Transcript Probabilistic Risk Assessment in Environmental Toxicology

Probabilistic Risk Assessment
in Environmental Toxicology
RISK: Perception, Policy & Practice Workshop
October 3-4, 2007
SAMSI, Research Triangle Park, NC
John W. Green, Ph.D., Ph.D.
Senior Consultant: Biostatistics
DuPont Applied Statistics Group
1
Topics Addressed in
Environmental Risk Assessment
• Present & proposed regulatory methods
– Concerns
– Micro- vs macro-assessments
• Variability vs Uncertainty
• Exposure and Toxicity
– Exposure models (Monte Carlo, PBA)
• extensive literature on exposure
– Toxicity
• Species Sensitivity Distributions (Monte Carlo)
– Combining the two for risk assessment
2
3
Deterministic Probabilistic
Toxicity
Exposure
TER
4
Assessment of Toxicity
• Species level assessments
– Laboratory toxicity experiments
– Greenhouse studies
– Field studies
• Ecosystem level assessment
– Most sensitive species
– Mesocosm studies
– Species Sensitivity Distribution
5
Species Level Assessment:
NOEC (aka NOAEL) and ECx
• LOEC = lowest tested conc at which a
statistically significant adverse effect is
observed
• NOEC = highest tested conc < LOEC
– LOEC, NOEC depend on experimental
design & statistical test
• ECx = conc producing x% effect
– ECx depends on experimental design and
model and choice of x
6
Ecosystem level assessment




Current Method
Determine the NOEC (or EC50) for each
species representing an ecosystem
Find the smallest NOEC (or EC50)
Divide it by 10, 100, or 1000
(uncertainty factor)
Regulate from this value
 or argue against it
7
Ecosystem level assessment
Probabilistic Approach
• Collect a consistent measure of toxicity
from a representative set of species
– EC50s or NOECs (not both)
• Fit a distribution (SSD) to these
numerical measures
• Estimate concentration, HC5, that
protects 95% of species in ecosystem
• Advantages and problems with SSDs
8
9
Selection of Toxicity Data
SSD by Habitat
Visual groupings are not taxonomic classes but defined
by habitat , possibly related to mode of action
10
How Many Species?
• Newman’s method: 40 to 60 species
– Snowball’s chance…
– Might reduce this by good choice of
groups to model
• Aldenberg-Jaworski: 1 species will do
– If you make enough assumptions,…
• 8 is usual target
• 5 is common
• 20-25 in some non-target plant studies 11
Which Distribution to Fit?
• Normal, log-normal, log-logistic, Burr
III…?
– With 5-8 data points, selecting the “right”
distribution is a challenge
• Next slide gives simulation results
• Does it matter?
– Recent simulation study suggests yes
• 2nd slide following: uniform [0,1] generated
• Various distributions fit
– Actual laboratory data suggests yes
12
Power to Detect non-Lognormality
Exponential Distribution Generated
SW
KS
AD
CM
Sample Size
10
11
10
8
4
16
13
16
15
5
24
19
24
23
6
35
26
32
31
8
46
31
43
40
10
68
43
62
58
15
84
60
77
72
20
97
78
93
91
30
13
Does it Matter?
Q05 Simulations: True value =0.05
Uniform [0,1] Generated
Distribution
3rd Qrtl
Q5median
Ist Qrtl
Size
Exponential
0.2341
0.08295
-0.02438
4
Normal
0.19371
0.02227
-0.09323
4
Exponential
0.19859
0.06788
-0.01593
5
Lognormal
0.26667
0.1385
0.064521
5
Normal
0.16495
0.02547
-0.08768
5
Exponential
0.16714
0.05756
-0.01171
6
Lognormal
0.23317
0.13017
0.065593
6
Normal
0.13695
0.02157
-0.07665
6
Exponential
0.139
0.05249
-0.00116
8
Lognormal
0.1993
0.11927
0.063502
8
Normal
0.12884
0.02709
-0.05738
8
Exponential
0.11034
0.04692
0.004643
10
Lognormal
0.17223
0.10481
0.060777
10
Normal
0.10975
0.02209
-0.04842
10
14
Which Laboratory Species?
One EUFRAM case study fits an SSD to the
following
Aquatic toxicologists can comment (and have)
on whether these values belong to a meaningful
population
15
Variability and Uncertainty
Uncertainty reflects lack of knowledge of the
system under study
Ex1: what distribution to fit for SSD
Ex2: what mathematical model to use to
estimate ECx
Increased knowledge will reduce uncertainty
Variability reflects lack of control
inherent variation or noise among individuals.
Increased knowledge of the animal or plant
species will not reduce variability
16
Variability & Uncertainty
• The fitted distribution is assumed log-normal
– Defined by the population mean and variance
• Motivated in part by standard relationship shown below
– Randomly sample from the χ2(n-1) distribution.
– Then randomly sample from a normal with the above variance,
and mean equal to sample mean
– Note: If formulas below are used, only variability is captured

ns

2
2
( n 1)
  x  t( n 1)
s
n 1
17
Spaghetti plot
Probabilities (vertical variable values) associated with a given value
of log(EC50) are themselves distributed
For a given log(EC50) value, the middle 95% of these secondary
probabilities defines 95% confidence interval for proportion of
species affected at that conc
18
For a given proportion (value of y), the values of Log(EC50) (horizontal
variable) that might have produced the given y-value are distributed.
For a given y value, the middle 95% of these x-values defines 95%
confidence bounds on the distribution of log(ECy) values.
19
Summary Plot for SSD
20
Putting it All Together
Joint Probability
Curves
Plot exposure and
toxicity distributions
together to
understand the
likelihood of the
exposure
concentration
exceeding the toxic
threshold of a given
percent of the
21
population
Calculating Risk
The risk is given by
Pr[Xe>Xs]
where Xe = exposure, Xs =sensitivity or toxicity
This is an “average” probability that exposure
will exceed the sensitivity of species exposed
Not clear that this captures the right risk
Work needed here
22
Conclusions
• PRA can bring increased reality to risk
management by
– communicating uncertainty more realistically
– separating uncertainty from variability
– clarifying risk of environmental effects
• PRA is only as good as the assumptions
and theories on which it rests
• The bad news is that implementation is
running ahead of understanding
23
Conclusions
• SSDs based on tiny datasets unreliable
• Need to identify what populations are
appropriate subjects for SSD is vital
• 2-D Monte Carlo methods often assume
independent inputs or specific correlations
– Not realistic in many cases
• PBA can accommodate dependent inputs
– But can lead to wide bounds
– Have other limitations restricting use
• MCMC can accommodate correlated inputs
– But are mathematically demanding
24