y
I 5
"
EPA
(*00-
M_ EPA/6CO/4-89/001a
S*\- September 1989
QG\c^ Revision 1
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF RESEARCH AND DEVELOPMENT
ENVIRONMENTAL MONITORING SYSTEMS LABORATORY
CINCINNATI. OHIO 45268
DATE: September 1989
SUBJECT: Supplement to "Short-term Methods for Estimating
the Chronic Toxicity of Effluents and Surface
Waters to Freshwater Organisms," (EPA/600/4-89/001)
The attached material on the Linear Interpolation Method, a point
estimation technique, was prepared to provide background information
and examples for the use of this method for the analysis of data from
the Fathead Minnow Larval Survival and Growth Test and the
Ceriodaphnia Survival and Reproduction Test described in the recently
completed second edition of the Agency manual, "Short-term Methods
for Estimating the Chronic Toxicity of Effluents and Receiving Waters
to Freshwater Organisms," EPA/600/4-89/001.
This material consists of 42 pages arranged in four parts to
facilitate insertion in the appropriate places in the existing
manual, as indicated below. Current pages in the manual with the
same numbers as the inserts should be discarded.
PART 1. REPLACEMENT PAGES FOR SECTION 2
Consists of 11 pages, numbered 4-11 and
12A-12C, for Section 2, to replace
-2 pp. 4-12 (replaces the entire Section) .
&
.... PART 2. REPLACEMENT PAGES FOR SECTION 9
eo
-r Consists of 9 pages, numbered 71A-71F and
/Y9 72-74, for Section 10 to replace
pp. 71-74.
PART 3. REPLACEMENT PAGES FOR SECTION 12
EJBD Consists of 9 pages, numbered 143A-143F and
ARCHIVE 144-146, for Section 12, to replace
EPA pp. 143-146.
600- W
4~ PART 4. INSERT FOR (NEW) APPENDIX J
89-
00 la Consists of 13 pages, numbered 250-262, for a
new appendix, Appendix J.
Questions about the inserts should be addressed to
Cornelius Weber, CAiality Assurance Research Division
(Comm'l: 513-569-7325; FTS: 684-7325 )•
-------
PART 1
REPLACEMENT PAGES FOR SECTION 2
(pp. 4-11, and 12A-12C)
EPA/600/4-OS/OOla
September 1989
Revision 1
-------
September 19&)
(Revision 1)
SECTION 2
CHRONIC TOXICITY TEST EMDPOINTS AND DATA ANALYSIS
2.1 EMDPOINTS
2.1.1 The objective of chronic aquatic toxlclty tests with effluents and pure
compounds Is to estimate the highest "safe" or "no-effect concentration" of
these substances. For practical reasons, the responses observed 1n these
tests are usually limited to hatchablllty, gross morphological abnormalities,
survival, growth, and reproduction, and the results of the tests are usually
expressed In terms of the highest toxicant concentration that has no
statistically significant observed effect on these responses, when compared to
the controls. The terms currently used to define the endpolnts employed In
the rapid, chronic and sub-chronic toxlclty tests have been derived from the
terms previously used for full life-cycle tests. As shorter chronic tests
were developed, It became common practice to apply the same terminology to the
endpolnts. The terms used 1n this manaul are as follows:
2.1.1.1 Safe Concentration - The highest concentration of toxicant that will
permit normal propagation of fish and other aquatic life In receiving waters.
The concept of a "safe concentration" Is a biological concept, whereas the
"no-observed-effect concentration" (below) Is a statistically defined
concentration.
2.1.1.2 No-Observed-Effect-Concentration (NOEC) - The highest concentration
of toxicant to which organisms are exposed In a full life-cycle or partial
life-cycle test, that causes no observable adverse effects on the test
organisms (I.e., the highest concentration of toxicant In which the values
for the observed responses are not statistically significantly different from
the controls). This value Is used, along with other factors, to determine
toxlclty limits In permits.
2.1.1.3 Lowest-Observed-Effect-Concentration (LOEC) - The lowest
concentration of toxicant to which organisms are exposed In a life-cycle or
partial life-cycle test, which causes adverse effects on the test organisms
(I.e. where the values for the observed responses are statistically
significantly different from the controls).
2.1.1.4 Effective Concentration (EC) - A point estimate of the toxicant
concentration that would cause an observable adverse affect on a quanta!, "all
or nothing," response (such as death, Immobilization, or serious
fncapacltatlon) In a given percent of the test organisms, calculated by point
estimation techniques. If the observable effect Is death or Immobility, the
term, Lethal Concentration (LC), may be used (see below). A certain EC or LC.
value might be judged from a biological standpoint to represent a threshold
concentration, or lowest concentration that would cause an adverse effect on
the observed response.
-------
September 1989
(Revision 1)
2.1.1.5 Lethal Concentration (LC) - Identical to EC when the observable
adverse effect Is death. For example, the LC50 from a Problt Analysis Is the
estimated concentration of toxicant that would cause death In 50% of the test
population.
2.1.1.6 Inhibition Concentration (1C) - A point estimate of the toxicant
concentration that would cause a given percent reduction In a non-quantal
biological measurement such as fecundity or growth. For example, an IC25
would be the estimated concentration of toxicant that would cause a 25%
reduction in mean young per female or growth.
2.2 RELATIONSHIP BETWEEN ENDPOINTS DETERMINED BY HYPOTHESIS TESTING AND POINT
ESTIMATION TECHNIQUES
2.2.1 If the objective of chronic aquatfc toxicity tests with effluents and
pure compounds 1s to estimate the highest "safe or no-effect concentration" of
these substances, It Is Imperative to understand how the statistical endpolnts
of these tests are related to the "safe" or "no-effect" concentration. NOECs
and LOECs are determined by hypothesis testing (Dunnett's Test, Bonferronl's
T-test, Steel's Many-One Rank Test, or Wllcoxon Rank Sum Test), whereas, LCs,
ECs, and ICs are determined by point estimation techniques (Problt Analysis or
Linear Interpolation Method). There are Inherent differences between the use
of a NOEC or LOEC derived from hypothesis testing to estimate a "safe"
concentration, and the use of a LC, EC, 1C, or other point estimate derived
from curve fitting, Interpolation, etc.
2.2.2 Most point estimates, such as the LC, EC, or 1C are derived from a
mathematical model that assumes a continuous dose-response relationship. By
definition, any LC, EC, or 1C value Is an estimate of some amount of adverse
effect. Thus the assessment of a "safe" concentration must be made front a
biological standpoint rather than with a statistical test. In this Instance,
the biologist must determine some amount of adverse effect that Is deemed to
be "safe," In the sense that from a practical biological viewpoint It will not
affect the normal propagation of fish and other aquatic life In receiving
waters. Thus, to use a point estimate such as an LC, EC, 1C to determine a
"safe" concentration would require the specification by biologists or
lexicologists of what level of adverse effect would be deemed acceptable or
"safe".
2.2.3 The use of NOECs and LOECs, on the other hand, assumes either (1) a
continuous dose-response relationship, or (2) a non-continuous (threshold)
model of the dose-response relationship.
2.2.3.1 In the case of a continuous dose-response relationship, it is also
assumed that adverse effects that are not "statistically observable" are also
not Important from a biological standpoint, since they are not pronounced
enough to test statistically significant against some measure of the natural
variability of responses.
-------
September 1989
(Revision 1)
2.2.3.2 In the case of non-continuous dose-response relationship, It Is
assumed that there exists a true threshold, or concentration below which there
Is no adverse effect on aquatic Hfe, and above which there Is an adverse
effect. The purpose of the statistical analysis In this case Is to estimate
as closely as possible where that threshold lies.
2.2.3.3 In either case, It Is Important to realize that the amount of the
adverse effect that Is statistically observable (LOEC) or not observable
(NOEC) 1s highly dependent on all aspects of the experimental design, such as
the number of concentrations of toxicant, number of replicates per
concentration, number of organisms per replicate, and use of randomization.
Other factors that affect the sensitivity of the test Include the choice of
statistical analysis, the choice of an alpha level, and the amount of
variability between responses at a given concentration.
2.2.3.4 Where the assumption of a continuous dose-response relationship is
made, by definition some amount of adverse effect might be present at the
NOEC, but is not great enough to be detected by hypothesis testing.
2.2.3.5 Where the assumption of a non-continuous dose-response relationship
is made, the NOEC would Indeed be an estimate of a "safe" or "no-effect"
concentration if the amount of adverse effect that appears at the threshold is
great enough to test as statistically significantly different from the
controls in the face of all aspects of the experimental design mentioned
above. If, however, the amount of adverse effect at the threshold were not
great enough to test as statistically different, some amount of adverse effect
might be present at the NOEC. In any case, the estimate of the NOEC with
hypothesis testing Is always dependent on the aspects of the experimental
design mentioned above. For this reason, the reporting and examination of
some measure of the sensitivity of the test (either the minimum significant
difference or the percent change from the control that this minimum difference
represents) is extremely important.
2.2.4 In summary, the assessment of a "safe" or "no-effect" concentration
cannot be made from the results of statistical analysis alone, unless (1) the
assumptions of a strict threshold model are accepted, and (2) 1t Is assumed
that the amount of adverse effect present at the threshold is statistically
detectable by hypothesis testing. In this case, estimates obtained from a
statistical analysis are Indeed estimates of a "no-effect" concentration. If
the assumptions are not deemed tenable, then estimates from a statistical
analysis can only be used in conjunction with an assessment from a biological
standpoint of what magnitude of adverse effect constitutes a "safe"
concentration. In this Instance, a "safe" concentration 1s not necessarily a
truly "no-effect" concentration, but rather a concentration at which the
effects are judged to be of no biological significance.
2.2.5 A better understanding of the relationship between endpolnts derived by
hypothesis testing (NOECs) and point estimation techniques (ECs, LCs, and ICs)
would be very helpful in choslng methods of data analysis. Birge et al.
(1985) reported that LCls derived from Probit Analyses of data from short-term
embryo-larval tests with reference toxicants were comparable to NOECs for
-------
September 1989
(Revision 1)
several organisms. Similarly, Norberg-King (1988) reported that the IC25s
were comparable to the NOECs for a set of Ceriodaphnia chronic tests with a
single reference toxicant. 'However, the scope of these comparisons was very
limited, and sufficient information is not yet available to establish an
overall relationship between these two types of endpoints, especially when
derived from effluent toxicity test data.
2.3 PRECISION
2.3.1 Hypothesis Tests
2.3.1.1 When hypothesis tests are used to analyze toxicity test data, it is
not possible to express precision in terms of a commonly used statistic. The
results of the test are given in terms of two endpoints, the No-Observed-
Effect Concentration (NOEC) and the Lowest-Observed-Effect Concentration
(LOEC). The NOEC and LOEC are limited to the concentrations selected for the
test. The width of the NOEC-LOEC interval is a function of the dilution
series, and differs greatly depending on whether a dilution factor of 0.3 or
0.5 is used in the test design. It is not possible to place confidence limits
on the NOEC and LOEC derived from a given test, and it is difficult to
quantify the precision of the NOEC-LOEC endpoints between tests. If the data
from a series of tests performed with the same toxicant, toxicant
concentrations, and test species, were analyzed with hypothesis tests,
precision could only be assessed by a qualitative comparison of the NOEC-LOEC
intervals, with the understanding that maximum precision would be attained if
all tests yielded the same NOEC-LOEC interval. In practice, the precision of
results of repetitive chronic tests is considered acceptable if the NOECs vary
by no more than one concentration interval above or below a central tendency.
Using these guidelines, the "normal" range of NOECs from toxicity tests using
a 0.5 dilution factor (two-fold difference between adjacent concentrations),
would be four-fold.
2.3.2 Point Estimation Techniques
2.3.2.1 Point estimation techniques have the advantage of providing a point
estimate of the toxicant concentration causing a given amount of adverse
(inhibiting) effect, the precision of which can be quantitatively assessed (1)
within tests by calculation of 95% confidence limits, and (2) across tests by
calculating a standard deviation and coefficient of variation.
2.4 DATA ANALYSIS
2.4.1 Role of the Statistician
2.4.1.1 The choice of a statistical method to analyze toxicity test data and
the interpretation of the results of the analysis of the data from any of the
toxicity tests described in this manual can become problematic because of the
inherent variability and sometimes unavoidable anomalies in biological data.
Analysts who are not proficient in statistics are strongly advised to seek the
assistance of a statistician before selecting the method of analysis and using
any of the results.
-------
September 1989
(Revision 1)
2.4.1.2 The statistical methods recommended in this manual are not the only
possible methods of statistical analysis. Many other methods have been
proposed and considered. Certainly there are other reasonable and defensible
methods of statistical analysis of this kind of toxicfty data. The methods
contained in this manual have been chosen because they are (1) applicable to
most different toxfcity test data sets for which they are recommended, and (2)
hopefully "easily" understood by non-statisticians.
2.4.2 Plotting of the Data
2.4.2.1 The data should be plotted, both as a preliminary step to help detect
problems and unsuspected trends or patterns in the responses, and as an aid in
Interpretation of the results. Further discussion and plotted sets of data
are Included in the methods and the Appendices.
2.4.3 Data Transformations
2.4.3.1 Transformations of the data, e.g., arc sine square root and logs,
are used where necessary to meet assumptions of the proposed analyses,
such as the requirement for normally distributed data.
2.4.4 Independence, Randomization, and Outliers
2.4.4.1 Statistical independence among observations is a critical assumption
In all statistical analyses of toxicity data. One of the best ways to insure
independence is to properly follow rigorous randomization procedures.
Randomization techniques should be employed at the start of the test,
Including the randomization of the placement of test organisms 1n the test
chambers and randomization of the test chamber location within the array of
chambers. Discussions of statistical independence, outliers and
randomization, and a sample randomization scheme, are included in Appendix A.
2.4.5 Replication and Sensitivity
2.4.5.1 The number of replicates employed for each toxicant concentration is
an Important factor in determining the sensitivity of chronic toxicity tests.
Test sensitivity generally increases as the number of replicates is increased,
but the point of diminishing returns in sensitivity may be reached rather
quickly. The level of sensitivity required by a hypothesis test or the
confidence interval for a point estimate will determine the number of
replicates, and should be based on the objectives for obtaining the toxicity
data.
2.4.5.2 In a statistical analysis of toxicity data, the choice of a
particular analysis and the ability to detect departures from the assumptions
of the analysis, such as the normal distribution of the data and homogeneity
of variance, Is also dependent on the number of replicates. More than the
minimum number of replicates may be required in situations where 1t is
Imperative to obtain optimal statistical results, such as with tests used in
-------
September 1989
(Revision 1)
enforcement cases or when it is not possible to repeat the tests. For
example, when the data are analyzed by hypothesis testing, the nonparametric
alternatives cannot be used unless there are at least four replicates at each
toxicant concentration.
2.5 CHOICE OF ANALYSIS
2.5.1 The recommended statistical analysis of most data from chronic toxiclty
tests with aquatic organisms follows a decision process illustrated in the
flow chart in Figure 1. An initial decision is made to use point estimation
techniques (Probit Analysis or Linear Interpolation Method) and/or to use
hypothesis testing (Dunnett's Test, Bonferroni's T-test, Steel's Many-One Rank
Test, or Wilcoxon Rank Sum Test). If hypothesis testing is chosen, subsequent
decisions are made on the appropriate procedure for a given set of data,
depending on the results of tests of assumptions, as illustrated in the flow
chart. A specific flow chart is included in the analysis section for each
test.
2.5.2 Since a single chronic toxicity test might yield information on more
than one parameter (such as survival, growth, and reproduction), the lowest
estimate of a "no-observed-effect concentration" for any of the
responses would be used as the "no-observed-effect concentration" for
each test. It follows logically that in the statistical analysis of the data,
concentrations that had a significant toxic effect on one of the observed
responses would not be subsequently tested for an effect on some other
response. This is one reason for excluding concentrations that have shown a
statistically significant reduction in survival from a subsequent statistical
analysis for effects on another parameter such as reproduction. A second
reason is that the exclusion of such concentrations usually results in a more
powerful and appropriate statistical analysis.
2.5.3 Analysis of Growth and Reproduction Data
2.5.3.1 Growth data from the fathead minnow larval survival and growth test
are analyzed using hypothesis testing or point estimation techniques according
to the flow chart in Figure 1.
2.5.3.2 Reproduction data from the Ceriodaphnia survival and reproduction
test, after eliminating data from concentrations with a significant mortality
effect as determined by Fisher's Exact Test, are analyzed using hypothesis
testing or point estimation techniques according to the flow chart in Figure 1.
2.5.4 Analysis of Algal Growth Response Data
2.5.4.1 The growth response data from the algal toxicity test, after an
appropriate transformation if necessary to meet the assumptions of normality
and homogeneity of variance, may be analyzed by hypothesis testing according
to the flow chart in Figure 1. Point estimates, such as the EC1, ECS, EC10,
or EC50, would also be appropriate in analyzing algal growth data.
-------
September 1989
(Revision 1)
DATA (SURVIVAL. GROWTH REPRODUCTION. ETC.)
{~
POINT
ESTIMATIC
_
HYPOTHESIS 1
IN 4
•ESTING
i| TRANSFORMATION?!
ENDPOINT EST.
EC, LC. I
1
HOMOGENEOUS V
NO
\ '
T-TEST WIT
BONFERRON]
ADJUSTMEN1
L_
U ^HAPTRH-HTI K
WRMAL DISTRIBUTION!
| 1 BARTLETT
ARIANCE
t
STPCT 1
NO STATISTICAL ANALYS
RECOMMENDED
v
EQUAL NUMBER OF
REPLICATES?
YES 1
J" DUNNETT'S STEEL'S
; TEST RANK
*
ON-NORMAL DISTRIBUTION
CTEROGENEOUS
VARIANCE
IS ^_
••
4 OR MORE
REPLICATES?
YES
f
EQUAL NUMBER OF
REPLICATES?
iYES
MANY-ONE
TEST
NO
1
f
MILCOXON RANK SUM
TEST HITH
BONFERRONI ADJUSTMENT
ENDPOINT ESTIMATES
NOEC, LOEC
1
Figure 1. Flow chart for statistical analysis of test data.
10
-------
September 1989
(Revision 1)
2.5.5 Analysis of Mortality Data
2.5.5.1 Mortality data from the fathead minnow larval survival and growth
test and the fathead minnow embryo-larval survival and teratogenicity test are
analyzed by Probit Analysis, if appropriate (see discussion below). The
mortality data can also be analyzed by hypothesis testing, after an arc sine
transformation (see Appendix B), according to the flow chart in Figure 1.
2.5.5.2 Mortality data from the Ceriodaphnia survival and reproduction test
are analyzed by Fisher's Exact Test (Appendix G) prior to the analysis of the
reproduction data. The mortality data may also be analyzed by Probit
Analysis, if appropriate (see discussion below).
2.6 HYPOTHESIS TESTS
2.6.1 Dunnett's Procedure
2.6.1.1 Dunnett's Procedure is used to determine the NOEC. The procedure
consists of an analysis of variance (ANOVA) to determine the error term, which
is then used in a multiple comparison method for comparing each of the
treatment means with the control mean, in a series of paired tests (see
Appendix C). Use of Dunnett's Procedure requires at least three replicates
per treatment to check the assumptions of the test. In cases where the
numbers of data points (replicates) for each concentration are not equal, a
t-test may be performed with Bonferroni's adjustment for multiple comparisons
(see Appendix D), instead of using Dunnett's Procedure.
2.6.1.2 The assumptions upon which the use of Dunnett's Procedure is
contingent are that the observations within treatments are normally
distributed, with homogeneity of variance. Before analyzing the data, these
assumptions must be tested using the procedures provided in Appendix B.
2.6.1.3 If, after suitable transformations have been carried out, the
normality assumptions have not been met. Steel's Many-One Rank Test should be
used if there are four or more data points (replicates) per toxicant
concentration. If the numbers of data points for each toxicant concentration
are not equal, the Wilcoxon Rank Sum Test with Bonferroni's adjustment should
be used (see Appendix F).
2.6.1.4 Some Indication of the sensitivity of the analysis should be provided
by calculating (1) the minimum difference between means that can be detected
as statistically significant, and (2) the percent change from the control mean
that this minimum difference represents for a given test.
2.6.1.5 A step-by-step example of the use of Dunnett's Procedure is provided
in Appendix C.
2.6.2 Bonferroni's T-Test
2.6.2.1 Bonferroni's T-test is used as an alternative to Dunnett's Procedure
when the number of replicates is not the same for all concentrations. This
test sets an upper bound of alpha on the overall error rate, in contrast to
11
-------
September 1989
(Revision 1)
Dunnett's Procedure, for which the overall error rate Is fixed at alpha.
Thus Dunnett's Procedure Is a more powerful test.
2.6.2.2 The assumptions upon which the use of Bonferronl's T-test Is
contingent are that the observations within treatments are normally
distributed, with homogeneity of variance. These assumptions must be tested
using the procedures provided In Appendix B.
2.6.2.3 The estimate of the safe concentration derived from this test Is
reported 1n terms of the NOEC. A step-by-step example of the use of
Bonferronl's T-test Is provided In Appendix D.
2.6.3 Steel's Many-One Rank Test
2.6.3.1 Steel's Many-One Rank Test 1s a multiple comparison method for
comparing several treatments with a control. This method Is similar to
Dunnett's Procedure, except that It Is not necessary to meet the assumption
for normality. The data are ranked, and the analysis Is performed on the
ranks rather than on the data themselves. If the data are normally or nearly
normally distributed, Dunnett's Procedure would be more sensitive (would
detect smaller differences between the treatments and control). For data that
are not normally distributed, Steel's Many-One Rank Test can be much more
efficient (Hodges and Lehmann, 1956).
2.6.3.2 It Is necessary to have at least four replicates per toxicant
concentration to use Steel's test. Unlike Dunnett's Test, the sensitivity of
this test cannot be stated In terms of the minimum difference between
treatment means and the control mean.
2.6.3.3 The estimate of the safe concentration 1s reported as the NOEC. A
step-by-step example of the use of Steel's Many-One Rank Test Is provided In
Appendix E.
2.6.4 Wllcoxon Rank Sum Test
2.6.4.1 The Wllcoxon Rank Sum Test Is a nonparametrlc test for comparing a
treatment with a control. The data are ranked and the analysis proceeds
exactly as 1n Steel's Test except that Bonferronl's adjustment for multiple
comparisons Is used Instead of Steel's tables. When Steel's test can be used
(1. e., when there are equal numbers of data points per toxicant
concentration), It will be more powerful (able to detect smaller differences
as statistically significant) than the Wllcoxon Rank Sum Test with
Bonferronl's adjustment.
2.6.4.2 The estimate of the safe concentration Is reported as the NOEC. A
step-by-step example of the use of the Wllcoxon Rank Sum Test Is provided In
Appendix F.
12A
-------
September 1989
(Revision 1)
2.6.5 A Caution In the Use of Hypothesis Testing
2.6.5.1 If In the calculation of an NOEC by hypothesis testing, two tested
concentrations cause statistically significant adverse effects, but an
Intermediate concentration did not cause statistically significant effects,
the results should be used with extreme caution.
2.7 POINT ESTIMATION TECHNIQUES
2.7.1 Probit Analysis
2.7.1.1 Problt Analysis 1s used to calculate an LC50 or other appropriate
point estimate by analyzing percentage (quanta!) data from concentration-
response tests. The analysis can provide an estimate of the concentration of
toxicant affecting a given percent of the test organisms and provide a
confidence interval for the estimate.
2.7.1.2 The assumption upon which the use of Problt Analysis Is contingent
Is a normal distribution of log tolerances. If the normality assumption is
not met, and at least two partial mortalities were not obtained, Problt
Analysis should not be used. In cases where Probit Analysis is not
appropriate, the LC50 and confidence interval may be estimated by the moving
average angle or Spearman-Karber method (see Peltier and Vleber, 1985). If a
test results in 100* survival and 100% mortality in adjacent treatments (all
or nothing effect), a LC50 may be estimated using the graphical method.
2.7.1.3 It 1s Important to check the results of Problt Analysis to determine
if the analysis is appropriate. The chi-square test for heterogeneity
provides one good test of appropriateness of the analysis. In cases where
there is a significant chi-square statistic, where there appears to be
systematic deviation from the model, or where there are few data in the
neighborhood of the point to be estimated, Problt results should be used with
extreme caution.
2.7.1.4 The natural rate of occurrence of a measured response, such as
mortality in the test organisms (referred to as the natural spontaneous
response), may be used to adjust the results of the Problt Analysis if such a
rate is judged to be different from zero. If a reliable, consistent estimate
of the natural spontaneous response can be determined from historical data,
the historical occurrence rate may be used to make the adjustment. In cases
where historical data are lacking, the spontaneous occurrence rate should
optimally be estimated from all the data as part of the maximum likelihood
procedure. However, this can require sophisticated computer software. An
acceptable alternative is to estimate the natural occurrence rate from the
occurrence rate in the controls. In this Instance, greater than normal
replication in the controls would be beneficial.
2.7.1.5 A discussion of Probit Analysis, along with a computer program for
performing the Probit Analysis, are included in Appendix I.
12B
-------
September 1989
(Revision 1)
2.7.2 LINEAR INTERPOLATION METHOD
2.7.2.1 -Linear Interpolation Method Is a procedure to calculate a point
estimate of the effluent or other toxicant concentration (Inhibition
Concentration, 1C) that causes a given percent reduction (e.g., 25%, 50%,
etc.) In the reproduction or growth of the test organisms. The procedure was
designed for general applicability 1n the analysis of data from short-term
chronic toxlclty tests.
2.7.2.2 Use of the Linear Interpolation Method fs based on the assumptions
that the responses (1) are monotonically non-Increasing (the mean response for
each higher concentration is less than or equal to the mean response for the
previous concentration), (2) follow a piecewise linear response function, and
(3) are from a random, Independent, and representative sample of test data.
The assumption for piece-wise linear response cannot be tested statistically,
and no defined statistical procedure 1s provided to test the assumption for
monotonldty. Where the observed means are not strictly monotonlc by
examination, they are adjusted by smoothing. In cases where the responses at
the low toxicant concentrations are much higher than 1n the controls, the
smoothing process may result in a large upward adjustment In the control mean.
2.7.2.3 The Inability to test the monotonldty and plecewlse linear
assumptions for this method makes it difficult to assess when the method 1s,
or Is not, producing reliable results. Therefore, the method should be used
with caution when the results of a toxiclty test approach an "all or nothing"
response from one concentration to the next in the concentration series, and
when it appears that there is a large deviation from monotonictty. See
Appendix J for a more detailed discussion of the use of this method and a
computer program available for the calculations.
12C
-------
September 1989
(Revision 1)
PART 2
REPLACEMENT PAGES FOR SECTION 10
(pp. 71A-71F, and 72-74)
-------
September 1989
(Revision 1)
12.3.8.7 To quantify the sensitivity of the test, the minimum significant
difference (MSD) that can be statistically detected may be calculated.
USD = d Sw V U/ni) + (1/n)
Where d = the critical value for the Dunnett's procedure
SN = the square root of the within mean square
n = the common number of replicates at each concentration
(this assumes equal replication at each concentration)
n-\ = the number of replicates in the control.
12.3.B.8 In this example:
MSD = 2.36 (0.052) V U/4) + (1/4)
= 2.36 (0.052H0.707)
= 0.087
12.3.8.9 Therefore, for this set of data, the minimum difference that can be
detected as statistically significant is 0.087 ing.
12.3.8.10 This represents a 12% reduction 1n mean weight from the control.
12.3.9 Calculation of the 1C
12.3.9.1 The growth data in Table 2 are utilized in this example. As seen in
Table 2 and Figure 10, the observed means are not monotom'cally non-increasing
with respect to concentration (The mean response for each higher concentration
Is not less than or equal to the mean response for the previous concentration,
and the responses between concentrations do not follow a linear trend).
Therefore, the means are smoothed prior to calculating the 1C. In the
following discussion, the observed means are presented by Yt and the
smoothed means by Mj.
12.3.9.2 Starting with the control mean, YI = 0.^14, we see that
Y| > Yg. Set MI = YI. Comparing Yg to YS, ?2 < Y3-
12.3.9.3 Calculate the smoothed means:
M2 = Ma = (Y2 + Ya)/2 = 0.675
12.3.9.4 For the remaining observed means, MS > Y4 > YS > Yg. Thus,
M4 becomes Y4, MS becomes YB, etc., for the remaining concentrations.
Table 19 contains the smoothed means, and Figure 10 provides a plot of the
smoothed concentration response curve.
12.3.9.5 An IC25 and IC50 can be estimated using the Linear Interpolation
Method. A 25% reduction In weight, compared to the controls, would result in
a mean weight of 0.536 mg. where M](l - p/100) = 0.714(1 - 25/100). A 50S
reduction In weight, compared to the controls, would result In a mean weight
of 0.357 mg, where MI(! - p/100) = 0.714(1 - 50/100). Examining the
smoothed means and their associated concentrations
71A
-------
0.77-
0.75-
0.73-
0.71
0.69
0.07
o.as
0.63
0.57
0.55
0.51 '
0.49
0.47-
0.45-
0.49
0.41-
0.39-
0.37-
0.35-
vamaou. npucm MUM VDCHT
COMMICn THE OBKVTID MEAN T4I4JS
C OJOOCTS T» SMOOTHED MBAN TjUJUH
—I—
32
84
—I—
128
*» n>
(D T3
256
512
SODIUM PENTACHLOROPHENATE (UC/L)
Figure 10. Plot of raw data, observed means, and smoothed means
for the fathead minnow growth data in Tables 2 and 19.
• VO
CD
-------
September 1989
(Revision 1}
TABLE 19. FATHEAD MINNOW MEAN GROWTH
RESPONSE AFTER SMOOTHING
NaPCP
Cone
(ug/L)
Control
32
64
128
256
512
1
1
2
3
4
5
6
Ml
(nig)
0.714
0.675
0.675
0.624
0.580
0.471
(Table 19), the response 0.536 mg is bracketed by C5 = 256 ug/L and
Ce = 512 ug/L. For the 50? reduction (0.357 mg), the response
(0.471 ug) at the highest toxicant concentration (512 ug/L) is greater
than 50% of the control (0.357 mg). Thus the IC50 is specified as
greater than 512 ug/L.
12.3.9.6 Using Equation 1 from Appendix J, the estimate of the IC25 is
calculated as follows:
ICp = Cj + [M|M - p/100) - Mj](CJ+1 - Cj)
IC25 = 256 + [0.714(1 - 25/100) - 0.580](512 - 256)
W.471 - 0.580)
= 360 ug/L
13.3.9.7 When the Bootstrap program (BOOTSTRP) was used to analyze this set
of data, requesting 80 resamples, the mean estimate of the IC25 was 349.7
ug/L, with a standard deviation of 62.3 ug/L (coefficient of variation =
17.8%). The empirical 95% confidence interval for the true mean was (253.3 -
451.3). The BOOTSTRP computer program output for the IC25 for this data set
is shown in Figure 11.
12.3.9.8 When BOOTSTRP was used to analyze this set of data for the IC50,
requesting 80 resamples, the output indicated that the response of the highest
concentration of toxicant exceeded 50% of the control. Thus, the IC50 could
not be calculated. The BOOTSTRP computer program output is shown in Figure 12.
71C
-------
September 1989
(Revision 1)
THE NUMBER OF RESAMPLES IS 80
*** LISTING OF GROUP CONCENTRATIONS (% EFF.) AND RESPONSE MEANS **«
CONC. (JSEFF) RESPONSE MEAN MEAN AFTER POOLING
.000 .715 .715
32.000 .674 .675
64.000 .677 .675
128.000 .623 .623
256.000 .581 .581
512.000 .471 .471
THE LINEAR INTERPOLATION ESTIMATE OF THE TOTAL IMPACT CONCENTRATION
FROM THE INPUT SAMPLE IS 360.3287.
«««»«««K«ff«*«»««K««*ft«««Ktt«««««««««**«««Ktt*«»ft««K«K««tt«*««Kff
* BOOTSTRAP PROCEDURE TO ESTIMATE VARIABILITY «
* OF THE ESTIMATED ICp *
THE MEAN OF THE BOOTSTRAP ESTIMATES IS 349. 6990.
THE STANDARD DEVIATION OF THE BOOTSTRAP ESTIMATES IS 62.3066.
AN EMPIRICAL 94.9* CONFIDENCE INTERVAL FOR THE
BOOTSTRAP ESTIMATE IS- (253.2589,451.3332).
«*» NOTE: THE ABOVE BOOTSTRAP CALCULATIONS WERE BASED ON 79
INSTEAD OF 80 RESAMPLINGS. THOSE RESAMPLES NOT
USED HAD ESTIMATES ABOVE THE HIGHEST CONCENTRATION / % EFF.
Figure 11. BOOTSTRP program output for the IC25.
71D
-------
September 1989
(Revision 1}
THE NUMBER OF RESAMPLES IS 60
**» LISTING OF GROUP CONCENTRATIONS (56 EFF.) AND RESPONSE MEANS *»*
CONC. (£EFF) RESPONSE MEAN MEAN AFTER POOLING
.000 .715 .715
32. 000 .674 .675
64.000 .677 .675
128.000 .623 .623
256.000 .581 .581
512.000 .471 .471
*** NO LINEAR INTERPOLATION ESTIMATE CAN BE CALCULATED FROM THE INPUT
DATA, SINCE NONE OF THE (POSSIBLY POOLED) GROUP RESPONSE MEANS
WERE LESS THAN 50.058 OF THE CONTROL RESPONSE MEAN.
«**««X«X«tf*«XXXX««ffXX*XXttX«XX«KXXKXXKXXXX«XXXKK«tfXXKX«RXft«*«
* BOOTSTRAP PROCEDURE TO ESTIMATE VARIABILITY *
* OF THE ESTIMATED ICp «
ft*«XX«X»«XXXX«Xft««XXffKX«*XXX«XXXXXXX«XXft«XXXKXX«XXXKXXKX««X«
«» BOOTSTRAP ESTIMATES OF ICp FOR ALL RESAMPLES WERE ABOVE THE
HIGHEST CONCENTRATION / % EFF.
Figure 12. BOOTSTRP program output for the IC50.
71E
-------
September 1989
(Revision 1)
13. PRECISION AND ACCURACY
13.1 PRECISION
13.1.1 Information on the single laboratory precision of the fathead minnow
larval survival and growth test is presented in Table 20. The range of NOECs
was only two concentration intervals, indicating good precision.
13.1.2 An interlaboratory study of Method 1000.0 described in the first
edition of this manual (Horning and Weber, 1985), was performed using seven
blind samples over an eight month period (DeGraeve, et. al., 1988). In this
study, each of the 10 participating laboratories was to conduct two tests
simultaneous with each sample, each test having two replicates of 10 larvae
for each of five concentrations and the control. Of the 140 tests planned,
135 were completed. Only nine of the 135 tests failed to meet the acceptance
criterion of 80% survival in the controls. Of the 126 acceptable survival
NOECs reported, an average of 41% were median values, and 89% were within one
concentration interval of the median (Table 21). For the growth (weight)
NOECs, an average of 32* were at the median, and 84% were within one
concentration interval of the median (Table 22). Using point estimate
techniques, the precision (CV) of the IC50 was 19.5% for the survival data and
19.8% for the growth data. If the mean weight acceptance criterion of 0.25 mg
for the surviving control larvae, which is now included in this revised
edition of the method, had been applied to the results of the interlaboratory
study, 40 of the 135 completed tests would have been considered unacceptable
(Horberg-King, 1988).
13.2 ACCURACY
13.2.1 The accuracy of toxicity tests can not be determined.
71F
-------
September 1989
(Revision 1)
TABLE 20. PRECISION OF THE FATHEAD MINNOW LARVAL SURVIVAL
AND GROWTH TEST, USING MAPCP AS A REFERENCE TOXICANTS.b
NOEC
Test (ug/L)
1 256
2 128
3 256
4 128
5 128
LOEC
(ug/L)
512
256
512
256
256
Chronic
Value
(ug/L)
362
181
362
181
181
Pickering, 1988.
bFor a discussion of the precision of data from chronic toxicity
tests see Section 4, Quality Assurance.
72
-------
September 1989
(Revision 1)
TABLE 21. COMBINED FREQUENCY DISTRIBUTION FOR SURVIVAL NOECs
FOR ALL LABORATORIES*
NOEC Fr
Tests wltFTwo
Sample
1. Sodium Pentachlorophenate (A)
2. Sodium Pentachlorophenate (B)
3. Potassium Dlchromate (A)
4. Potassium Dlchromate (B)
5. Refinery Effluent 301
6. Refinery Effluent 401
7. Utility Waste 501
Median
35
42
47
41
26
37
56
*,b
53
42
47
41
68
53
33
equency
Reps
>2C
12
16
6
18
6
10
11
(%) Distribution
Tests with Four Reps
Median
57
56
75
50
78
56
56
±ifc
29
44
25
50
22
44
33
>*
14
0
0
0
0
0
11
aFrom DeGraeve et. al., 1988.
bPercent of values within one concentration intervals of the median.
cPercent of values within two or more concentrations Intervals of the median.
73
-------
September 1989
(Revision 1)
TABLE 22. COMBINED FREQUENCY DISTRIBUTION FOR WEIGHT NOECs
FOR ALL LABORATORIES*
1.
2.
3.
4.
5.
6.
7.
Sample
Sodium Pentachlorophenate (A)
Sodium Pentachlorophenate (B)
Potassium Dichromate (A)
Potassium Dichromate (B)
Refinery Effluent 301
Refinery Effluent 401
Utility Waste 501
Tests
Median
59
37
35
12
35
37
11
NOEC Fre
with Two
±ib
41
63
47
47
53
47
61
Suency
eps
>2C
0
0
18
41
12
16
28
(%) Distribution
Tests with
Median +
57
22
88
63
75
33
33
Four
i- ,
43
45
0
25
25
56
56
Reps
2c
0
33
12
12
0
11
11
aFrom DeGraeve et. al., 1988.
^Percent of values within one concentration intervals of the median.
cPercent of values within two or more concentrations Intervals of the median.
74
-------
September 1989
(Revision 1)
PART 3
REPLACEMENT PAGES FOR SECTION 12
(pp. 143A-143F, and 144-146)
-------
September 1989
(Revision 1)
The mean reproduction for concentration "1" Is considered significantly less
than the mean reproduction for the control If tj 1s greater than the
critical value. Since ts Is greater than 2.23, the 12.5% concentration has
significantly lower reproduction than the control. Hence the NOEC and the
LOEC for reproduction are 6.25% and 12.5%, respectively.
13.3.8.7 To quantify the sensitivity of the test, the minimum significant
difference (MSD) that can be statistically detected may be calculated.
MSD = d Sw V d/ni) + (1/n)
Where d = the critical value for the Dunnett's procedure
SN = the square root of the within mean square
n = the common number of replicates at each concentration
(this assumes equal replication at each concentration
nj = the number of replicates in the control.
13.3.8.8 In this example:
MSD = 2.23 (5.64) V d/10) + (1/10)
= 2.23 (5.64H0.45)
= 5.66
13.3.8.9 Therefore, for this set of data, the minimum difference that can be
detected as statistically significant Is 5.66.
13.3.8.10 This represents a 25% decrease In mean reproduction from the
control.
13.3.9 Calculation of the 1C
13.3.9.1 The reproduction data in Table 4 are utilized in this example. As
can be seen from Figure 7, the observed means are not monotonlcally
non-increasing with respect to concentration. Therefore, the means are
smoothed prior to calculating the 1C.
13.3.9.2 Starting with the observed control mean, Yj = 22.4, and
the observed mean for the lowest effluent concentration, ?2 = 26.3, we see
that YI is less than Y2.
13.3.9.3 Calculate the smoothed means;
MI = MZ » (Yi + Yg)/2 = 24.35
13.3.9.4 Since YS = 34.6 Is larger than Mg, average YS with the
previous concentrations:
M! = Me a M3 = (Mi + M£ + Y3)/3 = 27.7.
143A
-------
50-
CO
40
2 30 1?
o
Ob
o
H
I 201
10-
0 •)
I
0.00
1.50
INDIVIDUAL NUUBER OF YOUNG
CONNECTS THE OBSERVED UEAN VALUE
CONNECTS THE SMOOTHED MEAN VALUE
3.12 8.35
EFFLUENT CONCENTRATION (X)
12.50
25.00
•X3 n
3 -J
Figure 7. Plot of raw data, observed means, and smoothed means for
Cerlodaphnia reproduction data.
-------
September 1989
(Revision 1)
13.3.9.5 Additionally. Y4 = 31.7 is larger than Ma, and is pooled with
the first three means. Thus:
(M! + Mg + MS + 74)74 = 28.7 = M] = Mg • MS = M4
13.3.9.6 Since M4 > TS = 9.4, set MS = 9.4. Likewise, MS > Ye » 0,
and MS becomes 0. Table 15 contains the smoothed means and Figure 7 gives a
plot of the smoothed means and the Interpolated response curve.
TABLE 15. CERIODAPHNIA REPRODUCTION MEAN
RESPONSE AFTER SMOOTHING
Effluent
Cone
W
Control
1.56
3.12
6.25
12.5
25.0
1
1
2
3
4
5
6
Mi
28.75
28.75
28.75
28.75
9.40
0.00
13.3.9.7 An IC25 and IC50 can be estimated using the Linear Interpolation
Method. A 251 reduction in reproduction, compared to the controls, would
result in a mean reproduction of 21.56 young per adult, where M-jll - p/100)
a 28.75(1 - 25/100). A 50% reduction In reproduction, compared to the
controls, would result in a mean reproduction of 14.38 young per adult, where
M](l - p/100) - 28.75(1 - 50/100). Examining the smoothed means and their
associated concentrations (Table 15), the two effluent concentrations
bracketing 21.56 young per adult are €4 = 6.25% effluent and Cs = 12.5%
effluent. The two effluent concentrations bracketing a response of 14.4 young
per adult are also 64 = 6.25% and Cs = 12.5%.
13.3.9.6 Using Equation 1 from Appendix J, the IC25 estimate Is 8.6% effluent:
icp = Cj + [Mid - p/ioo) - MJ]
-------
September 1989
(Revision 1)
13.3.9.9 The IC50 estimate is 10.9% effluent:
icp = Cj + [MI(I - p/ioo) - MJ](CJ+I - c0)
-------
September 1989
(Revision 1)
THE NUMBER OF RESAMPLES IS 80
«** LISTING OF GROUP CONCENTRATIONS (X EFF.) AND RESPONSE MEANS ««*
CONC. (XEFF) RESPONSE MEAN MEAN AFTER POOLING
. 000 22. 400 28. 750
1.560 26.300 28.750
3.120 34.600 28.750
6.250 31.700 28.750
12.500 9.400 9.400
25.000 .000 .000
THE LINEAR INTERPOLATION ESTIMATE OF THE TOTAL IMPACT CONCENTRATION
FROM THE INPUT SAMPLE IS 8.5715.
* BOOTSTRAP PROCEDURE TO ESTIMATE VARIABILITY «
* OF THE ESTIMATED ICp «
THE MEAN OF THE BOOTSTRAP ESTIMATES IS 8.6486.
THE STANDARD DEVIATION OF THE BOOTSTRAP ESTIMATES IS .1102.
AN EMPIRICAL 95. OX CONFIDENCE INTERVAL FOR THE
BOOTSTRAP ESTIMATE IS ( 8.4150, 8.8677).
Figure 8. BOOTSTRP program output for the IC25,
143E
-------
September 1989
(Revision 1}
THE NUMBER OF RESAMPLES IS 80
*** LISTING OF GROUP CONCENTRATIONS (X EFF.) AND RESPONSE MEANS »*«
CONG. (XEFF) RESPONSE MEAN MEAN AFTER POOLING
.000 22.400 28.750
1.560 26.300 28.750
3.120 34.600 28.750
6.250 31.700 26.750
12.500 9.400 9.400
25.000 .000 .000
THE LINEAR INTERPOLATION ESTIMATE OF THE TOTAL IMPACT CONCENTRATION
FROM THE INPUT SAMPLE IS 10.8931.
****«*#«###*«*«*«******«#*****«**********«*#*«*********»#***
* BOOTSTRAP PROCEDURE TO ESTIMATE VARIABILITY «
* OF THE ESTIMATED ICp *
THE MEAN OF THE BOOTSTRAP ESTIMATES IS 11.0473.
THE STANDARD DEVIATION OF THE BOOTSTRAP ESTIMATES IS .2205.
AN EMPIRICAL 95. OX CONFIDENCE INTERVAL FOR THE
BOOTSTRAP ESTIMATE IS ( 10.5800* 11.4854).
Figure 9. BOOTSTRP program output for the IC50.
143F
-------
September 1989
(Revision 1)
14.1.2.3 An second Interlaboratory study of Method 1002.0 (using the first
edition of this manual; Horning and Weber, 1985), was coordinated by Battelle,
Columbus Division, and Involved 11 participating laboratories (DeGraeve et al.,
1989). All participants used 10% DMW (101 PERRIERR Water) as the culture and
dilution water, and used their own formulation of food for culturlng and
testing the Cerlodaphnla. Each laboratory was to conduct at least one test
with each of eight blind samples. Each test consisted of 10 replicates of one
organism each for five toxicant concentrations and a control. Of the 116 tests
planned, 91 were successfully Initiated, and 70 (77%) met the survival and
reproduction criteria for acceptability of the results (80% survival and nine
young per Initial female). The overall precision (CV) of the test was 27% for
the survival data (7-day LCSOs) and 40% for the reproduction data (ICSOs).
14.2 ACCURACY
14.2.1 The accuracy of toxlclty tests cannot be determined.
144
-------
September 1989
(Revision 1)
TABLE 16. SINGLE LABORATORY PRECISION OF THE CERIODAPHNIA SURVIVALMD
REPRODUCTION TEST, USING NAPCP AS A REFERENCE TOXICANT* .»>
Test
1C
2d
3
4*
5
6
7
8
9
NOEC
(mg/U
0.25
0.20
0.20
0.30
0.30
0.30
0.30
0.30
0.30
LOEC
(mg/Ll
0.50
0.60
0.60
0.60
0.60
0.60
0.60
0.60
0.60
Chronic
Value
(mg/L)
0.35
0.35
0.35
0.42
0.42
0.42
0.42
0.42
0.42
aFor a discussion of the precision of data from chronic toxlclty
tests see Section 4, Quality Assurance.
bData from tests performed by Philip Lewis, Aquatic Biology Branch,
EMSL-Clnclnnatl. Tests were conducted In reconstituted hard water
(hardness = 180 mg CaCOa/L; pH = 8.1).
^Concentrations used In Test 1 were: 0.03, 0.06, 0.12, 0.25, 0.50,
1.0 mg NaPCP/L.
^Concentrations used In Tests 2 and 3 were: 0.007, 0.022, 0.067,
0.20, 0.60 mg NaPCP/L.
eConcentratfons used In Tests 4 through 9 were: 0.0375, 0.075,
0.150, 0.30, 0.60 mg NaPCP/L.
145
-------
September 1989
(Revision 1)
TABLE 17. INTERLABORATORY PRECISION OF CERIODAPHNIA SURVIVAL
AND REPRODUCTION TEST
1
Endpofnts (% Effluent)
Analyst
3
4
4
5
5
6
6
10
10
11
Test
1
1
2
1
2
1
2
1
2
1
Reproduction
NOEC
12
6
6
6
12
12
6
6
6
12
LOEC
25
12
12
12
25
25
12
12
12
25
Survival
NOEC
25
12
25
12
12
25
25
12
12
25
LOEC
50
25
50
25
25
50
50
25
25
50
iFrom Nelhelsel et al., 1988a.
146
-------
September 1989
(Revision 1}
PART 4
INSERT FOR (NEW) APPENDIX J
(pp. 250-262)
-------
September 1989
(Revision 1)
APPENDIX J
LINEAR INTERPOLATION METHOD
1. GENERAL PROCEDURE
1.1 The Linear Interpolation Method Is used to calculate a point estimate of
the effluent or other toxicant concentration that causes a given percent
reduction (e.g., 25%, 50%, etc.) In the reproduction or growth of the test
organisms (Inhibition Concentration, or 1C). The procedure was designed for
general applicability In the analysis of data from short-tern chronic toxiclty
tests, and the generation of an endpolnt from a continuous model that allows a
traditional quantitative assessment of the precision of the endpoint, such as
confidence limits for the endpolnt of a single test, and a mean and
coefficient of variation for the endpoints of multiple tests.
1.2 The Linear Interpolation Method assumes that the responses (1) are
monotonlcally non-Increasing, where the mean response for each higher
concentration 1s less than or equal to the mean response for the previous
concentration, (2) follow a piecewise linear response function, and (3) are
from a random, Independent, and representative sample of test data. If the
data are not monotonlcally non-Increasing, they are adjusted by smoothing
(averaging). In cases where the responses at the low toxicant concentrations
are much higher than in the controls, the smoothing process may result in a
large upward adjustment in the control mean. Also, no assumption is made
about the distribution of the data except that the data within a group being
resampled are Independent and Identically distributed.
2. DATA SUMMARY AND PLOTS
2.1 Calculate the mean responses for the control and each toxicant
concentration, construct a summary table, and plot the data.
3. MONOTONICITY
3.1 If the assumption of monotonicity of test results 1s met, the observed
response means (if) should stay the same or decrease as the toxicant
concentration Increases. If the means do not decrease monotonlcally, the
responses are "smoothed" by averaging (pooling) adjacent means.
3.2 Observed means at each concentration are considered in order of
Increasing concentration, starting with the control mean (V-\). If the mean
observed response at the lowest toxicant concentration (72) is equal to or
smaller than the control mean (Y-|), it Is used as the response. If it is
larger than the control mean, 1t is averaged with the control, and this
average is used for both the control response (M])and the lowest toxicant
concentration response (M2). This mean 1s then compared to the mean
observed response for the next higher toxicant concentration (73). Again,
if the mean observed response for the next higher toxicant concentration Is
smaller than the mean of the control and the lowest toxicant concentration, it
250
-------
September 1969
(Revision 1}
Is used as the response. If It Is higher than the mean of the first two, 1t
fs averaged with the first two, and the mean 1s used as the response for the
control and two lowest concentrations of toxicant. This process 1s continued
for data from the remaining toxicant concentrations. A numerical example of
smoothing the data Is provided below. (Note: Unusual patterns In the
deviations from monoton1city may require an additional step of smoothing).
Where Yf decrease monotonlcally, the Y^ become Mj without smoothing.
4. LINEAR INTERPOLATION METHOD
4.1 The method assumes a linear response from one concentration to the next.
Thus, the 1C Is estimated by linear Interpolation between two concentrations
whose responses bracket the response of Interest, the (p) percent reduction
from the control.
4.2 To obtain the estimate, determine the concentrations Cj and
which bracket the response Mid - p/100), where MI Is the smoothed control
mean response and p 1s the percent reduction In response relative to the
control response. The linear interpolation estimate is calculated as follows:
ICp = Cj + [Mid - p/100) - Mj](CJ+1 - Cj) d)
where: Cj = The tested concentration whose observed
mean response is greater than M](l - p/100).
= The tested concentration whose observed
mean response is less than MI(! - p/100).
MI = Smoothed mean response for the control.
Mj • Smoothed mean response for concentration J.
Mj+i = Smoothed mean response for concentration J+l.
p = Percent reduction in response relative to
the control response.
ICp » The estimated concentration at which there 1s
p% reduction from the smoothed mean control response.
This ICp is reported for the test, together with
the 95% confidence Interval from the Bootstrap Method,
as described below.
4.3 If Cj is the highest concentration tested, then the ICp is specified as
"greater than Cj".
251
-------
September 1989
(Revision 1)
5. CONFIDENCE INTERVALS
5.1 Due to the use of a linear Interpolation technique to calculate an
estimate of the ICp, standard statistical methods for calculating confidence
Intervals are not applicable for the ICp. This limitation 1s avoided by
using the Bootstrap Method proposed by Efron (1982) for deriving point
estimates and confidence Intervals.
5.2 In the Linear Interpolation Method, the smoothed response means are
used to obtain the ICp estimate reported for the test. The Bootstrap Method
1s then used to determine the 951 confidence Interval for the true mean. In
the Bootstrap Method, the test data, Yjf, are randomly resampled with
replacement, to produce a new set of data, Yji*. that is statistically
equivalent to the original data set, but which produces a new and somewhat
different estimate of the ICp (ICp*). This process 1s repeated many times
(80 times In the Linear Interpolation Method described In Marcus and
Holtzman, 1988), resulting 1n multiple "data" sets, each with an associated
ICp estimate. The distribution of the ICp estimates derived from the
sets of resampled data approximates the sampling distribution of the ICp
estimate. The standard error of the ICp is estimated by the standard
deviation of the individual ICp estimates. Empirical confidence
Intervals are derived from the quantiles of the ICp empirical
distribution. For example, If the test data are resampled a minimum of 80
times, the empirical 2.5% and 97.5% confidence limits are approximately the
second smallest and second largest ICp estimates (Battelle, 1987).
5.3 The width of the confidence Intervals calculated by the Bootstrap
Method Is related to the variability in the data. When the Intervals are
wide, the reliability of the 1C estimate Is in question. However, narrow
intervals do not necessarily Indicate that the estimate 1s highly reliable,
because of undetected violations of assumptions and the fact that confidence
limits based on the empirical quantiles of a Bootstrap distribution of 80
resamples may be unstable.
5.4 The Bootstrap Method is computationally intensive, and not amenable to
hand calculations. For this reason, all of the calculations associated with
the Linear Interpolation Method have been incorporated into a single
computer program, BOOTSTRP, described in Paragraph 7 below.
6. MANUAL CALCULATIONS
6.1 Data Summary and Plots
6.1.1 The data used in this example are the Ceripdaphnia reproduction data
used in the example In Section 12. Table J.I includes the raw data and the
mean reproduction for each concentration. Data are included for all animals
tested regardless of death or survival of the organism. If an animal died
during the test without producing young, a zero is entered. If death
occurred after producing young, the number of young produced prior to death
is entered. A plot of the data is provided in Figure J.I.
252
-------
50
ro
in
OJ
o -l
0.00
**** INDIVIDUAL NUMBER OP YOUNG
CONNECTS THE OBSERVED UEAN VALUE
CONNECTS THE SMOOTHED MEAN VALUE
1.56
3.12 6.25
EFFLUENT CONCENTRATION (X)
12.50
25.00
< rt-
I"?
c»
Figure J.I. Plot of observed and smoothed means for Cerlodaphnia reproduction data.
-------
September 1989
(Revision 1)
TABLE J.I. CERIODAPHNIA REPRODUCTION DATA
Effluent Concentration (%)
Replicate
1
2
3
4
5
6
7
8
9
10
Mean (Yj)
1
Control
27
30
29
31
16
15
18
17
14
27
22.4
1
1.56
32
35
32
26
18
29
27
16
35
13
26.3
2
3.12
39
30
33
33
36
33
33
27
38
44
34.6
3
6.25
27
34
36
34
31
27
33
31
33
31
31.7
4
12.5
10
13
7
7
7
10
10
16
12
2
9.4
5
25.0
0
0
0
0
0
0
0
0
0
0
0
6
6.2 Monotonicity
6.2.1 As can be seen from the plot, Figure J.I, the observed means are not
monotonlcally non-Increasing with respect to concentration. Therefore, the
means must be smoothed prior to calculating the 1C.
6.2.2_ Starting with ttie control mean, YI = 22.4, and ¥2 = 26.3, we see
that Y] Is less than Y2.
6.2.3 Calculate the smoothed means;
MT = MZ = (Y! + Y2)/2 = 24.35
6.2.4 Since J$ = 34.6 Is larger than M2, average YS with the previous
concentrations:
MI = M2 = MS = (Mi + M2 + Ya)/3 = 27.7.
6.2.5 Additionally, Y4 = 31.7 Is larger than M3, and Is pooled with the
first three means. Thus:
+ M2 + Ma + Y4)/4 = 28.7 = MI = M2 = MS = MA
254
-------
September 1989
(Revision 1)
6.2.6 Since M4 > Y5 = 9.4, set MS = 9.4. Likewise, MS > ?e - 0,
and Mg becomes 0. Table J.2 contains the smoothed means and Figure J.I
gives a plot of the smoothed response curve.
TABLE J.2. CERiODAPHNIA REPRODUCTION MEAN
RESPONSE AFTER SMOOTHING
Cone
Control
1.56
3.12
6.25
12.5
25.0
1
1
2
3
4
5
6
«i
28.75
28.75
28.75
28.75
9.40
0.00
6.3 Linear Interpolation
6.3.1 Estimates of the IC25 and IC50 can be calculated using the Linear
Interpolation Method. A 251 reduction In reproduction » compared to the
controls, would result 1n a mean reproduction of 21.56 young per adult, where
Mi(1 - p/100) = 28.75(1 - 25/100). A 50% reduction in reproduction,
compared to the controls, would result In a mean reproduction of 14.38 young
per adult, where MI(! - p/100) = 28.75(1 - 50/100}. Examining the smoothed
means and their associated concentrations (Table 15), the two effluent
concentrations bracketing 21.56 young per adult are €4 = 6.25* effluent and
Cs = 12.5* effluent. The two effluent concentrations bracketing a response
of 14.38 young per adult are also 04 = 6.25 and Cs = 12.5.
6.3.2 Using Equation 1 from 4.2, the IC25 estimate Is 8.6% effluent:
ICp = Cj + [Mi(1 - p/100) - Mj](CJ+1 - Cj)
IC25 = 6.25 + [28.75(1 - 25/100) - 28.753(12.5 - 6.25)
(9.40 - 28.75)
• 8.57% effluent
6.3.3 The IC50 estimate is 10.9% effluent:
ICp = Cj + [M](l - p/100) - Mj](CJ+1 - Cj)
IC50 = 6.25 + [28.75(1 - 50/100) - 28.75](12.5 - 6.25)
- 10.89% effluent (9'40 - Z8'75)
255
-------
September 1989
(Revision 1)
6.4 Confidence Intervals
6.4.1 Confidence intervals for the ICp are derived using the Bootstrap
Method. As described above, this method involves randomly resampling the
individual observations and recalculating the ICp at least 80 times, and
determining the mean ICp, standard deviation, and empirical 95% confidence
interval. For this reason it is not practical to perform these calculations
manually. However, a computer program, BOOTSTRP, described below, 1s
available to carry out all of the calculations, including the Bootstrap
Method, required for the Linear Interpolation Method.
7. COMPUTER CALCULATIONS
7.1 The computer program, BOOTSTRP, prepared for the Linear Interpolation
Method, was written in Fortran for IBM compatible PCs. The program was
developed by the Battelle Laboratories, Columbus, Ohio, with funding from the
Environmental Research Laboratory, U. S. Environmental Protection Agency,
Duluth, Minnesota (Norberg-King, 1988). A compiled version of the program and
program documentation are available from EMSL-Cincinnati.
7.2 BOOTSTRP performs the following functions: (1) calculates the observed
response means (7,), (2) checks the responses for monotonicity, (3)
calculates smoothed means (M-j) if necessary, (4) uses the means, Mf, to
calculate the initial ICp of choice by linear interpolation, (5) performs a
user-specified number of Bootstrap Method resamples, (6) calculates the mean
and standard deviation of the Bootstrap ICp estimates, and (7) provides an
empirical 95% confidence interval to be used with the initial ICp.
7.3 A maximum number of 8 concentrations and 10 replicates per concentration
are allowed by the program. Equal replication across all concentrations is
not required. The value of p can range from 1% to 99%.
7.4 Data Input.
7.4.1 Data may be entered on the screen or read from an external file.
Instructions for creating external data files, such as with the use of Word
Perfect, are included with the documentation.
7.4.2 When data are entered on the screen, the program prompts the user for
the following information:
1. Concentration group number
2. Concentration amount (i.e. percent effluent)
3. Response (i.e. weight, number of young)
7.4.2.1 After data values have been entered, the program displays them on the
screen and prompts the user to verify them. An example of sample data input
on the screen is shown in Figure J.2.
7.4.3 When data are entered from an existing file, the program prompts the
user for the file name. An example of sample data input using an existing
file is shown in Figure J.3.
256
-------
September 1989
(Revision 1)
ENTER "S" IF DATA KILL BE INPUT TO THE PROGRAM ON THE SCREEN.
ENTER "F" IF DATA WILL BE INPUT THROUGH AN INPUT FILE.
ENTER "S" OR "F"i S
WHEN PROMPTED FOR THE CONCENTRATION GROUP NUMBER, THE NUMBER SHOULD
BE AN INTEGER FROM 1 TO 8. GROUP NUMBER 1 CORRESPONDS TO THE CONTROL
GROUP, GROUP NUMBER 2 CORRESPONDS TO THE LOWEST CONCENTRATION GROUP,
CONTINUING TO THE HIGHEST ASSIGNED GROUP NUMBER WHICH CORRESPONDS TO
THE HIGHEST CONCENTRATION GROUP.
ENTER THE CONCENTRATION GROUP NUMBER (1,2,...)
(ENTER "X" TO EXIT THE INPUT PROCEDURE): 1
ENTER THE CONCENTRATION (IN MG/L, % EFFLUENT, ETC.): .000
ENTER THE RESPONSE VALUE: 27
YOU HAVE ENTERED THE FOLLOWING VALUES:
CONCENTRATION ID = 1
CONCENTRATION = .000
RESPONSE = 27.000-
PRESS RETURN IF THESE VALUES ARE CORRECT.
PRESS "X", THEN RETURN, IF ANY OF THE VALUES ARE INCORRECT:
THESE VALUES HAVE BEEN SUCCESSFULLY INPUT TO THE PROGRAM.
THE NEXT SET OF VALUES CAN NOW BE ENTERED.
Figure J.2. Example of BOOTSTRP program data Input
on the screen.
257
-------
September 1989
(Revision 1)
ENTER "S" IF DATA WILL BE INPUT TO THE PROGRAM ON THE SCREEN.
ENTER "F" IF DATA WILL BE INPUT THROUGH AN INPUT FILE.
ENTER "S" OR "F": F
ENTER THE INPUT FILE NAME (SPECIFYING THE DRIVE AND
SUBDIRECTORY IF NECESSARY): cerlcp.2
ENTER THE VALUE OF P, THE DESIRED PERCENT REDUCTION IN RESPONSE
RELATIVE TO THE CONTROL GROUP (P = 50 IS THE DEFAULT): 25
THE VALUE OF P IS 25.0
ENTER THE NUMBER OF BOOTSTRAP RESAMPLES TO BE TAKEN
(80 IS THE RECOMMENDED NUMBER): 80
Figure J.3. Example of BOOTSTRP program data Input
from an existing data file.
258
-------
September 1989
(Revision 1)
7.4.4 After all of the data have been entered, the user is asked to enter the
ICp estimate desired (e.g., IC25 or IC50) and the number of Bootstrap Method
resamples that are to be taken. The program has the capability of performing
any number of resamples from 2 - 200. However, Marcus and Holtzman (1986)
recommend that a minimum of 80 Bootstrap Method resamples be used (see Figure
J.3 for example).
7.5 Data Output
7.5.1 BOOTSTRP program output includes the following:
1. A table of .the test concentrations, observed response means (7j),
and smoothed (pooled) means (Mj).
2. The linear interpolation estimate of the ICp using the means, Mj.
(This ICp is reported for the test.)
3. The mean ICp and standard deviation from the Bootstrap Method
resampling.
4. The empirical 95% confidence interval calculated by the Bootstrap
Method for the ICp. (This confidence interval is used for ICp
obtained in Item 2, above.
7.6 Output From Ceriodaphnia Data Analysts
7.6.1 BOOTSTRP program output for the analysis of the Ceriodaphnia
reproduction data in Table J.I is provided in Figures J.4 and J.5.
7.6.2 Using 80 resamples, the mean of the IC25 estimates was 8.6, with a
standard deviation of 0.22 (coefficient of variation = 2%), and the empirical
confidence interval was (8.4 - 8.9).
7.6.3 Using 80 resamples, the mean of the IC50 estimates was 11.0, with a
standard deviation of 0.22 (coefficient of variation = 2%). The empirical 95S
confidence interval was (10.6 - 11.5).
259
-------
September 1989
(Revision 1)
THE NUMBER OP RESAMPLES IS 80
»•» LISTING OF GROUP CONCENTRATIONS (X EFF.) AND RESPONSE MEANS «»
CONC. (*EFF) RESPONSE MEAN MEAN AFTER POOLING
.000 22.400 28.750
1.560 26.300 28.750
3.120 34.600 28.750
6.250 31.700 28.750
12.500 9.400 9.400
25.000 .000 .000
THE LINEAR INTERPOLATION ESTIMATE OF THE TOTAL IMPACT CONCENTRATION
FROM THE INPUT SAMPLE IS 8.5715.
««**««««**««««*»#««««»**#**«**»«****»***«***«*****»««******
* BOOTSTRAP PROCEDURE TO ESTIMATE VARIABILITY *
* OF THE ESTIMATED ICp
THE MEAN OF THE BOOTSTRAP ESTIMATES IS 8. 6486.
THE STANDARD DEVIATION OF THE BOOTSTRAP ESTIMATES IS .1102.
AN EMPIRICAL 95. 0* CONFIDENCE INTERVAL FOR THE
BOOTSTRAP ESTIMATE IS ( 8.4150, 8.8677).
Figure J.4. Example of BOOTSTRP program output
for the IC25.
260
-------
September 1989
(Revision 1}
THE NUMBER OF RESAMPLES IS 80
*** LISTING OF GROUP CONCENTRATIONS <* EFF.) AND RESPONSE MEANS *«*
CONC. (J6EFF) RESPONSE MEAN MEAN AFTER POOLING
. 000 22.400 28.750
1.560 26.300 28.750
3.120 34.600 28.750
6.250 31.700 28.750
12.500 9.400 9.400
25.000 .000 .000
THE LINEAR INTERPOLATION ESTIMATE OF THE TOTAL IMPACT CONCENTRATION
FROM THE INPUT SAMPLE IS 10.8931.
* BOOTSTRAP PROCEDURE TO ESTIMATE VARIABILITY *
* OF THE ESTIMATED ICp *
THE MEAN OF THE BOOTSTRAP ESTIMATES IS 11.0473.
THE STANDARD DEVIATION OF THE BOOTSTRAP ESTIMATES IS .2205.
AN EMPIRICAL 95. OX CONFIDENCE INTERVAL FOR THE
BOOTSTRAP ESTIMATE IS ( 10.5800, 11.4854).
Figure J.5. Example of BOOTSTRP program output
for the IC50.
261
-------
September 1989
(Revision 1)
REFERENCES
1. Efron, B. 1982. The Jackknife, the Bootstrap, and other resampling
plans. CBMS 38, Soc. Industr. Appl. Math., Philadelphia, PA.
2. DeGraeve, G. M., J. D. Cooney, T. L. Pollock, N. G. Relchenbach,
J. H. Dean, M. D. Marcus, and D. 0. Mclntyre. 1988. Fathead
minnow 7-day test: round robin study. Intra- and Interlaboratory
study to determine the reproduclblllty of the seven-day fathead
minnow larval survival and growth test. Battelle Columbus
Division, Columbus, Ohio.
3. Marcus, A. H., and A. P. Holtzman. 1988. A robut statistical method
for estimating effects concentrations In short-term fathead minnow
toxidty tests. Manuscript submitted to the Criteria and
Standards Division, U. S. Environmental Protection Agency, by
Battelle Washington Environmental Program Office, Washington, DC,
June 1988, under EPA Contract No. 69-03-3534. 39 pp.
4. Norberg-King, T. J. 1988. An interpolation estimate for chronic
toxicity: The ICp approach. Technical Report 05-88, National
Effluent Toxicity Assessment Center, Environmental Research
Laboratory, U. S. Environmental Protection Agency, Duluth,
Minnesota.
262
ammrnot namm ana MIW.-UVOOJM
------- |