FDA MANUAL OF INTERPRETATIONS
Interpretation Number: 07-IV-@.02-101
Guide Contents
National Shellfish Sanitation Program
U.S. Food and Drug Administration
Shellfish Safety Team
Division of Cooperative Programs
Office of Compliance
Date: November 27, 2001
Final: May 17, 2002
Revised: August 13, 2004
Reissued: September 1, 2004
Model Ordinance Reference: Chapter IV
@.02 D, E, F and G
Key Words: Weighted 90th
Percentile, Adverse Pollution Condition, Systematic Random Sampling, Estimated
90th
Percentile
Question: What is the procedure for
determining the value of the 90th percentile to be used in the analysis
of sample data
derived in the transition to a different MPN procedure?
Interpretation: A weighted 90th
percentile value is calculated for each set of samples derived in the transition
to a
different MPN procedure.
Rationale: A number of states have
availed themselves of the advantages afforded by the action of
the 8th National
Shellfish Sanitation Workshop in allowing the use of a virtual limitless
combination of tubes and
dilutions in MPN procedures used in support of the National
Shellfish Sanitation Program
(NSSP). A change in the combination of tubes and/or
dilutions from those
traditionally used in the NSSP alters the precision or variability of
the test and thus its
associated 90th percentile. When a change in MPN procedures is
instituted, new data with a
different 90th percentile must be phased into the existing
sample database. During
this phase-in period a "hybrid" 90th percentile value must
be calculated and used as the
variability component of the bacteriological standard against
which the variability of
sample data is to be compared. This "hybrid" 90th percentile
value is calculated by
weighting the relative contributions of each MPN method to the
sample database. The
resulting value is known as the weighted 90th percentile.
Weighted 90th
percentile values can be used equally effectively with either Adverse
Pollution Condition (APC) or
Systematic Random Sampling (SRS) regimes.
Calculations: The value of the weighted
90th percentile from a data set derived in the transition to
a different MPN
procedure is calculated in the following manner:
- Convert
the 90th percentile values for both MPN procedures to their respective
base 10
logarithmic values.
- Multiply
the logarithmic values for each MPN procedure by the number of samples in
the database examined by that
procedure.
- Add
these logarithmic values, then divide by the total number of samples examined.
- Take
the antilog of this value.
- Round
off conventionally to the nearest whole number.
- This value is the weighted 90th percentile against which
sample data is compared.
- Recalculate
the weighted 90th percentile when new data is added to the database.
- Once
all accumulated data is from the same MPN procedure and the transition in
methodologies is complete, the corresponding 90th percentile value
for this MPN procedure is then used for comparing sample data.
Example 1
Data was gathered for a sampling station under
the APC sampling regime. The growing area
which encompasses this sampling station is in
the approved classification. The first ten samples in
the database were examined by the traditional
5-tube, decimal dilution MPN test for fecal
coliforms. The remaining five samples
required under APC sampling were analyzed by the 12-tube, single dilution MPN test for fecal
coliforms. The 90th percentile value for the 5-tube, decimal
dilution MPN test for fecal coliforms is
43. The 90th percentile value for the 12-tube, single
dilution MPN test is 28. The weighted 90th
percentile value which results from this data will lie
somewhere between the 90th percentile
values of the MPN procedures used. Its proximity to either
method's 90th percentile value will
depend on the relative number of samples analyzed from each
method. Since most of the samples in this
example were derived from the 5-tube MPN test, the 90th
percentile value calculated will be weighted
toward 43.
To calculate the weighted 90th
percentile for this data set:
- The
90th percentile values of 43 for the 5-tube, decimal dilution MPN
test and 28 for the 12-tube, single dilution MPN test are
converted to base 10 logarithms. This gives base 10 log
values of 1.633 and 1.447 respectively.
- The
base 10 log values are then multiplied by the number of samples in the database
examined by each MPN procedure used. Ten
of 15 samples were analyzed by the 5-tube,
decimal dilution MPN test. The remaining
5 of 15 were examined by the 12-tube, single
dilution test. This gives 1.633 for the
5-tube test x 10 samples = 16.330 and 1.447 for the 12-tube, single dilution test x 5 samples =
7.235.
- These
values are added together and the resultant divided by the total number of
samples in
the database being used. Thus, 16.330 +
7.235 = 23.565, 23.565/15 =1.571.
- The
antilog of this value is taken. In this example, the antilog of 1.571 is
37.239.
- The
antilog value is rounded off to the nearest whole number which in this example
is 37.
- The weighted 90th percentile for this data set is 37.
Thirty-seven (37) is the 90th percentile value which cannot be
exceeded more than 10% of the time by the sample station data in this data
set under the APC sampling regime for this station to remain in the approved
classification status. When new data is added to the database of this sampling
station, the value of the weighted 90th percentile would have
to be recalculated until the transition in methodologies is completed and
all the
data from this sampling station is derived from the same MPN procedure.
At this time, the corresponding 90th percentile value of 28 for
the 12-tube, single dilution MPN procedure in use will be employed in comparisons
with sample data.
Example 2
Data was derived from a sampling station under
the SRS sampling regime. The growing area
which encompasses this sampling station is also
in the approved classification for fecal coliforms.
The first 18 of 30 samples were analyzed using
the 5-tube, decimal dilution MPN test. The
remaining 12 of 30 samples were examined using a
3-tube, decimal dilution MPN test. The 90th
percentile values for the 5-tube, decimal
dilution test in the approved classification status is 43.
That for the 3-tube, decimal dilution MPN test
is 49. Again the value for the weighted 90th
percentile will be somewhere between the
respective 90th percentile values of both MPN methods.
Its proximity to either is a function of the
number of samples in the data set contributed by each
MPN procedure. In this example, a somewhat
greater number of samples were derived from use of
the 5-tube, decimal dilution MPN test; so that,
the value of the 90th percentile will be weighted in
that direction also.
To calculate the weighted 90th
percentile for this data set
- The 90th percentile
values of 43 for the 5-tube, decimal dilution MPN test for fecal coliforms
and 49 for the 3-tube, decimal dilution MPN
test for fecal coliforms are converted to base 10
logs. This gives base 10 log values of 1.633
for the 5-tube, decimal dilution test and 1.690 for the
3-tube, decimal dilution MPN test.
- These base 10 log values are then
multiplied by the number of samples in the database
analyzed by each MPN procedure. In this
example, 18 of 30 samples were examined by the
5-tube, decimal dilution MPN test: and, 12
of 30 samples were analyzed by the 3-tube, decimal
dilution MPN test. This gives 1.633 for the
5-tube, decimal dilution MPN test x 18 samples =
29.394 and 1.690 for the 3-tube, decimal dilution
MPN test x 12 samples = 20.280.
- These values are added
together and the resultant divided by the total number of samples in
the database being used. Thus, 29.394 + 20.280
=49.674, 49.674/30 = 1.656
- The antilog of this
value is determined. In this example, the antilog of 1.656 is 45.269.
- This antilog value is
rounded to the nearest whole number which in this example is 45.
- The weighted 90th percentile value for this data
set is 45. Forty-five (45) is the value of the 90th percentile
which will be compared to the estimated 90th percentile calculated
from the data in the sample data set collected under the
SRS sampling regime and examined using the two
different MPN methods. To remain in the
approved status the estimated 90th percentile
calculated from this data set must be less
than or equal to the value determined for the weighted
90th percentile of the data
set. Again the weighted 90th percentile will have to be
recalculated as
new data becomes available. This
recalculation must continue until the transition in
methodologies is completed and all the
data from this sampling station has been derived from
the same MPN procedure. At this time, the
corresponding 90th percentile of 49 for the 3-tube,
decimal dilution MPN procedure in use will
be employed in comparisons to the estimated 90th percentiles calculated
directly from the sampling data.
Example 3
Data in this example was collected from
a sampling station under the SRS sampling regime.
This sampling station is in an area classified
as restricted. The first 24 of the 30 samples collected
were analyzed by the 5-tube, decimal dilution
MPN test for fecal coliforms. The remaining 6
samples of the 30 collected were analyzed using
a 5-tube, fivefold dilution MPN test for fecal
coliforms. The 90th
percentile value for each of these MPN procedures is 260 and 190 respectively.
The value of the weighted 90th
percentile for this data set will be somewhere between 190 and 260.
The proximity to either value will depend on the
respective number of samples analyzed by each
MPN method. In this example, most of the
samples were derived from the 5-tube, decimal dilution
MPN test. Consequently, the 90th
percentile value will be heavily weighted in that direction.
To calculate the weighted 90th
percentile for this data set:
- The
90th percentile values of 260 for the 5-tube, decimal dilution MPN
test for fecal
coliforms and 190 for the 5-tube,
fivefold dilution MPN test for fecal coliforms are converted
to base 10 logs. This gives a base 10
logarithmic value of 2.415 for the 5-tube, decimal dilution
MPN test and 2.279 for the 5-tube,
fivefold MPN test.
- These base 10 log values are
then multiplied by the number of samples in the database
analyzed by each MPN procedure. In this
example, the 5-tube, decimal dilution MPN was used
in the analysis of 24 of the 30 samples
while the 5-tube, fivefold dilution MPN was used to test
the remaining 6 samples. Hence, 2.415,
the log 90th percentile value for the 5-tube, decimal
dilution MPN test is multiplied by 24, the
number of samples tested by this MPN procedure to
give 57.960; and, 2.279, the log 90th percentile value for the
5-tube, fivefold dilution MPN test is multiplied by 6, the number of samples
obtained using this MPN procedure to give 13.674.
- These values are added together
and subsequently divided by the total number of samples
analyzed by both methods. In this
example, 57.960 + 13.674 = 71.634, 71.634/30 = 2.388.
- The
antilog of this value is determined. In this example the antilog of 2.388
is 244.343.
- This
antilog is conventionally rounded to the nearest whole number which in this
example is
244.
- The weighted 90th percentile value for the data set is
244. Two hundred forty-four (244) is
the value of the 90th percentile which will be compared to the
estimated 90th percentile
calculated from the data in the sample
data set collected under the SRS sampling regime and
examined using the two MPN methods. To
remain in the restricted classification, the estimated
90th percentile calculated from
the data set will have to be less than or equal to the value of the
weighted 90th percentile
obtained from the data set. This weighted 90th percentile value
will
need to be recalculated as more data
becomes available and until such time as the transition in
methodologies is completed and all the
samples have been derived from the same MPN
procedure. When this occurs, the
corresponding 90th percentile of 190 for the 5-tube, fivefold
dilution MPN procedure in use will be
employed in comparisons to the estimated 90th percentile
calculated directly from the sampling
data.
Example 4
Data in this example was collected from a
sampling station under the APC sampling regime.
This sampling station is in the approved
classification and 5 of 15 samples in the database were
tested by the 5-tube, decimal dilution MPN test
for total coliforms. The remaining 10 samples in
the database were analyzed by the 3-tube,
decimal dilution MPN test for total coliforms. The 90th
percentile value for each of these MPN tests
were 230 and 330 respectively. The value of the
weighted 90th percentile will be
somewhere between 230 and 330. Its proximity to either value
depends on the respective number of samples analyzed
by each MPN procedure. In this example,
the preponderance of samples were tested by the
3-tube MPN procedure. As a result, the value of
the 90th percentile will be weighted
more heavily toward 330.
To calculate the weighted 90th
percentile for this data:
- The
90th percentile values of 230 for the 5-tube, decimal dilution MPN
test for total
coliforms and 330 for the 3-tube,
decimal dilution MPN test for total coliforms are converted to
base 10 logarithms. This gives base 10
log values of 2.362 and 2.519 respectively.
- These base 10 log values are
then multiplied by the number of samples in the database
analyzed by each MPN procedure. In this
example, 5 of 15 samples in the database were
analyzed by the 5-tube, decimal dilution
MPN test. The remaining 10 of 15 samples were
examined by the 3-tube, decimal dilution
test. Thus, the base 10 log value of 2.362, the 90th percentile
of the 5-tube MPN procedure for total coliforms is multiplied by the
5 samples tested by this MPN method to give 11.810. In
addition, the base 10 log value of 2.519, the 90th percentile
of the 3-tube MPN test for total
coliforms is multiplied by the 10 samples examined
by this MPN procedure to give 25.190.
- These values are added together
and the resultant divided by the total number of samples in
the database being analyzed. In this
example, 11.810 + 25.190 = 37.000, 37.000/15 = 2.467.
- The antilog of this value is
determined. For this example, the antilog of 2.467 is 293.089
- This antilog is rounded off to
the nearest whole number which in this case is 293.
- The weighted 90th percentile for
this data set is 293. Two hundred ninety three (293) is the value for the
90th percentile
that cannot be exceeded more than 10% of the time by this sampling
station under APC for it to remain in
approved classification status. The value for the weighted
90th percentile must be
recalculated as more data becomes available. This will continue until the
transition in methodologies is completed
and all samples in the database have been analyzed
using the same MPN procedure. When this
happens, the corresponding 90th percentile of 330
for the 3-tube, decimal dilution MPN
procedure in use will be employed in comparisons with
the sample data.
Other References:
- Schaum's Outline Series
Theory and Problems of Statistics, Second Edition, 1994, McGraw Hill, Inc.
- U.S. DHEW/PHS/FDA Shellfish
Sanitation Branch, Proceedings 8th National Shellfish Sanitation Workshop, January 16-18, 1974, New Orleans, LA.
Contact:
U.S. Food and Drug Administration
Shellfish
Safety Team
5100 Paint Branch Parkway (HFS-626)
College Park, Maryland 20740-3835
Distribution:
Shellfish Specialists
Division of Federal State Relations
Shellfish Sanitation Group/Office
of Seafood
Interstate Shellfish
Sanitation Conference
Canada
Chile
Republic of Korea
New Zealand