pest through Pest Risk Analysis, very little has been done
on evaluating the efficacy of phytosanitary measures. The scientific literature
includes several papers on the evaluation of efficacy for pest-commodity
specific measures, but there is very little available on general concepts
associated with this subject. This continues to be a fundamental problem
for the phytosanitary community where there is an important and growing
need to fully apply the principles of technical justification and equivalence
under the SPS Agreement.
2.
Probit - a brief review
The only quantitative
evaluation of the efficacy of phytosanitary measures that is widely used
today is the quantification of the efficacy of treatments (chemical, heat,
etc), mostly for fruit flies.
There are many methods
to describe the response of a population to increasing doses of a treatment,
including the Log-linear, Logit, and probit models. When the criterion
for the population response is mortality, the Lethal Dose (LD), Lethal
Concentration (LC), general mortality factor (Q), among others, have also
been proposed. In plant quarantine, the expression most used to describe
the efficacy of treatments is the probit.
The response of a
population to a dose reflects the genetic variability of the natural populations.
Usually few individuals will die with lower doses; most of the individuals
will die with average doses; and few individuals will only die with higher
doses. It is accepted (although not always true) that the statistical distribution
of the individuals responding to increasing doses fits a normal or Gaussian
distribution (bell shaped curve). The variability of the population (spread
of the data points) is measured by its standard deviation(s). The graph
in Figure 1 represents the cumulative and distributed response of a population
exposed to increasing doses of a chemical product. The data were normalized,
that is the zero value in the X axis represents the mean dose and the s
is 1. The X scale is presented in multiples of the s (or normal
equivalent deviates). The Y axis presents the proportion of individual
that dies in each dose. The graph presents also a probit scale; that is,
the same s scale, where 5 was added to avoid zero and negative values.
Figure 1
Cumulative (dashed) and distributed (continuous) dose-response curves
Probit only represents
a proportion of a population, normally distributed, that responds to a
dose. To have information on the number of individuals affected by the
dose, the proportion has to be multiplied by the total number of individual
in the population.
2.1
Probit 9
Probit 9 value is
usually required for quarantine treatments for fruit flies and corresponds
to a mortality of 0.999968 of the population. That is: for populations
with less then 31,250 (1/{1-0.999968}) individuals there would be less
than one survivor. The number of survivals is proportional to the population
size. 10 survivors would be expected for a population of 312,500 individuals.
The reasons for selecting these criteria for quarantine treatment were
never given (Landolt et al. 1984) and may be relatively arbitrary to the
extent that the objective was mainly to achieve an extremely strict requirement.
However, for products
where the pest prevalence is lower, the requirement of a probit 9 treatment
may not be technically justified. For instance, a consignment of 50,000
units with a prevalence of 1% would require a probit 8 (0.998 mortality)
for less then one survivor. If the pest presents a probability of 0.4 to
survive transport conditions, of 0.2 to be transferred to a suitable host,
of 0.5 to find favorable environmental conditions, and of 0.3 to reproduce
in the host, then a treatment with a probit 6 (0.834 mortality) would be
enough to avoid establishment. The requirement of unnecessary higher probit
treatments could involve higher costs, higher residues, lower product shelf-live,
and a unjustified barrier to trade (see Follett and McQuates 2001 for an
interesting discussion on these points).
3.
A holistic approach
From the field in
one country to establishment in another country there is a chain of events
that reduces the pest prevalence in one consignment of a plant or plant
product as illustrated in simplified form below.
Figure 2
Population losses in the production/commercialization chain
For phytosanitary
purposes it is convenient to have a holistic approach to this system. For
example, a post-harvest treatment with a known mortality rate has no meaning
if we don't know the initial prevalence[1]
in the treated consignment, because we don’t know how many individuals
will survive. Also, the design of an inspection system could be optimized
only if we know the probabilities associated with pest entry and establishment.
It is not logical to design a very sensitive, expensive inspection system
to detect a very low prevalence if the pest has a poor chance to become
established.
The
establishment of a pest has essentially two components:
·the
prevalence of a pest in the consignment that enters the country, and
·the
probabilities of establishment of the pest.
The
entry of a pest does not mean introduction (establishment). Many factors,
as described in ISPM No. 11 (Pest Risk Analysis for quarantine pests) could
interact to allow, or not, the establishment, as in the following examples:
-
probability of pest surviving existing
pest management procedures;
·probability
of transfer to a suitable host;
-
probability
of the environment be suitable in the PRA area, etc.
It is also interesting
to note the observations of Liebhold et al. (1995): “Founder populations
are typically small and consequently are at great risk of extinction. Generally,
the smaller the founder population, the less likely is establishment. Though
many scientists have referred to a “minimum viable population,” there is
rarely a distinct threshold. Instead it is more realistic to consider the
probability of establishment as being a continuous function of the initial
population size. This function reflects many characteristics of the species,
such as its intrinsic rate of reproduction, mate location abilities, and
genetic diversity”. This is in agreement with the statement of Dr.
Alexei Sharov (Virginia Polytechnic Institute and State University-personal
communication): In many cases, the dispersal pattern and the probability
of finding a mate are critical for pest establishment. Insects that mate
before dispersal have a higher probability of establishment. In the destination
area, the initial population numbers are extremely low. So if insects disperse
first, then they will probably never find a mate. This is true even for
insects with very sensitive pheromone communication mechanisms (e.g. gypsy
moth).
Equation
1 estimates the probable number of establishments:
Establishments
= Prevalence * Probability
1
From Equation 1 we
can estimate the necessary prevalence to allow for one (1) establishment,
in function of the probabilities. If the values of the three probabilities
listed above are 0.5, 0.2 and 0.7, then it is necessary for 14 individuals
to enter (1/(0.5*0.2*0.7)) in order to have one establishment. This is
because 14*0.5*0.2*0.7 = 1. However, if the importation occurs, for example,
in the winter, then the third probability could be 0.1 and then it would
be necessary for 100 individuals to enter for one establishment (100*0.5*0.2*0.1
= 1).
We conclude that,
to reduce the number of probable establishments we can either decrease
the prevalence or decrease the probabilities of establishments.
The phytosanitary measures can be applied at any point in the chain shown
in Figure 2, usually before the entry of the consignment. Other measures
could also by applied to detect infected consignments.
4.
Phytosanitary Measures (PMs)
Now
we can group the PMs, according to their strategy:
Group
1 Reduction of the population of the pest
in the consignment (prevalence)
The
strategy of this group is to reduce the population of the pest in the consignment
and consequently, to reduce the possibility of establishment. This can
be achieved by treatments or other procedures.
·Pre
Harvest (treatment in the field, pest free area, place or site of production,
testing, etc)
·Harvest
(removal of infested products, inspection for selection, stage of ripeness/maturity,
etc)
·Post
Harvest (handling, chemical/physical treatment, etc)
·Shipping
and distribution (volume[2],
transport environment, in transit or on arrival treatment, limits on distribution,
etc.)
·Pest
Free Areas (sites and places of production)
Group 2
Reduction of the probabilities of establishment
The
strategy of the second group of PMs is to reduce the probabilities
of establishment and so reduce the possibility of establishment. This group
includes measures using import management:
·Frequency
of importation
·Season
timing
·Port
of entry
·Restriction
on the end use
Group
3 Detection of infested consignments
The strategy of the
measures of the third group is to detect the consignments that present
infestation (prevalence) above an established threshold. After the detection,
the destruction, re-export or another PM of the other groups (treatment,
restriction of the end use) can be applied. The following measures fall
into this group:
·Inspection
·Testing
5.
The meaning of efficacy
2
Where
NEfficacy
is the necessary efficacy of the PM (proportion of reduction of the prevalence
before the PM) and prevalence is the prevalence (number of individuals)
before the application of the PM and probability is the probability
of establishment.
For
example, if we have a consignment of 50.000 units, with an infestation
rate of 5%, and the pest has .02 probability of establishment, then the
efficacy of a PM has to be greater than:
For
the Group 3 PMs, it is necessary to consider the efficacy of the sampling
and inspection system. The sampling model for inspection should be based
in the hypergeometric distribution (see draft ISPM on Inspection Methodology).
Transforming the Schilling (1968)[3]
approximation to estimate the number of samples required to detect a known
infection rate, we can get the proportion of a consignment that has to
be sampled to detect a specific prevalence:
3
Where Np is
the number of unities to be sampled, size is the size of the consignment,
CL is the confidence level (0.95, 0.99, etc) and prevalence
is the minimum number of individual to be detected.
Using
the same numbers of the example above the minimum number of individuals
to be detected is 50 (50.000 x 0.05 x 0.02). If we use a 0.95 confidence
level then the number of units to be sampled is:
The graph in Figure
4 presents the relation between the prevalence to be detected and the necessary
percentage of samples.
Figure 4
Percentage of sampling as function of the prevalence to be detected
For Group 3 PMs,
the efficacy may be thought of as the proportion of consignments with
prevalence above the fixed threshold that shall be detected. This corresponds
to the confidence level of the hypergeometric sampling method, as presented
in equation 3.
Summarizing we have:
·For
PMs that reduces the population in the consignment (Group 1) the efficacy
could be measured by proportion of reduction in the prevalence (or percent
mortality, probit, etc)
·For
PMs that reduce the probability of establishments (Group 2) the proportion
of reduction could measure the efficacy.
·For
PMs that detect infested consignments (Group 3) the efficacy could be the
proportion of consignments that will be detected.
6.
Appropriate Level of Protection (ALP)
The concept of ALP
introduced in Figure 3 above can also be represented by the following graph:
Figure 5
Iso-lines for one establishment, considering the concept of Appropriate
Level of Protection
According to the
nature of the pest and/or the strategic importance of the crop, or other
legitimate reason, a country may increase or decrease the level of protection
desired. Many different parallel lines can be drawn as iso-lines to represent
different levels of protection, as shown in figure 5 by the dashed lines.
These lines actually represent different confidence levels and can be adjusted
to meet the ALP requirements. The use of such presentations add transparency
to the phytosanitary requirements and facilitates the choice of a PM based
on efficacy.
7.
Measurement of efficacy
7.1
General considerations
Prevalence
It is usually difficult
to estimate the population size in absolute terms. In some cases, it would
be possible to estimate the infection rate in the field and to multiply
it by the estimated survival rate. The estimation of the rates should have
sound statistical bases to provide reliable numbers for the mean values
and variability. The most known and used statistical methods for estimations
of this kind are based on the assumption that the population is normally
distributed. However this is often not the true. In general, pests have
a clustered spatial distribution and, in these cases, the appropriate statistical
approach should be identified and applied. This is not a difficult procedure
in statistical sciences.
Chemical, heat,
radiation etc, treatments; transport environment (cold, etc.)
The statistical methods
for evaluation of the mortality rate of physical and chemical treatments
are well known. For quarantine purposes, the probit analysis is the de
facto standard. However the appropriateness of this technique for commodity
treatment bioassay data has been strongly questioned. The number of pest
individuals to be tested is proportional to the expected mortality rate.
A probit 9 treatment will require a much larger population size (~100.000
individuals) than a probit 8. See Liquido et al. (1997) for a very interesting
discussion on this matter, and Bartlett (1996) - pages 29-42, for the methodology
and mathematical example.
Probability of
establishment
The measurement
of the efficacy in reducing the probability of establishment, as discussed
in point 4.2, should be examined with special care because this has not
been well explored.
Some techniques used
in the study of population ecology could be used to illustrate the possible
effect of this kind of PM. As an example, Figure 6[4]
below shows a monthly graph of the humidity versus temperatures in two
locations in Brazil. The dashed square represents the zone of optimum development
for Ceratitis capitata[5](16-32oC
and 65-75% RH) as found elsewhere in the literature.
Figure 6
Climogram (Temperature x Relative Humidity) for Fortaleza (red) and Curitiba
(blue), Brazil and zone of optimum development for Ceratitis capitata
(dashed square).
The graphic shows
that in Curitiba the environmental conditions are sub-optimum all year
around, while in Fortaleza there are favorable conditions from September
to February.
The country could
permit the importation entering in Fortaleza only from March to August,
or only accept Curitiba as the entry port. These measures reduce the probability
of establishment.
The graph above does
not allow for any inference on the efficacy of the measure but the use
of spatial models could be a tool to evaluate the reduction of the probabilities
as function of environmental conditions (see the electronic paper of Alexei
Sharov[6]).
Also, Dr. Sharov stated (personal communication): Modeling the probability
of population establishment is definitely a difficult task but to my mind
not impossible. Estimating model parameters in other countries seems a
reasonable strategy. Of course parameter values may be biased, but biased
information is better than no information at all. There are various software
that compare climate conditions in various parts of the world. Specialized
natural enemies may be present in the country of origin but absent in the
destination country.
Another PM that could
be used to reduce the probability of establishment is restriction on the
end use. If we consider, for example, a virus in potatoes that will be
planted, then the probability that the pest gets to suitable environmental
conditions (soil) could be nearly 1 (100%). However if this commodity is
used for consumption then the probability will certainly be much lower.
The proportion of reduction in the probability could be used as a measure
of efficacy, considering of course all the necessary statistics.
Detection
The efficacy of a
detection system has two components: the efficacy of the sampling system
(how well the samples represent the consignment) and the efficacy of the
detection method (visual identification, testing, post-entry quarantine,
etc.). As discussed before, the confidence level of the sampling method
is important for measuring the efficacy of the sampling system.
The efficacy of the
detection method could be estimated by the relation between the number
of samples and the number of infested samples in one consignment. Efficacy
is necessarily pest-specific because visual identification depends on the
pest characteristics (size, symptoms, etc.). It is also important to consider
that the efficacy will depend on the ability of the inspectors and therefore
special care should be placed on the variability of the estimations. For
laboratory testing, the efficacy of the diagnostic method, considering
false-positive/negative response, etc., could be used.
7.2
Comparing the efficacy of different phytosanitary measures
a. Compare two
different PM with the same endpoint
To compare different
PMs with the same endpoint should not be complicated. To compare, for example,
the efficacy of a fumigation treatment with the efficacy of a heat treatment
it should be considered that, in both cases, the response (mortality) is
a result of a dose. In fumigation, the dose is characterized by the concentration
of the chemical and the period of exposure. As the pest would change its
metabolic rate with the environmental temperature, the response to the
same dose will change with the environmental temperature, and different
tests should be made in different temperatures to consider this additional
cause of variation. In heat treatment, the dose is characterized by the
temperature and also by the period of exposure. The additional cause of
variation, in this case, would be the size of the fruit, as larger fruits
will take more time to transfer the treatment temperature to its interior
and therefore different tests should be made with fruits of different sizes.
As the concepts are the same, the efficacies may be directly compared by
any suitable statistical technique for the comparison of means of different
treatments. Note that most statistical tests will require that the data
be drawn from the same population.
b. Compare one
PM with two or more PMs (systems approach) with the same endpoint
This case is similar
to the previous one. If the efficacy of the systems approach is measured
after the application of the last PM of the system, then the data will
reflect also the efficacy and variability of each of the PMs applied previously
and the statistical comparison between the mean efficacies is equal to
the previous case. However if the available data corresponds to the efficacy
of each of the PMs that compose the systems approach, then the statistical
requirements are slightly more complicated and have to take into account
the propagation of errors, as discussed in section 8.2 below.
c. Compare two
different PMs with different endpoints
It is useful to consider
that there are only three PM endpoints: Group 1 - to reduce the prevalence
in the commodity (see footnote on page 5); Group 2 - to reduce the probability
of establishment; and Group 3 - to increase the detection capability, as
discussed in points 4 and 5 above. For example, to compare the efficacy
of a fumigation treatment that kills 97% of the population with a treatment
that uses irradiation to sterilize 98% of the population, it is necessary
to consider that, conceptually and for quarantine purposes, a sterilized
pest individual is equivalent to a dead one and so the efficacies could
be directly compared.
An additional consideration
that could be raised at this point is that the right question seems to
be where or when the efficacy should be measured. If it is decided to measure
the efficacy of different PMs of group 1 (see points 4 and 5) just before
the commodity is delivered to the importing country (see Figure 2), with
all the required statistical care, then it would be possible to have a
reliable direct comparison between these efficacies.
Considering PMs that
have very different endpoints, as the PMs of Groups 1, 2 and 3, it is not
very likely that any of the measures of Groups 2 or 3 could substitute
any of the PMs of Group 1. However, possibilities may exist which are worth
exploring. Further discussion on this topic needs to be considered.
8. Error Analysis
(see the papers of Trinh,1996
and Muscat, 2001 for a deeper discussion on this subject.)
8.1
Standard Error and Confidence Level
When we need a quantitative
estimation of, for example, pest prevalence in a consignment, we would
sample the specific consignment with an appropriate sampling design. However,
the result (the mean prevalence) is a description of the sample
and does not necessarily represent the true population (consignment) mean.
The variance is a measure of the dispersion of the data, or how
the data spreads around the mean. The mean and the variance
give us the "best" values and describe how the data is dispersed around
the best value, respectively. To answer the question of how confident we
can be that the sample mean is truly the best value, we need another statistic
- the confidence level, as expressed in Equation 4 below. This is
a common statistical application used to measure the confidence in the
sample mean.
4
Where x
is
the sample mean, s2 is the sample variance, n
is the number of units sampled and t is the student's "t"
statistic. The values of x, s and n are estimated
from the sample numbers and the value of t is taken from tables
as function of n-1 and of the confidence limit (cl) (95 %,
99%, etc.). The square root of the variance divided by n
is called standard error. A confidence interval is a range defined
between a lower and an upper bound, which quantifies the percentage of
time that this range contains the parameter of interest.
For example, if the
mean prevalence (estimated from sampling 42 units) is 86.9 infested
units, the variance is 95.06, the value of t
(cl = 95%, n-1=41)
is 2.02 then the confident level is 3.0 infected units. This is
en expression of the confidence interval in absolute terms. This
number means that we can be 95% sure that the true population mean
is between 83.9 (86.9-3.0) and 89.9 (86.9+3.0). These intervals can be
also expressed in relative terms (percent of the mean). In these
case it would be expressed as 86.9 ±
3.5%
If we need greater
confidence then we could choose the t value for 99% cl. In
this case we are 99% confident that the true population mean would be between
82.8 and 91.0 (86.9±.
4.6%). In other words, if we sample the consignment 100 times we would
expect that in 99 cases the sample mean would be between the values 82.8
and 91.0. However it should be noted that Equation 4 is only valid for
normally distributed data. There are other methodologies to calculate confidence
levels for other distributions.
Other methods to
estimate the confidence levels of the efficacy of phytosanitary treatments
is described by Baker et al. (1990), Couey and Chew (1986), Vail et al.
(1993), and others.
8.2
Error propagation
The discussion on
this point is based on the papers of Trinh (1996) and Muscat (2001).
If we need to estimate
the confidence level for a variable calculated from the mathematical operation
of other variables estimated from sampling, then we need to know how the
error associated with each sampled variable propagate to the calculated
variable.
The simplest approach
is to calculate the square root of the sum of the squared individual errors.
If the operation is an addition or subtraction then the absolute
errors
are used. In multiplication and division the relative
errors are
used.
Suppose
that, in a systems approach, we need to estimate the probability (and the
confidence level) for one infested unit in a consignment, after consideration
of the mortalities due to a field treatment, due to post harvest handling
and due to the transport conditions. Also suppose that we have the following
information about the mean value of the proportion of the mortality (and/or
reduction in pest prevalence) and the respective 95% confidence levels:
M1
(reduction due to field treatment) =
0.9 ±.
0.05(relative: ±.
5.56%)
M2
(reduction due to post harvest handling)=
0.7 ±.
0.07(relative: ±.
10%)
M3
(reduction due to transport conditions) =
0.5 ±.
0.20(relative: ±.
40%)
The
respective survivals S (S=1-M) are:
S1
= 0.1 ±.
0.05
S2
= 0.3 ±.
0.07
S3
= 0.5 ±.
0.20
The
final survival (probability to have one infested unit) is:
S = 0.015 ±
41.6% or
S = 0.015 ±.
0.00624
As discussed before,
these number don't mean much if we don't know the prevalence in the consignment.
So, after measuring the size of the consignment and the initial infestation
rate, we could go further to add phytosanitary meaning to the mortality/survival
rates:
C (size of consignment)
= 5000 units ±.
50 units (±.1%)
I (infection rate
(10%)) = 0.1 ±.
0.002 (±.
20%)
N (number of infected
units) = C x I x S (note that N is the same prevalence in equation 1)
The number of units
expected to be infected, after the effect of M1, M2 and M3 in C will be:
N = 7.5 ±.
44.8%
N = 7.5 ±.3.36
units
If the confidence
levels were estimated within the 95% limit then we would be 95% sure the
consignment will have between 4 and 11 infested units.
9.
Equivalence of Phytosanitary Measures
The
concepts presented below were completely borrowed from Determination
of Efficacy Product Evaluation American
Dental Association Council on Scientific Affairs 1999[7].
These could be useful to begin a discussion on the equivalence of PMs.
In
comparing two different PMs, it could be demonstrated that one is equivalentor
at least as good as the other.
9.1
Demonstration of equivalency
The
equivalence of a given PM to another implies that the efficacy provided
by those PMs are so close as to suggest that the two PMs could be used
interchangeably without any meaningful effect on the outcome.
In
demonstrating equivalence, a quantitative definition of what is meant by
closeness of efficacies must be provided. This is done by specifying
two percentages, L% and U%, where L% (for “lower”) is less than 100% and
U% (for “upper”) is greater than 100% (together, these two percentages
are sometimes referred to as defining the “range of equivalence”). The
PM2 is considered equivalent to the PM1 if its observed
mean outcome response lies within the range from L% to U% of the true mean
outcome response for the PM1.
For
example, if L% is set equal to 90% and U% is set equal to 110%, then a
PM2 will be deemed equivalent to a PM1 if the observed
mean outcome response for the PM2 is greater than 90% of the
response for the PM1 and less than 110% of the response for
the PM1.
The
results of the study must support the inference that the observed
mean
score associated with the PM2 lies between 90% and 110% of the
observed mean score associated with the PM1. Among the
available statistic methods the Fieller Confidence Interval Approach and
the “Two One-sided Tests” approach could be used.
9.2
Demonstration of at least as good as
To
say that a given PM (PM2) is at least as good as a another
(PM1), the benefit provided by PM2 must be adequately
large enough so that the switch from PM1 to the PM2
will
not result in a meaningful loss of efficacy and, in fact, may enjoy a greater
efficacy than provided by PM1.
At
least as good as might better be understood
by considering its relationship to the property of equivalence.
For equivalence of a PM2 and PM1, the mean outcome
score for the PM2 is not too much higher nor too much lower
than that of the PM1, that is, the observed mean responses are
close. The property of at least as good as requires that
the mean of the PM2 not be too much higher than that of PM1.
It does not require that the mean of the PM2 be not too
much lower than the mean for the PM1. Thus, this property requires
that the observed mean score for the PM2 does not vary too much
from that for PM1 on the ineffective side.
In
demonstrating that a given PM2 is at least as good as a given PM1,
a quantitative definition of what is meant by large enough benefits
must be provided. This is done by specifying a single percentage, which
is designated as U% (note that U% is greater than 100%). The PM2
is considered to be at least as good as the PM1 if the
PM2 observed mean outcome response is no greater than U% of
the observed mean outcome response for PM1.
For
example, if U% is set as 110%, then a PM2 will be deemed as
at least as good as a PM1 if the observed mean outcome
response for the PM2 is no greater than 110% of the response
for the PM1.
The
results of the study must support the inference that the observed mean
score associated with the PM2 lies at or below 110% of the observed
mean score associated with the PM1.
This
criterion can be addressed in various ways. For example, the Fieller approach
to equivalence described above can be invoked, with the criterion satisfied
when the entire 90% Fieller Confidence Interval consists of values no greater
than 110%. Alternatively, a single, one-sided test can be performed to
determine if the observed mean score associated with the PM2
is less than 110% of the observed mean score associated with PM1.
10.
Putting it all together
Conceptually the
steps for deciding a phytosanitary requirement are very clear as shown
in Figure 7, and presented below.
Considerations of
the importing country:
1.Choice
of an Appropriate Level of Protection
2.Determination
of the final probability of establishment by risk assessment
3.Estimation
of the maximum pest limit (prevalence) in the consignment (see figure 3
and 5). This estimation should consider the application of measures to
reduce the probability of establishment, according to point 4.2.
The steps above correspond
to processes that occur after a consignment arrives in the importing country
(right side of Figure 2). Other steps are relative to the left side of
figure 2, and are of concern for the exporting country:
4.Estimation
of the initial pest prevalence in the product
5.Estimation
of the efficacy of the locally available phytosanitary measures
6.Estimation
the pest prevalence in the delivered consignment
The final step is
to compare the prevalence estimated in the steps 3 and 6, considering the
volume to be traded.
If the prevalence
estimated in point 6 is greater then the one estimated in point 3 then
the importing country could review its data or even its ALP level. On the
other side, the exporting country could increase the efficacy of any of
the available PM already in the system to add a new PM or to try to decrease
the initial prevalence.
Figure 7 Conceptual
flowchart of the establishment of a phytosanitary requirement
Many thanks to Robert Griffin (USDA) for the final
revision.
11.
References
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[1]prevalence in
this paper means number of individuals (or infected units) capable
of reproduction and spread, and not rate of infection.
