The Test for Significant
Toxicity (TST) – A “New”
Hypothesis Testing Approach
for Aquatic Bioassay Testing
Philip Markle
Environmental Scientist
pmarkle@lacsd.org
History of the TST

June 2010 – EPA released WET TST guidance
(EPA 833-R-10-003)

Also referred as:
– Bioequivalence Testing
– Alternative Null Hypothesis Testing



Accepted for FDA drug trials and evaluations
Originally proposed for use in toxicity testing in
1995 (Erickson and McDonald)
Recently proposed for CA’s WET Policy
Limitations of the TST

It is still a statistical hypothesis test
– Not very useful for comparing results
spatially or temporally
– Pass/Fail test, provides no information
on magnitude


Requires knowledge/use of a
“threshold” response – “b” or
bioequivalence factor
Probably (and debatably) best suited for
regulatory purposes
Statistical Hypothesis
Testing 101

Statistical speaking;
– You can’t “prove” anything with a
hypothesis test – we only “disprove”

The “White Swan” Parable:
Statistical Hypothesis
Testing 101



You can’t prove that “all swans are white”
If we see 10,000 white swans and no
non-white swans, we fail reject our
hypothesis
In the absence of evidence to the
contrary, we then assume the hypothesis
is true
“Proving” with Statistics

However, after observing just one nonwhite swan, we can then confidently
reject or disprove our hypothesis that all
swans are white
Statistical Hypothesis
Testing - Background

Null or “Initial” Hypothesis (Ho)
– Mean(sample)  Mean(control)



Conduct statistical analyses to try to
reject this hypothesis
If unable to reject, we assume the null
or “Initial” hypothesis is correct
Type I and Type II error
Type I and Type II Errors

Type I Error
– Probability of rejecting when the null or
“Initial” hypothesis when it is “true”
– Controlled directly by setting alpha ()

Type II Error
– Probability of accepting the null or
“Initial” hypothesis when it is “false”
– Also called “power” ()
– Controlled indirectly
Standard Hypothesis Testing
(NOEC)

With the NOEC:
– The initial hypothesis is
mean (sample)  mean (control)
In other words, the sample is non-toxic!
– If we don’t/can’t “prove” this to be
incorrect statistically, we assume it is
true
– Type I error = Identifying a non-toxic
sample as toxic
TST Hypothesis

With the TST:
– The hypothesis is
mean(effluent) =/< 0.75 * mean(control)
In other words, the sample is toxic!
– If we don’t/can’t “prove” this to be
incorrect statistically, we assume it is
true – we assume the sample is toxic
– Type I error = Identifying a toxic sample
as non-toxic
Bioequivalence Factor (b)

In the EPA Guidance
– Set as an unacceptable or “toxic”
threshold

For Chronic:
– B = 0.75 = 25% Effect

For Acute
– B = 0.80 = 20% Effect
Regulatory Management
Decisions (RMDs)

Setting the Type I Error Rate–alpha ()
– How frequent will you reject the Ho when
it is true?

EPA desires that no more than 25% of
the tests with a 25% effect or more are
identified as “non-toxic”
 Alpha () is then set at 0.05 to 0.25,
depending on the test
Test/Species-Specific Alpha
Why the Different Alphas?

EPA’s Second Regulatory Management
Decision
– No more than 5% of tests with effects
less than 10% should be identified as
toxic
– Type II Error Rate – not really a “false
positive”

Alpha adjusted down until no more than
5% of tests with effects less than 10%
were identified as “toxic”
– Monte Carlo simulations
TST Equation (Welch’s t-test)
Mean (sample )  0.75  Mean ( control )
Variance (sample ) 0.5625  Variance ( control )

n (sample )
n ( control )

t=

t (calculated) < t (table/critical) = toxic

t (calculated) > t (table/critical) = non-toxic
Factors That Impact Ability to
Statistically Reject the
Hypothesis



Magnitude of Effect
Number of Replicates
Within Test Variability
TST Equation (Welch’s t-test)
Mean (sample )  0.75  Mean ( control )
Variance (sample ) 0.5625  Variance ( control )

n (sample )
n ( control )

t=

All tests (100%) with an effect of 25% will be
identified as “toxic”
The greater the within test variability, the
harder or less likely it will be to identify a
sample as being statistically different (nontoxic).
The more replication, the more likely it will be
to identify a sample as being statistically
different (non-toxic).


Effect of Variability:
Standard t-test
50
NOEC = Significant/toxic
NOEC = Not significant/non-toxic
Mean Young Produced
40
30
25% Reduction
20
Col 1 vs Response
10
0
Control
Effluent
Control
Effluent
Example:
TST test
40
TST = Non-toxic
TST = Toxic
Mean Young Produced
35
30
25
25% Effect or
75% of Control
20
15
Control
Effluent
Control
Effluent
Controllable Factors That Impact
Ability to Statistically Reject the
Hypothesis

Variability
– The greater the within test variability, the
harder or less likely it will be to identify a
sample as being statistically different.
– For the “regular” hypothesis test
• Less frequent identification of “toxicity”
– For the TST
• Less frequent identification of “no
toxicity”

Replication
Procedures That May Reduce
Variability

Maximize Mean Response
• CV = S.D. / Mean
From EPA Test of Significant Toxicity (TST) Document
EPA 833-R-10-003
Impact of Control Mean



At the 10th Percentile (17.7) - a 25%
effect is reduction of 4.4 neonates
At the 50th Percentile (25.5) - a 25%
effect is reduction of 6.4 neonates
At the 95th Percentile (35.6) - a 25%
effect is reduction of 8.9 neonates
Procedures That May
Increase Mean Response

Dilution Water Selection
– Match sample condition as much as
possible

Food Supplements, Combinations
– Specifically allowed (13.6.16.9.2)

Feeding Rates
– Twice or three times per day
– Amount of food
Fathead Minnow Feeding
Rate Example
Fathead Minnow Growth - Control Mean
1.65
Control Mean (mg)
1.45
1.25
1.05
0.85
0.65
0.45
0.25
1000 Artemia/Test Chamber
n = 267, Mean = 0.616 mg
0.4% Exceed 95th Percentile
1.1% Exceed 90th Percentile
2.2% Exceed 85th Percentile
7.1% Exceed 75th Percentile
50.9% Exceed 50th Percentile
1500 Artemia/Test Chamber
n=317, Mean = 0.801
9.5% Exceed 95th Percentile
20.5% Exceed 90th Percentile
30.3% Exceed 85th Percentile
53.3% Exceed 75th Percentile
97.2% Exceed 50th Percentile
Impact of Growth on CV
Fathead Minnow Growth - Control CV
Control CV (%)
40
30
20
10
0
1000 Artemia/Test Chamber
n = 267
3% Exceed 95th Percentile
9.4% Exceed 90th Percentile
9.7% Exceed 85th Percentile
15.7% Exceed 75th Percentile
40.4% Exceed 50th Percentile
1500 Artemia/Test Chamber
n=317
1.9% Exceed 95th Percentile
4.7% Exceed 90th Percentile
5.4% Exceed 85th Percentile
15.2% Exceed 75th Percentile
41.5% Exceed 50th Percentile
Procedures That May
Decrease Variability

Set Internal Control CV Criteria
Ceriodaphnia dubia Control CV
2010 through February 2011
140
Meets TAC
Failed TAC
National 50th Percentile
National 75th Percentile
National 95th Percentile
120
Control CV (%)
100
80
60
40
20
0
1/1/2010
3/1/2010
5/1/2010
7/1/2010
9/1/2010
11/1/2010
Date of Test Initiation
1/1/2011
3/1/2011
Procedures That May
Decrease Variability

Set Internal Control Mean Criteria
Mean Reproduction in Control
50
Ceriodaphnia dubia Control Reproduction Means
2010 through February 2011
40
30
20
Meets TAC
Failed TAC
Minimum TAC
National 50th Percentile
National 75th Percentile
National 95th Percentile
10
0
1/1/2010
3/1/2010
5/1/2010
7/1/2010
9/1/2010
Date of Testing
11/1/2010
1/1/2011
3/1/2011

Statistical and
Non-statistical Error
False Determinations of Toxicity
USEPA Non-Toxic "Blank" Samples1
Ceriodaphnia dubia Reproduction Results
Effect Relative to Control (%)
80
TST Non-Toxic
TST Toxic (14.8%)
60
40
20
0
-20
1
Data Source: USEPA's WET Interlaboratory Validation Study (EPA 821-B-01-004), Table 9.7.
Dose Response Evaluation
Eliminating multiple concentrations may
limit ability to evaluate spurious results.
35
Single Concentration
Test
Multiple Concentration Test
30
Number of Neonates

25
20
15
10
Non-Toxic
Toxic
5
0
Control
100%
Effluent
20%
Effluent
40%
Effluent
60%
Effluent
80%
Effluent
100%
Effluent
Conclusions

Same limitations as any hypothesis test
– Implications associated with variability
and “power” shifted

Not a magical “black box”
– You need to be aware of the impact
variability, QA/QC, and test design may
have

May be useful for regulation
– NPDES Permits
– Possible use for remediation goals?
Questions?
Contact info: pmarkle@lacsd.org