Appendix D. Chemical Intake and Risk Equations
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TABLE OF CONTENTS 

D-1 Introduction ........................................................................................................................... 1

D-2 Calculation of Chemical Intake .............................................................................................. 1

D-2.1 Chemical Intake Calculations for Adults and Non-Infant Children ............................... 1

D-2.2 Total Chemical Intake ..................................................................................................... 2

D-2.3 Chemical Intake Calculations for Nursing Infants .......................................................... 4

D-2.3.1 Infant Average Daily Absorbed Dose ................................................................... 4

D-2.3.2 Chemical Concentration in Breast Milk Fat .......................................................... 5

D-3 Risk Estimation ..................................................................................................................... 9

D-3.1 Cancer Risks ................................................................................................................... 9

D-3.2 Non-cancer Hazard Quotients ....................................................................................... 11

D-4 References .......................................................................................................................... 12
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D-1 Introduction 

For this assessment, human health risks from multipathway exposure to PB-HAPS are 

estimated using the Multimedia Ingestion Risk Calculator (MIRC.) MIRC is a Microsoft Accessbased tool designed to assist in estimating risks via multiple ingestion pathways, including 

consumption of fruits and vegetables, livestock food products, fish, drinking water, and 

incidental soil ingestion. MIRC also estimates exposure to nursing infants from breast milk. 

Using chemical input concentrations for PB-HAPs of interest in air and soil and air-to-surface 

deposition rates from TRIM.FaTE, MIRC calculates the chemical’s concentrations in home- or 

farm-grown produce and animal food products using FFC algorithms adapted from EPA’s 

Human Health Risk Assessment Protocol for Hazardous Waste Combustion Facilities (hereafter 

referred to as HHRAP; EPA 2005a). MIRC uses these calculated concentrations, along with 

user-input chemical concentrations for fish and drinking water, to estimate chemical intake 

rates, as average daily doses (ADDs), for adults, children, and nursing infants. 

To estimate excess lifetime cancer risks, MIRC calculates lifetime ADDs for each chemical and 

multiplies them by cancer slope factors (CSFs) previously identified by EPA. MIRC estimates 

age-specific noncancer hazard quotients (HQs) as the ratio of age-specific ADDs to the 

reference dose (RfD) for a chemical. 

An explanation of the equations used by MIRC to calculate chemical intake is presented in 

Section D-2. The equations used by MIRC to estimate cancer risk and noncancer hazard are 

presented in Section D-3. References cited are identified in Section D-4. 

D-2 Calculation of Chemical Intake 

D-2.1 Chemical Intake Calculations for Adults and Non-Infant Children 

MIRC calculates human chemical intake rates from the ingestion of home-grown foods as ADDs 

normalized to body weight for each receptor (e.g., age group), chemical, and food type 

separately. ADDs, calculated using Equation D-1, are expressed in milligrams of chemical per 

kilogram of receptor body weight per day (mg/kg-day). 

Equation D-1. Average Daily Dose for Specified Receptor and Food Type 



































    365 days

(y)

(y) (y)

(i) (y,i) (i) (y)

(y,i)

EF

BW AT

C IR FC ED

ADD

where: 

ADD(y,i) = Average daily dose for receptor y from food type or ingestion medium i (mg 

chemical/kg body weight-day) 

C(i) = Concentration of chemical in food type i harvested from the contaminated area 

(mg chemical/kg food or mg food/L water) 

IR(y,i) = Ingestion rate for receptor y of food type i (kg/day or L/day) 

FC(i) = Fraction of food type i that was harvested from contaminated area (unitless) 

ED(y) = Exposure duration for receptor y (years) 

BW(y) = Body weight for receptor y (kg) 
2/15/2011 D-2 DRAFT 

AT(y) = Averaging time for calculation of daily dose (years) for receptor y, set equal to 

ED in MIRC 

EF(y) = Annual exposure frequency for receptor y (days) 

Equation D-1 takes into account the chemical concentration in each food type i (or in water), the 

quantity of food brought into the home for consumption, the loss of some of the mass of the 

foods due to preparation and cooking, how much of the food is consumed per year, the amount 

of the food obtained from contaminated areas, and the consumer’s body weight (EPA 1997, 

2003). In MIRC, ADDs are calculated separately for each chemical, home-grown food type, and 

consumer age group. 

ADD values, expressed as intakes, not absorbed doses, are appropriate for comparison with 

RfDs and for use with cancer slope factors (CSFs) to estimate risk, as discussed in Section D-3. 

An exception is the breast-milk exposure pathway, where the dose absorbed by the mother is 

relevant to calculating the dose available to and absorbed by her nursing infant, as discussed in 

Section D-2.3. 

MIRC evaluates only one contaminated area (set of environmental concentrations), or exposure 

scenario, at a time. For screening level assessments, all components of this equation are 

assumed to remain constant for consumers in a given age group over time (e.g., seasonal and 

annual variations in diet are not explicitly taken into account). To calculate an ADD(y,i) from the 

contaminated area for food group i over an entire lifetime of exposure, age-group-specific 

ingestion rates and body weights are used. In MIRC, the averaging time used to calculate the 

daily dose for an age group (ATy) is equal to the exposure duration for that group (EDy); 

therefore these variables drop out of Equation D-1. 

For each chemical assessed, total average daily exposure for receptor y (ADD(y)) may be 

estimated as the sum of chemical intake from all ingestion pathways combined: 

 Incidental soil ingestion; 

 Ingestion of fish; 

 Ingestion of homegrown fruits (exposed and protected); 

 Ingestion of homegrown vegetables (exposed, protected, and root); 

 Ingestion of animal products from home-raised animals: 

o Milk and other dairy products from cows, 

o Beef products, 

o Pork products, 

o Poultry, and 

o eggs; 

 Ingestion of drinking water from specified source; and 

 Ingestion of breast milk by infants. 

Note that the breast milk exposure pathway is limited to infants. 

D-2.2 Total Chemical Intake 

To estimate the total ADD, or intake of a chemical from all of the exposure media that a single 

individual in each age group is expected to contact (e.g., soil, local fish, five types of homegrown produce, and five types of home-raised animals or animal products), the media-specific 

chemical intakes are summed for each age group. Total average daily exposure for a particular 
2/15/2011 D-3 DRAFT 

age group y (ADD(y)) is estimated as the sum of chemical intake from all ingestion pathways 

combined, as illustrated in Equations D-2 through D-6 below. 

Equations D-2 to D-7. Total Average Daily Dose of a Chemical for Different Age Groups 

Equation D-2. ADD(1)  ADDbreastmilk

 Equation D-3.     

n

i

ADD ADD i 1 (1 2) (1 2, )

 Equation D-4.    

n

i

ADD ADD i 1 (3 5) (3 5, )

 Equation D-5.    

n

i

ADD ADD i 1 (6 11) (6 11, )

 Equation D-6.    

n

i

ADD ADD i 1 (12 19) (12 19, )

 Equation D-7.   n

i

ADD adult ADD adult i 1 ( ) ( , )

where i represents the i

th food type or ingestion medium and n equals the total number of food 

types or ingestion media, and ADD parameters are defined below: 

ADD(<1) = Total average daily dose of chemical for infants less than one year from 

ingestion of breast milk (mg/kg-day) 

ADD(1-2) = Total average daily dose of chemical from all ingestion sources for children 

ages 1 through 2 years (mg/kg-day) 

ADD(3-5) = Total average daily dose for children ages 3 through 5 years (mg/kg-day) 

ADD(6-11) = Total average daily dose for children ages 6 through 11 years (mg/kg-day) 

ADD(12-19) = Total average daily dose for children ages 12 through 19 years (mg/kg-day) 

ADD(adult) = Total average daily dose for adult age 20 up to 70 years (mg/kg-day) 

The lifetime average daily dose (LADD) is calculated as the time-weight average of the ADD

values for each age group (Equation D-8). 

Equation D-8. Lifetime Average Daily Dose (LADD) 





 



  



 



  



 



  



 



  



 



  



 



   70

50

70

8

70

6

70

3

70

2

70

1 LADD ADD( 1) ADD(1-2) ADD(3-5) ADD(6-11) ADD(12-19) ADD(adult)

The time-weighting factors simply equal the duration of exposure for the specified age category 

in years divided by the total lifespan, assumed to be 70 years. For risk assessments for 

chemicals with a subchronic RfD or for developmental effects in children, ADD(y) values for the 

child age groups are compared with the RfD (see Section D-3). 
2/15/2011 D-4 DRAFT 

D-2.3 Chemical Intake Calculations for Nursing Infants 

The scientific literature indicates that infants can be exposed to some chemicals via their 

mothers’ breast milk. The magnitude of the exposure can be estimated from information on the 

mother’s exposure, data on the partitioning of the chemical into various compartments of the 

mother’s body and into breast milk, and information on the infant’s consumption of milk and 

absorption of the chemical. To add this exposure pathway to the MIRC application, we adapted 

exposure algorithms and default assumptions from EPA’s Methodology for Assessing Health 

Risks Associated with Multiple Pathways of Exposure to Combustor Emissions (EPA 1998), 

hereafter referred to as MPE, as explained below. 

Note that this pathway generally is of most concern for lipophilic bioaccumulative chemicals 

(e.g., dioxins) that can cause developmental effects. The period of concern for the more 

hydrophilic chemicals that cause developmental effects generally is earlier, that is, from 

conception to birth. Hydrophilic chemicals generally exchange well between the maternal and 

fetal blood supplies at the placenta. 

D-2.3.1 Infant Average Daily Absorbed Dose 

The average daily dose of chemical absorbed by the infant (DAIinf) is estimated in MIRC with 

Equation D-9. This basic exposure equation relies on the concentration of the chemical in the 

breast milk, the infant’s breast-milk ingestion rate (IRmilk), the absorption efficiency of the 

chemical by the oral route of exposure (AEinf), the bodyweight of the infant (BWinf), and the 

duration of breast feeding (ED). Equation D-9 is EPA’s (EPA 1998) modification of an average 

daily dose for the infant model first published by Smith (1987) and includes variables for both 

the concentration of the chemical in the breast milk fat (Cmilkfat) and the concentration of the 

chemical in the aqueous phase of breast milk (Caqueous). The remainder of the DAIinf-associated 

equations assume that most chemicals of concern will partition either to the lipid phase or to the 

aqueous phase of breast milk, although some chemicals may partition significantly to both 

phases of milk. At present, MIRC is configured to estimate intake via the lipid phase only. For 

the equations below, we assume that Caqueous is equal to zero and hence drops out of the 

equation. 
2/15/2011 D-5 DRAFT 

Equation D-9. Average Daily Dose of Chemical to the Nursing Infant 

    

BW AT

C f C f IR AE ED

DAI

inf

milkfat mbm aqueous mbm milk inf

inf



        1

where: 

DAIinf = Average daily dose of chemical absorbed by infant (mg chemical/kg body 

weight-day) 

Cmilkfat = Concentration of chemical in lipid phase of maternal milk (mg chemical/kg milk 

lipid; calculated using Equation D-10) 

fmbm = Fraction of fat in breast milk (unitless) 

Caqueous = Concentration of chemical in aqueous phase of maternal milk (mg chemical/kg 

aqueous phase milk) 

IRmilk = Infant milk ingestion rate over the duration of nursing (kg milk/day) 

AEinf = 

Absorption efficiency of the chemical by the oral route of exposure (i.e., 

chemical-specific fraction of ingested chemical that is absorbed by the infant) 

(unitless) 

ED = Exposure duration, i.e., duration of breast feeding (days) 

BWinf = Body weight of infant averaged over the duration of nursing (kg) 

AT = Averaging time associated with exposure of interest; equal to ED (days) 

As mentioned above, Equation D-9 includes terms for the chemical in both the lipid- and nonlipid phases of milk. The remaining equations, however, assume that a chemical of concern will 

partition to the lipid phase of breast milk. The chemicals of interest for this assessment are 

expected to partition to the lipid phase only. 

D-2.3.2 Chemical Concentration in Breast Milk Fat 

EPA (1998) reviewed three first-order kinetics models for estimating chemical concentration in 

breast milk fat. The model selected for use in MPE is the model used in MIRC. It is a changingconcentration model that EPA adapted from a model by Sullivan et al. (1991). The model, 

shown in Equation D-10, estimates the average chemical concentration in the breast milk over 

the entire period of breast feeding by reference to a maximum theoretical steady-state 

concentration. Studies of lipophilic chemicals such as dioxins suggest that concentrations in the 

maternal milk are highest during the first few weeks of breast feeding and then decrease over 

time (ATSDR 1998). Equation D-10 accounts for the changing concentration in breast milk fat, 

but estimates one average value to represent the concentration over the entire duration of 

breast feeding. The model is dependent on the maternal body burden of the chemical and 

assumes that the chemical concentration in breast milk fat is the same as the concentration in 

general maternal body fat. According to reviewers of the model, this assumption warrants 

further investigation because milk fat appears to be synthesized in the mammary glands and 

may have lower chemical concentrations than general body fat stores (EPA 2001). 
2/15/2011 D-6 DRAFT 

Equation D-10. Chemical Concentration in Breast Milk Fat 

 













  













   

 



   elim pn  fat elac bf k t

fat elac

k t elim

fat elac fat elac bf

elim

elim fm

mat f

milkfat e

k

k

e

k k t

k

k f

DAI f C _ 1 1 1

_ _ _

where: 

Cmilkfat = Concentration of chemical in lipid phase of maternal milk (mg chemical/kg 

lipid) 

DAImat = Daily absorbed maternal chemical dose (mg chemical/kg maternal body 

weight-day; calculated using Equation D-11) 

ff = 

Fraction of total maternal body burden of chemical that is stored in maternal fat 

(mg chemical in body fat / mg total chemical in whole body; value from 

literature or EPA default) 

kelim = 

Chemical-specific total elimination rate constant for elimination of the chemical 

by non-lactating women (per day; e.g., via urine, bile to feces, exhalation; 

value from literature or calculated using Equation D-12) 

ffm = Fraction of maternal body weight that is fat stores (unitless) 

kfat_elac = 

Chemical-specific rate constant for total elimination of chemical in the lipid 

phase of milk during nursing (per day; value from literature or calculated using 

Equation D-13) 

tbf = Duration of breast feeding (days) 

tpn = Duration of mother’s exposure prior to parturition and initiation of breast 

feeding (days) 

Equation D-10 relies on the daily maternal absorbed intake (DAImat) to determine the 

concentration of the chemical in the breast milk fat. DAImat is multiplied by the fraction of the 

chemical that is stored in maternal fat (ff) to determine the amount (i.e., mass) of chemical in the 

fat. This product, divided by the chemical-specific elimination rate constant (kelim) for nonlactating adult women and the fraction of the mother’s weight that is fat (ffm), represents the 

maximum theoretical steady-state concentration of the chemical in an adult woman. If used 

alone to estimate the chemical concentration in breast milk fat, the equation as explained thus 

far is likely to overestimate the chemical concentration in milk fat because it does not account 

for losses due to breast feeding. Alone, this term (DAImat ff / kelim ffm) also assumes that the 

biological half-life of the chemical in the mother’s breast milk fat is small relative to the duration 

of the mother’s exposure. However, for chemicals with half-lives that are longer than the 

exposure duration, which are the chemicals of concern in the applications of MIRC to date, an 

additional term is needed to determine the average concentration in the milk fat over the 

duration of her exposure. 

To account for breast feeding losses and longer chemical half-lives in the mother than the 

exposure duration, an additional term is included in Equation D-10. This term includes a 

fraction dependent on two rate constants, kelim and the elimination constant for a lipophilic 

chemical in lactating women via the lipid phase of breast milk (kfat_elac), the duration of the 

mother’s chemical exposure prior to nursing (tpn), and the duration of breast feeding (tbf). The 

whole body concentration (DAImat ff / kelim ffm), the maximum theoretical steady-state 

concentration, is multiplied by the rate of elimination averaged over the duration of the mother’s 

exposure, including her exposure prior to and during lactation. To review the derivation of 

Equation D-10, see Appendix B of EPA (1998). 
2/15/2011 D-7 DRAFT 

To estimate an average daily dose absorbed by an infant’s mother, or DAImat, the average daily 

dose (ADD) (in mg/kg-day) for the chemical from all sources that MIRC calculates for adults 

(ADD(adult), described in Section D-2.1, Equation D-1), is multiplied by an absorption efficiency 

(AEmat) or fraction of the chemical absorbed by the oral route of exposure, as shown in Equation 

D-11. The value for AEmat can be estimated from absorption efficiencies for adults in general. 

Available data for some chemicals, in particular some inorganic compounds, indicate AE values 

for ingestion exposures of substantially less than 100 percent. For a few of these chemicals 

(e.g., cadmium), data also indicate lower AEs for the chemical when ingested in food or in soil 

than when ingested in water. However, it is reasonable to either assume 100 percent for the 

AEmat or to use the higher AEmat of the food and water AEmat values if available; hence, a single 

AEmat parameter is included in Equation D-11. 

Equation D-11. Daily Maternal Absorbed Intake 

DAImat  ADD(adult)  AEmat

where: 

DAImat = Daily maternal dose of chemical absorbed from medium i (mg/kg-day) 

ADD(adult) = Average daily dose to the mother (mg/kg-day) (calculated by MIRC – see 

Section D-2.1, Equation D-1) 

AEmat = 

Absorption efficiency of the chemical by the oral route of exposure (i.e., 

chemical-specific fraction of ingested chemical that is absorbed) by the mother 

(unitless) (value from literature or EPA default) 

Equation D-1, used to calculate ADD(adult), is based on many medium-specific ingestion rates that 

are normalized to body weight. The adult body weights to which the homegrown food ingestion 

rates are normalized are the body weights of the consumers in the original USDA survey (see 

Appendix B), which included both males and females. An assumption in the breast-milk 

exposure pathway is that those ingestion rates also are applicable to nursing mothers. The 

original data for ingestion rates for soil, drinking water, and fish are on a per person basis for 

males and females combined. MIRC divides those chemical intakes by an adult body weight for 

males and females combined as specified by the user (e.g., 71.4 kg mean value) to estimate the 

ADD normalized to body weight from those sources. If the user finds that those exposure media 

contribute the majority of the chemical intake for the risk scenario under consideration, the user 

may use alternative ingestion rates for those media and alternative body weights for nursing 

women. 

Elimination rates for chemicals often are reported as the half-life of the chemical in the body 

following a known dose of chemical. Many chemicals exhibit a two-phase elimination process, 

the first being more rapid than the second. For screening risks for persistent and 

bioaccumulative chemicals, the half-life of the slower phase of elimination, presumably from 

non-blood compartments of the body, is the more important of the two. Assuming first-order 

kinetics, Equation D-12 is used to convert a measured half-life for elimination of a chemical for 

adults or non-lactating women to an elimination rate constant (EPA 1998). The equation can be 

used to estimate any kind of chemical loss rate constant from a measured chemical half-life. 
2/15/2011 D-8 DRAFT 

Equation D-12. Biological Elimination Rate Constant for Chemicals for Non-lactating Women 

h

kelim

ln2 

where: 

kelim = Chemical-specific elimination rate constant for elimination of the chemical for 

non-lactating women (per day; e.g., via urine, bile to feces, exhalation) 

ln2 = Natural log of 2 (unitless constant) 

h = Chemical-specific biological half-life of chemical for non-lactating women 

(days) 

For chemicals transferred from the body of lactating women to breast milk, the rate of chemical 

elimination is augmented by the rate of chemical loss via the milk. The total elimination rate for 

lactating women sometimes is measured directly and reported in the literature. Where direct 

measurements are not available, and for chemicals that partition predominantly to the lipidphase of milk, EPA has used Equation D-13 to estimate the total chemical elimination rate for 

lactating women, kfat_elac (EPA 1998). 

Equation D-13. Biological Elimination Constant for Lipophilic Chemicals for Lactating Women 

fm mat

milk f mbm

fat elac elim f BW

IR f f k k



  _  

where: 

kfat_elac = 

Rate constant for total elimination of chemical during nursing (per day); 

accounts for both elimination by adults in general and the additional chemical 

elimination via the lipid phase of milk in nursing women 

kelim = 

Elimination rate constant for chemical from adults, including non-lactating 

women (per day; e.g., via urine, bile to feces, exhalation; chemical-specific; 

value from literature or calculated from half-life using Equation D-12) 

IRmilk = Infant milk ingestion rate over the duration of nursing (kg/d) 

ff = 

Fraction of total maternal body burden of chemical that is stored in maternal fat 

(mg chemical in body fat / mg chemical total in body; value from literature or 

EPA default) 

fmbm = Fraction of fat in breast milk (unitless) 

ffm = Fraction of maternal body weight that is fat stores (unitless) 

BWmat = Maternal body weight over the entire duration of the mother’s exposure to the 

chemical including during pregnancy and lactation (kg) 

Equation D-13 is based on a model from Smith (1987) and accounts for the additional 

elimination pathway for lipophilic chemicals via the breast milk fat. The term Kfat_elac is 

estimated by adding an estimate of the first-order elimination constant for breast feeding losses 

to kelim, which is the chemical-specific total elimination rate constant for non-lactating women. 

The breast feeding losses are estimated from the infant’s intake rate of breast milk (IRmilk), the 

fraction of the total maternal body burden of the chemical that is stored in maternal body fat (ff), 

the fraction of the mother’s breast milk that consists of fat (lipids) (fmbm), the mother’s body 

weight (BWmat), and the fraction of the mother’s weight that is body fat (ffm). In Equation D-13, 
2/15/2011 D-9 DRAFT 

the value for the mother’s body weight should be specific to women of child-bearing age, as 

opposed to a body weight value for both males and females that is used to estimate an adult 

average daily dose and the mother’s absorbed daily intake in Equation D-11. Smith’s (1987) 

model assumes that the chemical partitions to the lipid-phase of breast milk to the same degree 

that it partitions into the mother’s body fat. For highly lipophilic compounds, losses from breast 

feeding can be larger than losses by all other pathways (EPA 1998). 

D-3 Risk Estimation 

For persistent and bioaccumulative hazardous air pollutants (BP-HAPs), risks from inhalation of 

a chemical directly from air generally will be negligible compared with risks from ingestion of the 

chemical with foodstuffs grown in an area subject to air deposition of the chemical. For other 

(non-PB) HAPs, inhalation risks can be estimated separately and compared with risks 

associated with ingestion exposure to determine the focus of subsequent tiers of the risk 

assessment. Risk characterization for carcinogens with a linear mode of action at low doses is 

described in Section D-3.1. Risk characterization for chemicals likely to exhibit a threshold for 

response (e.g., non-cancer hazards) is described in Section D-3.2. 

D-3.1 Cancer Risks 

The estimated risk of developing cancer from exposure to a chemical from a specified source is 

characterized as the excess lifetime cancer risk (ELCR). The ELCR represents the incremental 

probability of an individual developing cancer over a lifetime as a result of lifetime exposure to 

the chemical. For a known or suspected carcinogen with a low-dose linear mode of action, the 

estimated ELCR is calculated as the product of the lifetime average daily dose (LADD) and the 

cancer slope factor (SF): 

Equation D-14. Calculation of Excess Lifetime Cancer Risk 

ELCR = LADD  CSF 

where: 

ELCR = Estimated excess lifetime cancer risk from a chemical summed across all 

exposure pathways and media (unitless) 

LADD = Lifetime average total daily dose from all exposure pathways and media 

(mg/kg-day) 

CSF = Oral carcinogenic potency slope factor for chemical (per mg/kg-day) 

As described in Section D-2.2, the LADD (in mg/kg-day) for a chemical is calculated to reflect 

age-related differences in exposure rates that are experienced by a hypothetical individual 

throughout his or her lifetime of exposure. The total chemical intake is normalized to a lifetime, 

which for the purposes of this assessment is assumed to be 70 years. 

EPA considers the possibility that children might be more sensitive than adults to toxic 

chemicals, including chemical carcinogens (EPA 2005b,c). Where data allow, EPA 

recommends development of lifestage-specific cancer potency CSFs. To date, EPA has 

developed a separate slope factor for early lifestage exposure for only one chemical (i.e., 1,1,1-

trichloroethane; EPA 2007), and current data availability for most chemicals preclude this 

approach. EPA has, therefore, examined options for default adjustments of the CSF to protect 

children. To date, the only mode of action (MOA) for carcinogenesis for which EPA has 

adequate data to develop a reasonable quantitative default approach is mutagenesis (EPA 
2/15/2011 D-10 DRAFT 

2005b,c). For carcinogens with a mutagenic MOA for cancer, EPA concluded that the 

carcinogenic potency of a chemical may be approximately tenfold greater for the first 2 years of 

life (i.e., birth up to second birthday) and threefold greater for the next 14 years of life (i.e., ages 

2 through 15) than for adults (EPA 2005c). These conclusions are represented by agedependent adjustment factors (ADAFs) of 10, 3, and 1 for the first two lifestages and for adults, 

respectively. 

These three lifestages do not match the age categories for the home-grown food ingestion 

rates, the age categories in MIRC. As a consequence, ADAFs for the age groups in MIRC are 

adapted as time-weighted average values as follows: 

  

3

6 5

2

10 1 yr 3 1 yr

10

3 5

1 2



    

 

( - )

( - )

( 1)

ADAF

ADAF .

ADAF

  

1

2

8

3 4 yrs 1 4 yrs

3

12 19

6 11



    



(adult)

( - )

( - )

ADAF

ADAF

ADAF

To estimate total lifetime risk from a lifetime of exposure to such a chemical, EPA recommends 

estimating the cancer risk for each of the three lifestages separately and then adding the risks 

for i = 1 to 6 age groups. 

Equations D-15 to D-21. Lifetime Cancer Risk: Chemicals with a Mutagenic MOA for Cancer 

Equation D-15. Risk(<1) = ADD(0-<1) x 10 x CSF x (1 yr/70 yr) 

Equation D-16. Risk(1-2) = ADD(1-2) x 6.5 x CSF x (2 yr/70 yr) 

Equation D-17. Risk(3-5) = ADD(3-5) x 3 x CSF x (3 yr/70 yr) 

 Equation D-18. Risk(6-11) = ADD(6-11) x 3 x CSF x (6 yr/70 yr) 

 Equation D-19. Risk(12-19) = ADD(12-19) x 2 x CSF x (8 yr/70 yr) 

 Equation D-20. Risk(adult) = ADD(adult) x 1 x CSF x (50 yr/70 yr) 

Equation D-21. ELCR   n

i

Risk i 1 ( )

In other words, Equation D-21 indicates that the total extra lifetime cancer risk (ELCR) equals 

the sum of the age-group-specific risks estimated by Equations D-15 through D-20, where: 

Risk(<1) = Risk from chemical ingestion in first year of life 

Risk(1-2) = Risk from chemical ingestion from first birthday through age 2 years 

Risk(3-5) = Risk from chemical ingestion from age 3 through 5 years of age 

Risk(6-11) = Risk from chemical ingestion from age 6 through 11 years of age 

Risk(12-19) = Risk from chemical ingestion from age 12 through 19 years of age 

Risk(adult) = Risk from chemical ingestion from age 20 to 70 years age 

ADD(<1) = Average daily dose for infants under one year of age (mg/kg-day) 

ADD(1-2) = Average daily dose from first birthday through age 2 years of age (mg/kg-day) 

ADD(3-5) = Average daily dose from age 3 through 5 years of age (mg/kg-day) 

ADD(6-11) = Average daily dose from age 6 through 11 years of age (mg/kg-day) 

ADD(12-19) = Average daily dose from age 12 through 19 years of age (mg/kg-day) 

ADD(adult) = Average daily dose for adults age 20 to 70 years of age (mg/kg-day) 
2/15/2011 D-11 DRAFT 

CSF = Oral carcinogenic potency slope factor for chemical (per mg/kg-day) 

Risk(i) = Risk from chemical ingestion for the ith age group 

ELCR = Total extra lifetime cancer risk (incremental or extra risk) 

n = Number of age groups (i.e., 6) 

D-3.2 Non-cancer Hazard Quotients 

Non-cancer risks are presented as hazard quotients (HQs), that is, the ratio of the estimated 

daily intake (i.e., ADD) to the reference dose (e.g., chronic RfD). If the HQ for a chemical is 

equal to or less than 1, EPA believes that there is no appreciable risk that non-cancer health 

effects will occur. If the HQ is greater than 1, however, EPA cautions that adverse health 

effects are possible, although an HQ above 1 does not indicate an effect will definitely occur. 

This is because of the margin of safety inherent in the derivation of all RfD values. The larger 

the HQ value, the more likely it is that an adverse effect may occur. 

For chemicals with a chronic RfD, MIRC calculates an HQ for each age group separately using 

Equation D-22 to indicate the potential for adverse health effects associated with chronic 

exposure via ingestion pathways. The HQ is the ratio of a long-term, daily average exposure 

normalized to the receptor's body weight (i.e., ADD) to the RfD for that chemical. 

Equation D-22. Hazard Quotient for Chemicals with a Chronic RfD 

RfD

ADD HQ 

where: 

HQ = Hazard quotient for chemical (unitless) 

ADD = Average daily ingested dose of chemical (mg/kg-day) from all food types and 

ingested media for the receptor 

RfD = Chronic oral reference dose for chemical (mg/kg-day) 

For chemicals for which the toxicity reference value is an RfD based on developmental effects in 

infants, children, or young animals, a shorter exposure duration (ED) and averaging time (AT) 

may be required. For this type of chemical (e.g., methylmercury, 2,3,7,8-TCDD), the 

appropriate ED/AT and sensitive lifestage for exposure may need to be estimated from the 

information provided in the critical developmental study(ies) from which the RfD was derived 

(e.g., in consultation with the RfD documentation in EPA’s IRIS or in a toxicological profile 

developed for the chemical). For screening-level risk assessments, however, a conservative 

approach is to compare the highest ADD from among the child age categories provided in MIRC 

to the RfD. 
2/15/2011 D-12 DRAFT 

D-4 References 

Agency for Toxic Substances and Disease Registry (ATSDR). 1998. Toxicological profile for 

chlorinated dibenzo-p-dioxins. Atlanta, GA: U.S. Department of Health and Human Services, 

Public Health Service. 

Smith, A.H. 1987. Infant exposure assessment for breast milk dioxins and furans derived from 

waste incineration emissions. risk analysis 7:347-353. 

Sullivan, M.J., S.R. Custance, and C.F. Miller. 1991. Infant exposure to dioxin in mother’s milk 

resulting from maternal ingestion of contaminated fish. Chemosphere 23(8-10): 1387-1396. 

U.S. Environmental Protection Agency (EPA). 1997. Exposure Factors Handbook. Volumes I, 

II, and III. Office of Research and Development, Washington, D.C. EPA-600-P-95-002Fa,b,c. 

August. Available at: http://www.epa.gov/nceawww1/efh/. 

U.S. Environmental Protection Agency (EPA). 1998. Methodology for Assessing Health Risks 

Associated with Multiple Pathways of Exposure to Combustor Emissions. National Center for 

Environmental Assessment, Cincinnati, OH. EPA-600-R-98-137. Available at: 

http://cfpub.epa.gov/ncea/cfm/recordisplay.cfm?deid=55525. 

U.S. Environmental Protection Agency (EPA). 2001. Peer Review of EPA’s Hazardous Waste 

Identification Rule Risk Assessment Model: Breast milk exposure model for the HWIR 3MRA 

Model. Prepared by Eastern Research Group for EPA Office of Solid Wastes. 68-W5-0057. 

U.S. Environmental Protection Agency (EPA). 2003. Chapter 10 In: Multimedia, Multipathway, 

and Multireceptor Risk Assessment (3MRA) Modeling System, Volume II: Site-based, Regional, 

and National Data. SAB Review Draft. EP-530/D-03-001b. Office of Research and 

Development, Athens, GA, and Research Triangle Park, NC, and Office of Solid Waste, 

Washington, D.C. July. Available at: 

http://www.epa.gov/osw/hazard/wastetypes/wasteid/hwirwste/risk03.htm. 

U.S. Environmental Protection Agency (EPA). 2005a. Human Health Risk Assessment 

Protocol for Hazardous Waste Combustion Facilities. Office of Solid Waste and Emergency 

Response, Washington, DC. EPA-530-R-05-006. September. Available at: 

http://www.epa.gov/osw/hazard/tsd/td/combust/risk.htm. 

U.S. Environmental Protection Agency (EPA). 2005b. Guidance on Selecting Age Groups for 

Monitoring and Assessing Childhood Exposures to Environmental Contaminants. Risk 

Assessment Forum. Washington, DC. November. EPA/630/P-03/003F. Available at: 

http://cfpub.epa.gov/ncea/cfm/recordisplay.cfm?deid=146583. 

U.S. Environmental Protection Agency (EPA). 2005c. Guidelines for Carcinogen Risk 

Assessment. Risk Assessment Forum, Washington, DC. EPA/630/P-03/001F. March. 

Available from: http://www.epa.gov/IRIS/cancer032505-final.pdf. 

U.S. Environmental Protection Agency (EPA). 2007. Toxicological Review of 1,1,1-

Trichloroethane (CAS No. 71-55-6) In Support of Summary Information on the Integrated Risk 

Information System (IRIS). Office of Research and Development, Washington, DC. 

EPA/635/R-03/006. August. Available at: http://www.epa.gov/iris