### Appendix D. Chemical Intake and Risk Equations[This page intentionally left blank.]2/15/2011 D-i DRAFT 

### TABLE OF CONTENTS D-1 Introduction .................................................................................................................. ......... 1 D-2 Calculation of Chemical Intake .............................................................................................. 1 

### D-2.1 Chemical Intake Calculations for A dults 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 .................................................................................................................... ...... 122/15/2011 D-ii DRAFT [This page intentionally left blank.]2/15/2011 D-1 DRAFT 

## 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                

   

 days 365 (y) (y) (y) (y) (i) (y,i) (i) (y,i) EF AT BW ED FC IR C 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 separatel y 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 pathw ay, 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 ( AT y ) is equal to the exposure duration for that group ( ED y ); 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 chemic al from all of the exposure media that a singleindividual 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 particular2/15/2011 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. breastmilk ADD ADD   )

1 (

Equation D-3. 

# 

   

###  n i i 

### ADD ADD 1 ) , 2 1 ( ) 2 1 (

Equation D-4. 

# 

   

###  n i i 

### ADD ADD 1 ) , 5 3 ( ) 5 3 (

Equation D-5. 

# 

   

###  n i i 

### ADD ADD 1 ) , 11 6 ( ) 11 6 (

Equation D-6. 

# 

   

###  n i i 

### ADD ADD 1 ) , 19 12 ( ) 19 12 (

Equation D-7. 

# 

 

###  n i i adult adult 

### ADD ADD 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 (adul t) = 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 (adult) (12-19) (6-11) (3-5) (1-2) 1) ( ADD ADD ADD ADD ADD ADD LADD
The time-weighting factors simply equal the duration of exposure for the specified age category in years divided by the total lifespan, assum ed 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 Calcul ations for Nursing Infants The scientific literature indicates that infants can be exposed to some chemicals via their mothers’ breast milk. The magnitude of the ex posure 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 effe cts 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 ( DAI inf

) 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 ( IR milk ), the absorption efficiency of the chemical by the oral route of exposure ( AE inf

), the bodyweight of the infant ( BW inf

), 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 ( C milkfat ) and the concentration of the chemical in the aqueous phase of breast milk ( C aqueous ). The remainder of the DAI inf

-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 c hemicals 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 C aqueous 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 

##     

#   

#   AT BW ED AE IR f C f C DAI inf inf milk mbm aqueous mbm milkfat inf    

   

 1

where:

DAI inf = Average daily dose of chemical absorb ed by infant (mg chemical/kg body weight-day)
C

milkfat = Concentration of chemical in lipid phase of maternal milk (mg chemical/kg milk lipid; calculated using Equation D-10) f mbm = Fraction of fat in breast milk (unitless)
C

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

milk = Infant milk ingestion rate over the duration of nursi ng (kg milk/day)

AE inf = Absorption efficiency of the chemical by the oral route of exposure (i.e., chemical-specific fraction of ingested chem ical that is absorbed by the infant) (unitless) ED = Exposure duration, i.e., duration of breast feeding (days) BW inf = 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 model s for estimating chemical concentration inbreast 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 m odel by Sullivan et al. (1991). The model, shown in Equation D-10, estimates the average c hemical 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 t he 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 Con centration in Breast Milk Fat 

#          

        

      
   bf elac fat pn elim t k
elac fat

elim t k
bf elac fat elac fat

elim
fm elim f

mat milkfat e k k e t k k k f k f DAI C

_ 1 1 1

_ _ _ where:

C milkfat = Concentration of chemical in lipid phase of maternal milk (mg chemical/kg lipid)
DAI mat = Daily absorbed maternal chemical dose (mg chemical/kg maternal body weight-day; calculated using Equation D-11)

f f = Fraction of total maternal body burden of c hemical that is stored in maternal fat (mg chemical in body fat / mg total chemical in whole body; value from literature or EPA default)

k

elim = Chemical-specific total elimination rate c onstant for elimination of the chemical by non-lactating women (per day; e.g., vi a urine, bile to feces, exhalation; value from literature or calculated using Equation D-12) f fm = Fraction of maternal body weight that is fat stores (unitless)

k

fat_elac = Chemical-specific rate constant for tota l elimination of chemical in the lipid phase of milk during nursing (per day; value from literature or calculated using Equation D-13) t bf = Duration of breast feeding (days)
t pn = Duration of mother’s exposure prior to parturition and initiation of breast feeding (days) Equation D-10 relies on the daily maternal absorbed intake ( DAI mat ) to determine the concentration of the chemical in the breast milk fat. DAI mat is multiplied by the fraction of the chemical that is stored in maternal fat ( f f ) to determine the amount (i.e., mass) of chemical in the fat. This product, divided by the chemical-specific elimination rate constant ( k elim ) for nonlactating adult women and the fraction of the mother’s weight that is fat (f fm ), 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 conc entration in milk fat because it does not account for losses due to breast feeding. Alone, this term ( DAI mat f f / k elim f

fm ) 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, k elim and the elimination constant for a lipophilic chemical in lactating women via the lipid phase of breast milk ( k fat

_ elac ), the duration of the mother’s chemical exposure prior to nursing ( t pn ), and the duration of breast feeding ( t bf

). The whole body concentration ( DAI mat f f / k elim f

fm ), the maximum theoretical steady-state concentration, is multiplied by the rate of elim ination 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 DAI mat , 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 ( AE mat ) or fraction of the chemical absorbed by the oral route of exposure, as shown in Equation D-11. The value for AE mat can be estimated from absorption efficiencies for adults in general. Available data for some chemicals, in particula r 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 AE mat or to use the higher AE mat of the food and water AE mat values if available; hence, a single AE mat parameter is included in Equation D-11. Equation D-11. Daily Maternal Absorbed Intake

mat (adult) mat AE ADD DAI   where:

DAI mat = 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)

AE mat 

### = Absorption efficiency of the chemical by the oral route of exposure (i.e., chemical-specific fraction of ingested chem ical that is absorbed) by the mother (unitless) (value from lit erature 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 report ed as the half-life of the chemical in the body following a known dose of chemical. Many chem icals 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 measur ed half-life for elimination of a chemical for adults or non-lactating women to an eliminatio n 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 Co nstant for Chemicals for Non-lactating Women



### h k

elim 

### 2 ln

 where:

k elim = Chemical-specific elimination rate const ant 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 lactati ng women to breast milk, the rate of chemical elimination is augmented by the rate of chemical lo ss 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 chem icals that partition predominantly to the lipidphase of milk, EPA has used Equation D-13 to estima te the total chemical elimination rate for lactating women, k fat

_ elac (EPA 1998). Equation D-13. Biological Elim ination Constant for Lipophilic Chemicals for Lactating Women

mat fm mbm f milk elim elac fat 

### BW f f f IR k k     

_ where:

k fat_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
k

elim = Elimination rate constant for chemic al 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) IR

milk = Infant milk ingestion rate ov er the duration of nursing (kg/d)

f f = Fraction of total maternal body burden of c hemical that is stored in maternal fat (mg chemical in body fat / mg chemical total in body; value from literature or EPA default) f mbm = Fraction of fat in breast milk (unitless)

f fm = Fraction of maternal body weight that is fat stores (unitless)
BW mat = Maternal body weight over the entire dura tion 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 chemical s via the breast milk fat. The term K fat

_ elac is estimated by adding an estimate of the first-order elimination constant for breast feeding losses to k elim , 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 ( IR milk ), the fraction of the total maternal body burden of the chemical that is stored in maternal body fat ( f f ), the fraction of the mother’s breast milk that consists of fat (lipids) ( f mbm ), the mother’s body weight ( BW mat ), and the fraction of the mother’s weight that is body fat ( f fm ). 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 neglig ible 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 expos ure 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 tota l 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 lifest age exposure for only one chemical (i.e., 1,1,1- trichloroethane; EPA 2007), and current data availab ility 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 acti on (MOA) for carcinogenesis for which EPA has adequate data to develop a reasonable quantit ative default approach is mutagenesis (EPA2/15/2011 D-10 DRAFT 2005b,c). For carcinogens with a mutageni c MOA for cancer, EPA concluded that the carcinogenic potency of a chemical may be approximat ely 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 ar e 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 5 6 2 yr 1 3 yr 1 10 10

5 3 2 1

    
  

)

- ( )

- ( 1) (

ADAF . ADAF ADAF 

##   

1 2 8 yrs 4 1 yrs 4 3 3

19 12 11 6

    
 

(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 C SF x (1 yr/70 yr) Equation D-16

. Risk (1-2) = ADD (1-2) x 6.5 x C SF 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 i 

### Risk 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 fr om 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 ( 1 2

- 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 th rough 5 years of age (mg/kg-day) ADD (6

- 11 ) = Average daily dose from age 6 thr ough 11 years of age (mg/kg-day) ADD ( 1 2

- 19 ) = Average daily dose from age 12 th rough 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 i th 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 calc ulates 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 t he 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 developm ental 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-leve l 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 

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