United States
Environmental Protection
Agency
Environmental Monitoring
Systems Laboratory
Cincinnati OH 45268
Research and Development
EPA/600/S4-89/002 Sept. 1989
&EPA Project Summary
Experimental Design and Data
Analysis Applicable to
Assays for Monitoring
Waterborne Viruses
Larry J. Wymer
Suitable statistical methods
applicable to assays for monitoring
waterborne viruses as described in
the "USEPA Manual of Methods for
Virology" (EPA-600/4-84-013) are
presented. These methods have been
selected to show the non-statistician
how measurement evaluations
should be made to analyze collected
waterborne virus data. The specific
experimental situations that have
been included pertain to relative
frequencies of virus types, estimates
of viral liter, assessing the precision
of these estimates, and comparing
results among subsamples. Also
included are numerous references
for additional information regarding
statistical theory and appropriate
statistical tables, many of which are
not commonly available from other
sources but are essential to per-
forming the analyses suggested in
this report.
This Project Summary was devel-
oped by EPA's Environmental Monitor-
ing Systems Laboratory, Cincinnati,
OH, to announce key findings of the
research project that is fully docu-
mented in a separate report of the
same title (see Project Report order-
ing information at back).
Introduction
Currently, the "USEPA Manual of
Methods for Virology" makes no mention
of the statistical treatment of accumulated
data. Given the effort and expense of
performing viral assays, it seems appro-
priate that guidelines for the evaluation of
data obtained from these assays be
available.
Single titrations are commonly per-
formed to monitor viruses in environ-
mental samples. The basic unit of infec-
tion, observable by its cytopathic effects
within the cell sheet, resulting in the
appearance of a plaque, is the plaque
forming unit (pfu). A pfu may consist of a
single virus, or it may be an aggregation
of two or more viruses. A pfu, regardless
of its exact composition, is taken as the
minimum level of exposure of an
organism to the virus.
Two critical assumptions are made
with respect to the formation and
observation of plaques obtained from
these assays. One assumption is that the
plaque count itself is not subject to error.
Potential sources of error in plaque
counting arise from the existence of
"false positives" among plaques counted
in the assay and overlapping of plaques
on the cell sheet. False positives may be
eliminated through the confirmation of
each plaque as being caused by a virus,
while the problem of overcrowding may
be minimized by using only those results
obtained at suitable dilutions of the test
material.
The second assumption made is that a
single pfu is sufficient to infect a cell.
This assumption of single hit kinetics
implies that the mean number of plaques
at any level of concentration is directly
proportional to the amount of test
material used in the inoculum. Cases
have been reported for which, apparently,
one or two virus particles may be
required for infection of the cell to occur.
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The single hit model may still be a
reasonable approximation to such data,
however, if the amount of test material
used for each inoculation is small enough
that the response is still approximately
proportional to the dosage.
Results
The Poisson distribution has wide-
spread application in the modeling of
experimental data consisting of the
number of times some event occurs over
a fixed interval of time, length, area, or
volume. When such counts follow a
Poisson distribution, the probability of x
occurrences of the event in a fixed
interval is given by the probability distri-
bution function (pdf):
f(x) = e-6e*/x!
The pdf for a Poisson process is
completely specified by its mean, 9. The
true value of 9 will depend on the amount
of material used, which for viral assays
corresponds to the volume, v, used in the
inoculum before dilution. Thus, 9 = w,
where t is the true mean density of pfu's
per unit volume of eluate ("pfu titer").
The assumption that plaque counts
follow a Poisson law is often made in
practice. However, little has been done to
validate this assumption. To this end,
plaque count data from 65 raw and
treated sewage sample titrations (Table
1) and from a round-robin soil study
involving 29 sandy loam and 29 sand
samples (Table 2) were utilized to deter-
mine whether the Poisson adequately
characterizes viral assay data. Fisher's
index of dispersion (D) was used as the
test statistic. Under the null hypothesis,
that the plaque counts within each trial
follow a Poisson process, D is approxi-
mately distributed as a x2 variable with k-
1 degrees of freedom, where k is the
number of independent counts obtained
from that trial. Generally, the number of
independent counts is equal to the
number of cell culture bottles used; how-
ever, in some cases the results from two
or more bottles are combined in order to
ensure that the expected count for each
grouping is at least five — a requirement
in order for the x2 approximation to apply.
Of the 29 sewage samples titrations
inoculated in BGM cell cultures, only 2
failed the test for a Poisson distribution
(San Lorenza influent under the virus
adsorption elution cartridge filter method
and Guaynabo influent under the beef
extract-celite precipitation method). Even
if all trials were truly Poisson distributed,
one would expect one or two rejections of
the null hypothesis (H0) among 29 such
tests, simply due to the level of type I
error (0.05) used. Thus, these results
indicate excellent agreement with a
Poisson assumption.
Of the 36 sewage sample titrations
inoculated in bovine kidney (MDBK) cell
cultures, 9 led to rejection of a random
dispersion of plaques throughout the
medium. This is much higher than the
rejection rate that would be expected if all
trials were Poisson processes and is,
therefore, reliable evidence that at least
some of the data are non-Poisson. The
MDBK cell line used in this assay, how-
ever, was later found to be contaminated;
although MDBK cells are not susceptible
to coxsackie virus infection, plaques of
this. type- were--identified among—those-
found on the cell sheet; Thus, the non-
random dispersion of plaques was af-
fected by the distribution of cell types
within the culture. These results illustrate
the use of a test for randomness in
identifying results that may be suspect.
Among the 29 sand sample trials
performed in the soil round-robin study,
none failed the test for a Poisson distri-
bution. However, 8 of the 29 sandy loam
trials resulted in rejection of the null
hypothesis that the distribution of the
plaques follows a Poisson law.
These results lead to the conclusion
that the assumption of a Poisson distribu-
tion is not unreasonable for plaque count
data, although testing of the assumption
whenever possible is warranted. Failure
to obey a Poisson distribution may be
due to the method used in processing the
sample, which differs among water,
sludge, and soil samples, or may result
from distribution of pfu's in the sample
itself.
Conclusions ^ _ _
Standard statistical reporting that
should be incorporated as part of every
viral monitoring assay includes:
1. Test for Poisson distribution of
plaques at a 0.05 critical level.
2. Confirmed virus pfu titer and associ-
ated 95% confidence interval.
3. Titers by virus type and associated
95% joint confidence intervals.
4. Relative proportions of virus types
, and associated 95% joint confidence
intervals.
When plaques are shown to follow a
Poisson distribution, 95% confidence
intervals for the Poisson parameter, e,
may be calculated from the cumulative
Poisson distribution function. Tables of
lower and upper 95% confidence lir
for Poisson counts and for lower al
upper simultaneous 95% confidenj
limits for up to five virus types
included in the full report. Because tl
Poisson distribution has only one paraif
eter, confidence limits for a PoissJ
mean are completely determined by t|
total count.
Tables of 95% confidence limits
binomial proportions and for 95% simij
taneous confidence limits for multinoml
proportions for up to five virus types
also included in the full report. TheJ
may be used in constructing confident
intervals for proportions of virus typq
found in the sample.
A significant departure from custome
— praetiee-is-reeommended in the-way
which plaques are selected for confj
mation and identification. It is recor
mended that all plaques be confirms
and identified to the extent possible; if|
is not practical to perform this assay
every plaque found in the experimer
then a sufficient number of cell cultuj
bottles should be randomly selected, ar,
all plaques in these bottles so assayed.!
this recommendation is followed, a direj
estimation of titer by virus type can
made. In addition, this procedure elir
inates bias that may result from allowir
the operator to select the specifi
plaques to be confirmed and typed.
Because all plaques in a bottle are 1
be picked, confirmation and identificatio
may be performed on each day, a
plaques are counted on the cell sheets.
Given the widespread availability
desktop computers to lab personnel, th
development of software to perform th
analysis of viral assay data is reconr
mended. The existence of such softwar
would eliminate the reliance on statistic;
tables, diminish the possibility of huma
~'" error r~eTTab le Standardization" of th
analysis and reporting of the results, an
reduce the time required to perform th
analyses. A full range application
recommended; this would incorporate nc
only data analysis but also data
data management, file handling,
reporting features.
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Table 1. Texts for Poisson Distribution of Plaque Counts Based on Fisher's Index of Dispersion: Puerto
Rico Sewage Treatment Plant Study
CF^ Method PPT* Method
Aibonito Effluent
Aibonito Influent
Barranquitas Effluent
Barranquitas Effluent (2)g
Caguas Effluent
Caguas Influent
Cazey Effluent
" - Cazey Influent
Cidra Effluent
Cidra Effluent(2)
Cidra Influent
Comer/o Effluent
Comerio Influent
Guaynabo STP Effluent
Guaynabo STP Influent
Gurabo Influent
Gurabo lnfluent(2)
Juncos Effluent
Juncos Influent
Narangito Effluent
Pueblito El Rio Influent
San Lorenzo Effluent
San Lorenzo Effluent(2)
San Lorenzo Influent
San Lorenzo lnfluent(2)
Villalba Effluent
Villalba Effluent(2)
Villalba Influent
Vista Monte Influent
BGM°
DP*
9
9
9
9
9
9
9
9
9
9
4
9
4
19
9
9
1
5
3
9
Cells
Of
2.392
4.667
11.871
13.101
5.213
5.529
4.446
4.357
10.492
6.366
0.500
7.352
3.236
20.760
8.385
4.083
0.818
4.267
13.0'
11.289
MDBKd Cells BGM Cells MDBK Cells
DF
9
9
9
9
9
9
9
4
9
9
9
4
9
9
9
4
9
9
2
2
9
8
9
9
2
D DF D DF D
8.702
14.147 5 1.857
4.882
11.479
7.364
44.735' 9 10.842 5 1.432
8.890 9 8.769 2 2.632
2.122 9 11.750
21.006"
20.889" 2 2.804
15.769 4 3.667 2 0.080
1.510 4 3.348
18.000" 4 5.750
7.346 2 5.804 2 1.625
14.404 1 7.364" 1 0.818
3.024
14.045 2 1.333
22.170" 1 0.600
0.028
4 5.545
13.500"
23.034"
37.462" 9 12.455
8.836
31.291"
2.848 2 3.000
"Indicates significant departure from Poisson distribution at 0.05 critical level
aVirus adsorption elution (VIRADEL) cartridge filter
bBeef extract - celite precipitation method
cBuffalo green monkey kidney cells
<*Madin and Dorby bovine kidney
eDegrees of freedom for chi-square test
'Index of dispersion
9(2) = Retrial
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Larry J. Wymeris with Computer Sciences Corporation, Fall Church, VA 22042.
Robert S. Safferman is the EPA Project Officer (sae below).
The complete report, entitled "Experimental Design and Data Analysis Applicable
to Assays for Monitoring Waterborne Viruses," (Order No. PB 89-148 571/AS;
Cost: $15,95, subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at
Environmental Monitoring Systems Laboratory
U.S. Environmental Protection Agency
Cincinnati, OH 45268
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati OH 45268
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POSTAGE & FEES PAID
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Penalty for Private Use $300
EPA/600/S4-89/002
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