Risk Assessment in Practice
EPIDEMIOLOGICAL STUDIES
Case-control studies begin by identifying patients with the outcome (disease) of interest
and looks backward (retrospective) to see if they had the exposure of interest. Cases,
people who have the outcome (disease) in question, are linked with controls, people from
the same population without the outcome (disease). Controls are chosen to look identical
to cases for baseline variables that are known to relate to the outcome. The effort is to
find the exposure(s) that occurs more frequently in the cases than the control(s).
Cohort Study: A longitudinal study that begins with the gathering of two groups of
patients (the cohorts), one which received the exposure of interest, and one which did not,
and then following this group over time (prospective) to measure the development of
different outcomes (diseases).
Cross-sectional study: Prevalence study. Survey of an entire population for the presence
or absence of a disease and/or other variable in every member (or a representative
sample) and the potential risk factors at a particular point in time or time interval.
Exposure and outcome are determined simultaneously.
1
Usual sequence of studies
A case-control study is generally easier to do than a cohort study. The case-control study
is ideal for rare diseases, because a cohort study would require too many patients in the
study group to be feasible. Similarly, the case-control study is ideal for a disease that
takes many years to develop, because a cohort study would require too long to complete.
A logical sequence is: first, a case-control study to determine the most important
exposure(s) associated with the specific outcome. Then, a cohort study to profile the
development over time of the outcome in a given population with differing amounts of
exposure.
2
EPIDEMIOLOGICAL MEASURES OF HEALTH OUTCOME
The Relative Risk is usually used in a prospective study (e.g. Cohort studies)
The
Outcome
+
-
+
a
The
Exposure
-
c
a / (a+b)
Risk Rate of
Developing
b
Relative Risk
Outcome in
(Risk Ratio)=
Exposed
population
(a / (a+b))
c / (c+d)
---------Risk Rate of
(c / (c+d))
d
Developing
Outcome in NONExposed
Relative Risk
Reduction =
(a/(a+b))-(c/(c+d))
--------------------(c/(c+d))
3
The Odds ratio is usually used in a retrospective study (e.g. Case-Control)
The Outcome
The Exposure
+
-
+
a
b
c
d
a/c
b/d
Odds of Being
Odds of Being
Exposed in Cases
Exposed in Controls
Odds Ratio = (a/c) / (b/d)
4
Relation between Relative Risk and Odds ratio
In a rare condition, a and c are very small compared to b and d. So, if one were able to do
a prospective study, and generate the Relative Risk (or Risk Ratio)...
Relative Risk = (a / (a+b)) / (c / (c+d))
In a rare condition, a would not add much to b. So, a+b ≈ b; and, similarly, c+d ≈ d.
So, the Relative Risk would = (a / b) / (c / d) OR (a * d) / (b * c)
This formula is identical to the Odds Ratio.
So, given a rare condition, the Odds Ratio approximates the Relative Risk (or Risk
Ratio).
5
Standardized Incidence Ratios (SIR)
The SIR is the ratio of some health outcome (e.g. cancer) incidence rate obs observed in
an exposed population over the expected incidence rate  for the general population.
SIR = obs / 
where obs and  are number of cases per 100,000. An SIR of 1.0 implies that the
incidence rates are the same for the exposed population and the standard population. An
SIR > 1.0 implies that the incidence rate is greater for the exposed population compared
to the standard population.
Using the SIR in risk analysis
A measure of health outcome used in risk analysis is the number of cases that are due to
exposure to the environmental toxics
H= (obs–) * 100,000 = ( SIR - 1 )100,000
.
6
USING THE EPA INTEGRATED RISK INFORMATION SYSTEM
The IRIS sytem
The Integrated Risk Information System (IRIS), prepared and maintained by the U.S.
Environmental Protection Agency (U.S. EPA), is an electronic database containing
information on human health effects that may result from exposure to various chemicals
in the environment.
http://www.epa.gov/iris/
The IRIS system is a collection of computer files covering individual chemicals. These
chemical files contain descriptive and quantitative information in the following
categories:

Oral reference doses and inhalation reference concentrations (RfDs and RfCs,
respectively) for chronic noncarcinogenic health effects.

Hazard identification, oral slope factors, and oral and inhalation unit risks for
carcinogenic effects.
7
The Reference Concentration (RfC): An estimate (with uncertainty spanning perhaps
an order of magnitude) of a continuous inhalation exposure to the human population
(including sensitive subgroups) that is likely to be without an appreciable risk of
deleterious effects during a lifetime. It can be derived from a NOAEL, LOAEL, or
benchmark concentration, with uncertainty factors generally applied to reflect limitations
of the data used. Generally used in EPA's noncancer health assessments.
The Reference Dose (RfD): An estimate (with uncertainty spanning perhaps an order of
magnitude) of a daily oral exposure to the human population (including sensitive
subgroups) that is likely to be without an appreciable risk of deleterious effects during a
lifetime. It can be derived from a NOAEL, LOAEL, or benchmark dose, with uncertainty
factors generally applied to reflect limitations of the data used. Generally used in EPA's
noncancer health assessments.
The Reference Value (RfV): An estimation of an exposure for [a given duration] to the
human population (including susceptible subgroups) that is likely to be without an
appreciable risk of adverse effects over a lifetime. It is derived from a BMDL, a NOAEL,
a LOAEL, or another suitable point of departure, with uncertainty/variability factors
applied to reflect limitations of the data used. [Durations include acute, short-term,
longer-term, and chronic and are defined individually in this glossary].
8
Slope Factor: An upper bound, approximating a 95% confidence limit, on the increased
cancer risk from a lifetime exposure to an agent. This estimate, usually expressed in units
of proportion (of a population) affected per mg/kg/day, is generally reserved for use in
the low-dose region of the dose-response relationship, that is, for exposures
corresponding to risks less than 1 in 100.
Unit Risk: The upper-bound excess lifetime cancer risk estimated to result from
continuous exposure to an agent at a concentration of 1 µg/L in water, or 1 µg/m3 in air.
The interpretation of unit risk would be as follows: if unit risk = 1.5 x 10-6, 1.5 excess
tumors are expected to develop per 1,000,000 people if exposed daily for a lifetime to 1
µg of the chemical in 1 liter of drinking water.
9
DETERMINATION OF REFERENCE DOSE
A no-observed-adverse-effect level” NOAEL is an experimentally determined dose at
which there was no statistically or biologically significant indication of the toxic effect of
concern.
In cases in which a NOAEL has not been demonstrated experimentally, the term "lowestobserved-adverse-effect level” (LOAEL) is used.
A safety factor is used to divide the NOAEL down to a level that is deemed safe for
human exposure. The term "safety factor" suggests, perhaps inadvertently, the notion of
absolute safety (i.e., absence of risk). While there is a conceptual basis for believing in
the existence of a threshold and "absolute safety" associated with certain chemicals, in
the majority of cases a firm experimental basis for this notion does not exist. The safety
factor is the product of the Uncertainty Factors (UFs) and the Modifying Factor (MF)
Standard Uncertainty Factors (UFs):
Use a 10-fold factor when extrapolating from valid experimental results in studies using
prolonged exposure to average healthy humans. This factor is intended to account for the
variation in sensitivity among the members of the human population and is referenced as
"10H".
10
Use an additional 10-fold factor when extrapolating from valid results of long-term
studies on experimental animals when results of studies of human exposure are not
available or are inadequate. This factor is intended to account for the uncertainty involved
in extrapolating from animal data to humans and is referenced as "10A".
Use an additional 10-fold factor when extrapolating from less than chronic results on
experimental animals when there are no useful long-term human data. This factor is
intended to account for the uncertainty involved in extrapolat- ing from less than chronic
NOAELs to chronic NOAELs and is referenced as "10S".
Use an additional 10-fold factor when deriving an RfD from a LOAEL, instead of a
NOAEL. This factor is intended to account for the uncertainty involved in extrapolating
from LOAELs to NOAELs and is referenced as "10L".
Modifying Factor (MF):
Use professional judgment to determine the MF, which is an additional uncertainty factor
that is greater than zero and less than or equal to 10. The magnitude of the MF depends
upon the professional assessment of scientific uncertainties of the study and data base not
explicitly treated above; e.g., the completeness of the overall data base and the number of
species tested. The default value for the MF is 1.
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Reference Dose (RfD)
The RfD is a benchmark dose operationally derived from the NOAEL by consistent
application of generally order-of-magnitude uncertainty factors (UFs) that reflect various
types of data sets used to estimate RfDs. The RfD is determined by use of the following
equation:
RfD = NOAEL / (UF x MF)
In general, the RfD is an estimate (with uncertainty spanning perhaps an order of
magnitude) of a daily exposure to the human population (including sensitive subgroups)
that is likely to be without an appreciable risk of deleterious effects during a lifetime. The
RfD is generally expressed in units of milligrams per kilogram of bodyweight per day
(mg/kg/day).
The RfD is useful as a reference point from which to gauge the potential effects of the
chemical at other doses. Usually, doses less than the RfD are not likely to be associated
with adverse health risks, and are therefore less likely to be of regulatory concern. As the
frequency and/or magnitude of the exposures exceeding the RfD increase, the probability
of adverse effects in a human population increases.
12
Example
Suppose the U.S. EPA has the following 90-day subchronic gavage study in rats
Dose
Observation
mg/kg/day
Control--no adverse effects observed
0
No statistically or biologically significant differences between treated
1
and control animals
2% decrease* in body weight gain (not considered to be of biological
5
significance); increased ratio of liver weight to body weight;
20% decrease* in body weight gain; increased* ratio of liver weight to
25
body weight; enlarged, fatty liver with vacuole formation;
Effect
Level
NOEL
NOAEL
LOAEL
Determination of the Reference Dose (RfD) Using the NOAEL
UF = 10H x 10A x 10S = 1000. (study is on animals and of subchronic duration)
MF = 0.8. subjective adjustment based on high number of animals (250) per dose group
RfD = NOAEL/(UF x MF) = 5/800 = 0.006 (mg/kg/day).
Determination of the Reference Dose (RfD) Using the LOAEL
UF = 10H x 10A x 10S x 10L = 10,000
RfD = LOAEL/(UF x MF) = 25/8000 = 0.003 (mg/kg/day).
13
APPLICATION OF SLOPE FACTORS/UNIT RISKS IN RISK ANALYSIS
To apply these estimates exposures must be provided as daily averages over a lifetime.
The slope factor is the cancer risk (proportion affected) per unit of dose. In the IRIS
chemical files the slope factor is expressed on the basis of chemical weight [milligrams of
substance per kilogram body weight per day (mg/kg/day)]. The slope factor can be used
to compare the relative potency of different chemical substances on the basis either of
chemical weight (as above) or moles of chemical (m moles/kg/day).
To estimate risks from exposures in food, one multiplies the slope factor (risk per
mg/kg/day), the concentration of the chemical in the food (ppm) and the daily intake (in
mg) of that food. The total dietary risk is found by summing risks across all foods.
For evaluating risks from chemicals found in certain other environmental sources, doseresponse measures are expressed as risk per concentration unit. These measures are called
the unit risk for air (inhalation) and the unit risk for drinking water (oral). The continuous
lifetime exposure concentration units for air and drinking water are usually micrograms
per cubic meter (ug/cu.m) and micrograms per liter (ug/L), respectively. If the fraction of
the agent is absorbed from the diet for humans and animals differs, the U.S. EPA applies
a correction when extrapolating the animal-derived value to humans.
14
For determining the concentrations of air or water at certain designated levels of lifetime
risk (risk-specific concentrations), the U.S. EPA calculates the ratio of that level of risk to
the unit risk for water or air. For example, one may want to know the water concentration
corresponding to an upper bound risk of 1 in 100,000 (E-5) given a water risk of 4.0E5/ug/L. This would be 2.5E-1 ug/L.
In summary, the quantities appropriate for calculating upper-bound risks for air, drinking
water, and food are, respectively, the air unit risk (risk per ug/cu.m of air), the drinking
water unit risk (risk per ug/L of drinking water) and the oral slope factor (risk per mg/kg
body weight/day), corresponding to dietary intake risk.
15
FINDING MORE INFORMATION ON RISK ASSESSMENT
The International Agency for Research on Cancer (IARC) produces monographs on
the carcinogenic risk of individual chemicals:
http://monographs.iarc.fr
They classify Carcinogenic Chemicals in 2 groups: Those in Group 1 are carcinogenic to
humans, and those in Group 2 are (A) probable or (B) possible carcinogenic to humans.
The California Office of Environmental Health Hazard Assessment (OEHHA)
provides a wealth of information of their own on risk assessment
http://www.oehha.ca.gov/air/hot_spots/index.html
The Agency for Toxic Substances and Disease Registry (ATSDR) provides the
Minimal Risk Levels (MRLs) for Hazardous Substances
http://www.atsdr.cdc.gov/mrls
16
EXAMPLE OF POPULATION EXPOSURE RESPONSE (PER) CURVES FOR
LEAD IN THE AIR
Toxicokinetic dose model for exposure to lead in the air (Lai et al., JIAOEH, 1997)
Log(PbB)=1.9652+0.2356 log PbA
where PbB (g/100ml) is the concentration of Lead in the blood of a human resulting
from lifetime exposure to air with a lead concentration of PbA (g/m3)
Note on sensitivity analysis: Dashed line is Lead model 2, Log(PbB)=a’+0. 6 log PbA
17
Epidemiological dose/response model for for lung cancer
Cumulative lead dose in relation to Standardized Incidence Rate (SIR) of lung cancer
(Lundstrom et al., SJWEH, 1997)
18
Proposed model of health effect
D= ∫ dt PbB(t)
Let obs observed in an exposed population be equal to the expected incidence rate  for
the general population when there is no exposure, i.e. obs = for D=0, and then let obs
increase as D increases, in such a way that obs =1 when D=infinite. In other words, let
obs - =0 for D=0, and let obs - =1 - for D=infinite.
By dividing by (1 -), we get
obs - /(1 -)=0 for D=0, and (obs -(1 -) =1 for D=infinite
Taking (1-) on the LHS and RHS we get
obs - /(1 -)=1 for D=0, and 1-(obs -(1 -) =0 for D=infinite
A mathematical model for that relationship is
obs - /(1 -)=exp-3D/Ds,
where Ds is the dose it takes for a 95% reduction in obs - /(1 -). This dose is
referred to as the saturation (lethal) dose.
Rearranging we get
obs - /(1 -)=1-exp-3D/Ds,
obs - =(1 -)(1-exp-3D/Ds),
obs =+(1 -)(1-exp-3D/Ds),
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SIR=obs/1+(1/  -1)(1-exp-3D/Ds)
Finally, since
H = (SIR-1) 
20
We get
H=(1/  -1)(1-exp-3D/Ds)
Uncertainty assessment of the individual risk H[p]
1) The exposure variable PbA is log-normal, so that
logPbA ~ Normal( E[logPbA], var[logPbA] )
2) The dose PbB for a given year is given by
logPbB=a+b logPbA so that
logPbB ~ Normal( E[logPbB], var[logPbB] )
with E[logPbB]= a+b E[logPbA], and
var[logPbB]= b2 var[ logPbA]
3) The Standardized Incidence Rate SIR is given by
21
SIR = 1+(1/ -1)(1-exp-3D/Ds)
where the cumulated dose D=Sum(PbBi). For  and D<< Ds, we have (1/ -1)~1/
and (1-exp-3D/Ds) ~ 3D/Ds so that
SIR ~ 1+3D/(Ds) ~ 1+3/(Ds) Sum(PbBi)
4) The health outcome is
H=(SIR-1) ~ /Ds Sum(PbBi)
Note: for  and D<< Ds, the health outcome H is linear with the dose D.
Theorem: If X = log Y ~ Normal( E[log Y], var[log Y] ) then
E[Y] = exp ( E[log Y] + var [log Y] /2 ) and
Var[Y] = E[Y]2 { exp(var[logY]) – 1 }
Use the above theorem to derive the expected value and variance of the health H as a
function of the expected value and variance of log PbA.
22
An Application of the Holistochastic Human Exposure
Methodology to Naturally Occurring Arsenic in
Bangladesh Drinking Water
Serre, M.L., A. Kolovos, and G. Christakos K. Modis
The framework
23
BME exposure mapping of Ground Water Arsenic
24
Linear Population Exposure/Response curve
The lifetime probability P[cancer; p] of developing bladder
cancer is related to the Arsenic concentration X(p) as
follows
P[cancer; p] = PB+k X(p)
where PB = background bladder cancer, k = slope factor
25
Health outcome
A measure of the health outcome caused by Arsenic is
H[p] = P[cancer; p] - PB = k X(p)
BME mapping of individual risk H[p]
26
BME mapping of population health impact L= H*Pop
27
28
An Application of Risk Assessment using a Linear and
Log-Linear Dose-Response Relationship
Let Y be the incidence rate corresponding to exposure level
X, and let Y0 be the incidence rate for an initial (e.g.
background, control, etc.) level X0.
In risk assessment we evaluate health impacts in terms of the
increase in incidence rate
Y= Y-Y0
(1)
that is attributable to the increase in exposure X= X-X0.
The attributable fraction AF = Y/Y corresponds to the
fraction of the incidence rate Y that is attributable to the
exposure X. Hence Y can be expressed in terms of AF
using
Y= Y AF.
(2)
The relative risk is defined as RR = Y/Y0. It follows that the
AF can be calculated from the RR using the following
equation
AF=Y /Y=(Y-Y0)/ Y=1-1/RR.
(3)
From that equation we see that the higher the RR, the closer
to 1 will the AF be.
29
Linear risk
Assume that the relation between exposure X and resulting
incidence rate Y is linear, i.e.
Y =  + Y X
(4)
Then the relative risk is also linear
RR=Y/Y0=(+Y X)/( +Y X0)
=1+Y (X-X0)/( +Y X0) =1+(YY0) (X-X0)
or equivalently
RR =1+RR (X-X0),
(5)
where RRYY0. Hence, the relative risk is equal 1 when
X=X0, and the slope of the relative risk RR with respect to X
is RRYY0.
The AF is given by AF=(Y-Y0)/ Y=1-( +Y X0)/( +Y X).
Hence AF=1 when both  =0 and X0=0, and AF decreases
when either  or X0 (or both) are greater than 0.
Alternatively AF=1-1/RR1-1/(1+RR (X-X0)), which can be
calculated based on RR instead of  and Y.
The risk assessment will consist in obtaining RR from the
literature, calculating RR=1+RR (X-X0), and then calculating
Y as follow:
If Y is known, calculate Y using the AF equations (3) and
(4), i.e.
30
Y= Y AF= Y (1-1/RR)= Y (1-1/(1+RR (X-X0)))
(6)
If Y0 is known, calculate Y directly from the RR as follow
Y=Y-Y0= Y0(RR-1)= Y0 RR (X-X0)
(7)
Example:
We are interested to calculate the increased incidence rate YY0 attributed to an increase of PM from the background
level PM0 to the current level PM . An Epidemiology study
reports that the relative risk RR10=Y10/Y0 is 1.14 for a 10
ug/m3 increase in PM.
Using Eq. (5) we have
1.14 =1+RR 10 (ug/m3),
which can be rewritten as
RR =(1.14 - 1)/10 (ug/m3) = 0.014 per ug/m3.
The increase in incidence rate Y attributable to exposure X
is then calculated using either equation (6) or (7).
Log linear risk
Assume that the relation between exposure X and resulting
incidence rate Y is log linear, i.e.
Log(Y) = log() +  X or equivalently Y =  exp( X)
31
Then the relative risk is also exponential
RR=Y/Y0=exp(logY (X-X0))
(8)
Hence, the relative risk is equal 1 when X=X0, and it
increases exponentially with (X-X0) .
The AF is given by AF=(Y-Y0)/Y=1-exp(-logY (X-X0). Hence
if logY =0 the AF=0. As logY increases, AF increases also.
AF is equal to 1 when both logY and X are very large.
The risk assessment will consist in obtaining logY from the
literature, and then calculating Y as follow:
If we know the background incidence rate Y0 then we may
use
Y=  exp logY X0 (exp logY (X-X0)-1) = Y0 (exp logYX -1)
If instead X is the current level and if we know the current
incidence rate Y then we use
Y=  exp logY X (1- exp -logY (X-X0)) = Y (1- exp-logYX)
Note: If logY <<1, then exp -logYX~1-logYX and Y ~
Y logYX , i.e. the health effect is linear with exposure.
Example:
We are interested to calculate the increased incidence rate YY0 attributed to an increase of PM from the control level
PM0 to the current level PM. An Epidemiology study reports
that the relative risk RR10= Y10/Y0 is 1.14 for a 10 ug/m3
increase in PM, then we get logY using
32
Y10/Y0 = RR = exp(logY (PM10-PM0))
which can be rearranged to
logY = log(RR)/(PM10-PM0)= log(1.14)/10 = 0.0131 per
ug/m3
Then the increased Y-Y0 attributed to an increase of PM from
the backgroun level PM0 to the current level PM is
Y= Y (1-exp -logYX) = Y (1 - exp -0.0131 (PM- PM0) )
33