Health Hazards and Risk Assessment

4% of exam

Dose-response toxicity for carcinogens and noncarcinogens, exposure routes and pathways and chronic daily intake, and occupational health including PPE and noise exposure.

3 concepts

Exam areas

A. Dose-response toxicity

Dose–Response Toxicity (Carcinogens and Noncarcinogens)

How a contaminant dose becomes a quantified health risk along two NCEES tracks: linear-no-threshold cancer risk (Risk = CDI×CSF) and the noncancer hazard quotient (HI = CDI/RfD).

Risk assessment is where toxicology becomes arithmetic, and on the FE Environmental exam it is graded on whether you pick the right track. The NCEES handbook splits health effects into two families that never mix: carcinogens, treated as having no safe dose so risk rises linearly from the origin, and noncarcinogens, treated as having a threshold below which the body copes. Master which equation belongs to which family—

\text{Risk} = \text{CDI}\times\text{CSF}

for cancer,

\text{HI} = \text{CDI}/\text{RfD}

for everything else—and most points in this area are yours. These relationships live in the Safety chapter of the FE Reference Handbook under Risk Assessment/Toxicology, not the Environmental Engineering chapter, which is exactly where candidates waste time looking.

Reading a dose–response curve

Toxicologists administer increasing doses to a test population and plot the percentage that responds (a defined symptom, or death) against the logarithm of dose in

\text{mg}/(\text{kg}\cdot\text{day})

. The result is the classic sigmoid: a region of no apparent effect, a steeply rising middle, and a plateau at

100\%

. The position and steepness of that curve are the entire story—a curve shifted left means a more potent toxicant, and a steep slope means a small dose change produces a large response change. The single most quoted point on the curve is its midpoint, the dose that affects half the population.

LD50, LC50, and potency ranking

The

\text{LD}_{50}

(median lethal dose) is the single dose expected to kill

50\%

of test animals, usually by oral or dermal exposure, expressed in

\text{mg}/\text{kg}

of body weight. Its airborne cousin, the

\text{LC}_{50}

(median lethal concentration), is the air concentration expected to kill half the animals over a fixed

1

- or

4

-hour exposure. The counter-intuitive rule examiners exploit: a smaller

\text{LD}_{50}

means a more toxic substance, because less of it is lethal. Botulinum toxin (

\text{LD}_{50}\approx 0.00001\ \text{mg}/\text{kg}

) is therefore millions of times more potent than table salt (

\approx 4{,}000\ \text{mg}/\text{kg}

\text{LD}_{10}

and

\text{LC}_{10}

are defined identically at the

10\%

response level.

NOAEL, LOAEL, and the reference dose

For noncarcinogens the design point is not the median but the threshold. The

\text{NOAEL}

(No Observed Adverse Effect Level) is the highest tested dose at which no harmful effect appears; the

\text{LOAEL}

is the lowest dose at which one does. Regulators take the

\text{NOAEL}

from an animal study and divide by a total uncertainty factor

\text{UF}

(compounding factors of

10

for animal-to-human extrapolation, sensitive subpopulations, data gaps, and so on) to obtain the reference dose

\text{RfD}

—the chronic daily dose a healthy person could absorb for a lifetime without adverse effect. The safe human dose simply scales the

\text{RfD}

by body weight,

\text{SHD} = \text{RfD}\cdot W

\text{RfD} = \dfrac{\text{NOAEL}}{\text{UF}}, \qquad \text{SHD} = \text{RfD}\cdot W = \dfrac{\text{NOAEL}\cdot W}{\text{UF}}

Track 1 — carcinogens and the cancer slope factor

Carcinogens are assumed to have no threshold: even one molecule carries some probability of initiating a tumor, so the dose–response line is forced through the origin and linearized at low dose. Its slope is the cancer slope factor

\text{CSF}

, in units of

[\text{mg}/(\text{kg}\cdot\text{day})]^{-1}

. The excess lifetime cancer risk is the dimensionless product of dose and slope. EPA treats added risk between

10^{-6}

and

10^{-4}

as the acceptable range—one extra cancer in a million to one in ten thousand exposed people.

\text{Risk} = \text{CDI}\times\text{CSF}

Track 2 — noncarcinogens and the hazard index

Below the threshold the body detoxifies, so the metric is not a probability but a ratio: the hazard quotient

\text{HQ}=\text{CDI}/\text{RfD}

, the fraction of the safe dose actually received. Summing the quotients of every contaminant and pathway gives the hazard index

\text{HI}

. An

\text{HI}\le 1.0

means cumulative exposure stays within safe limits;

\text{HI}>1.0

flags the possibility of an adverse effect. Note the asymmetry that trips candidates: cancer risks add as small probabilities, while noncancer hazards add as quotients—and a single

\text{HQ}

can exceed

1

even when others are tiny.

\text{HI} = \sum_i \text{HQ}_i = \sum_i \dfrac{\text{CDI}_i}{\text{RfD}_i}

Chemical interactions

Real exposures involve mixtures, and the handbook flags three interaction modes you should recognize qualitatively. Additive effects sum (

2+3=5

), as with several organophosphate pesticides; synergistic effects exceed the sum (

2+3=20

), the textbook case being asbestos plus cigarette smoke; antagonistic effects fall short (

6+6=8

), as when one solvent competes for the same metabolic pathway. The hazard-index method assumes additivity, which is conservative for antagonists and non-conservative for synergists—worth a sentence if a problem asks you to critique the approach.

Exam strategy

Your first move on any risk question is to classify the contaminant: carcinogen or not. Carcinogen means

\text{Risk}=\text{CDI}\times\text{CSF}

, a probability you compare to

10^{-6}

–

10^{-4}

; noncarcinogen means

\text{HI}=\text{CDI}/\text{RfD}

, a ratio you compare to

1

. Watch the units:

\text{CSF}

carries inverse-dose units so the product is dimensionless, while

\text{RfD}

shares the dose units of

\text{CDI}

so the quotient is dimensionless—if your answer has stray units, you used the wrong factor. Match your reported precision to the data: slope factors, reference doses, and intakes are typically two-significant-figure quantities, so a risk or hazard quotient should not be quoted to more digits than its inputs justify. Remember that smaller

\text{LD}_{50}

equals more toxic, that

\text{RfD}=\text{NOAEL}/\text{UF}

(divide, never multiply, by the uncertainty factor), and that a problem giving you a

\text{CSF}

is implicitly telling you the chemical is a carcinogen.

Key equations

Cancer risk (linear, no threshold)

\text{Risk} = \text{CDI}\times\text{CSF}

Excess lifetime cancer probability (dimensionless). CDI = chronic daily intake in $\text{mg}/(\text{kg}\cdot\text{day})$ ; CSF = cancer slope factor in $[\text{mg}/(\text{kg}\cdot\text{day})]^{-1}$ . Acceptable EPA range $10^{-6}$ to $10^{-4}$ .

Hazard quotient

\text{HQ} = \dfrac{\text{CDI}}{\text{RfD}}

Fraction of the safe dose received for one noncarcinogen and pathway (dimensionless). RfD = reference dose in $\text{mg}/(\text{kg}\cdot\text{day})$ .

Hazard index

\text{HI} = \sum_i \dfrac{\text{CDI}_i}{\text{RfD}_i}

Sum of hazard quotients over all noncarcinogens and routes. $\text{HI}>1.0$ indicates possible adverse effect.

Reference dose from NOAEL

\text{RfD} = \dfrac{\text{NOAEL}}{\text{UF}}

Chronic safe daily dose, $\text{mg}/(\text{kg}\cdot\text{day})$ . NOAEL = no-observed-adverse-effect level from the animal dose-response curve; UF = total uncertainty factor (often $10$ – $10{,}000$ ).

Safe human dose

\text{SHD} = \text{RfD}\cdot W = \dfrac{\text{NOAEL}\cdot W}{\text{UF}}

Allowable daily intake in $\text{mg}/\text{day}$ for a person of body weight $W$ (kg).

Median lethal dose / concentration

\text{LD}_{50},\ \text{LC}_{50}

Dose ( $\text{mg}/\text{kg}$ ) or air concentration killing $50\%$ of test animals. Smaller value = more toxic. $\text{LD}_{10}/\text{LC}_{10}$ defined at $10\%$ .

Hazard index pass/fail

\text{HI} \le 1.0 \ \Rightarrow\ \text{acceptable}, \qquad \text{HI} > 1.0 \ \Rightarrow\ \text{possible adverse effect}

EPA decision rule for noncarcinogenic risk characterization.

Acceptable carcinogenic risk band

10^{-6} \le \text{Risk} \le 10^{-4}

EPA range for incremental lifetime cancer risk used in site cleanup decisions.

Worked examples

Cancer risk from a chlorinated solvent

Problem. A resident has an estimated chronic daily intake of a carcinogenic solvent of $\text{CDI} = 3.0\times10^{-4}\ \text{mg}/(\text{kg}\cdot\text{day})$ . The oral cancer slope factor is $\text{CSF} = 0.055\ [\text{mg}/(\text{kg}\cdot\text{day})]^{-1}$ . Is the incremental lifetime cancer risk within EPA's acceptable range?

Solution. Carcinogen → use

\text{Risk}=\text{CDI}\times\text{CSF}

\text{Risk} = (3.0\times10^{-4})(0.055) = 1.65\times10^{-5}

. Units cancel:

[\text{mg}/(\text{kg}\cdot\text{day})]\times[\text{mg}/(\text{kg}\cdot\text{day})]^{-1}

= dimensionless. The exact product

1.65\times10^{-5}

is carried through the calculation; because both inputs hold only two significant figures, the reported risk rounds to

1.7\times10^{-5}

—about

17

extra cancers per million exposed. Sanity check: the value lies between

10^{-6}

and

10^{-4}

, so it falls inside EPA's acceptable band (though above the

10^{-6}

point of departure). Final answer:

\text{Risk} \approx 1.7\times10^{-5}

(full product

1.65\times10^{-5}

), within the acceptable range.

\text{Risk} = (3.0\times10^{-4})(0.055) = 1.65\times10^{-5} \approx 1.7\times10^{-5}

Reference dose and hazard quotient

Problem. An animal study gives a $\text{NOAEL}$ of $5\ \text{mg}/(\text{kg}\cdot\text{day})$ for a noncarcinogen. Apply a total uncertainty factor of $1{,}000$ . If a child's chronic daily intake is $2.1\times10^{-3}\ \text{mg}/(\text{kg}\cdot\text{day})$ , find the reference dose and the hazard quotient.

Solution. Reference dose:

\text{RfD} = \text{NOAEL}/\text{UF} = 5/1000 = 5.0\times10^{-3}\ \text{mg}/(\text{kg}\cdot\text{day})

. Hazard quotient:

\text{HQ} = \text{CDI}/\text{RfD} = (2.1\times10^{-3})/(5.0\times10^{-3}) = 0.42

. Sanity check:

\text{HQ}<1

, so the dose is below the safe threshold—no adverse effect expected. Dividing (not multiplying) by UF gives a small, protective RfD, as intended. With both intake and RfD known to two significant figures, the quotient is reported as

0.42

(two sig figs), not

0.420

. Final answer:

\text{RfD} = 5.0\times10^{-3}\ \text{mg}/(\text{kg}\cdot\text{day})

\text{HQ} = 0.42

\text{HQ} = \dfrac{2.1\times10^{-3}}{5.0\times10^{-3}} = 0.42

Cumulative hazard index for a mixture

Problem. Groundwater contains three noncarcinogens. Their chronic daily intakes and reference doses [both $\text{mg}/(\text{kg}\cdot\text{day})$ ] are: A, $\text{CDI}=3.0\times10^{-3}$ , $\text{RfD}=4.0\times10^{-3}$ ; B, $\text{CDI}=1.2\times10^{-2}$ , $\text{RfD}=8.0\times10^{-2}$ ; C, $\text{CDI}=6.0\times10^{-4}$ , $\text{RfD}=2.0\times10^{-3}$ . Compute the hazard index and interpret it.

Solution. Compute each hazard quotient, then sum (additivity assumption).

\text{HQ}_A = 3.0\times10^{-3}/4.0\times10^{-3} = 0.75

\text{HQ}_B = 1.2\times10^{-2}/8.0\times10^{-2} = 0.15

\text{HQ}_C = 6.0\times10^{-4}/2.0\times10^{-3} = 0.30

\text{HI} = 0.75 + 0.15 + 0.30 = 1.20

. Sanity check: no single contaminant exceeds its RfD (all

\text{HQ}<1

), yet the cumulative

\text{HI}=1.20>1.0

—the mixture as a whole signals a possible adverse effect. This is the lesson examiners test: hazard adds. Final answer:

\text{HI} = 1.20

, exceeds

1.0

→ possible adverse effect.

\text{HI} = 0.75 + 0.15 + 0.30 = 1.20

Common pitfalls

•Mixing the two tracks: carcinogens use $\text{Risk}=\text{CDI}\times\text{CSF}$ (a probability), noncarcinogens use $\text{HI}=\text{CDI}/\text{RfD}$ (a ratio). If the problem hands you a CSF the chemical is a carcinogen; if it hands you an RfD or NOAEL it is not.
•Reading $\text{LD}_{50}$ backwards. A smaller $\text{LD}_{50}$ means MORE toxic—less mass kills half the population. Ranking chemicals by toxicity means ranking by ascending $\text{LD}_{50}$ .
•Multiplying by the uncertainty factor. The RfD is $\text{NOAEL}/\text{UF}$ —you DIVIDE to make the safe dose smaller and more protective.
•Forgetting hazard quotients add. Several contaminants each with $\text{HQ}<1$ can sum to $\text{HI}>1$ ; you must total all pathways and chemicals before deciding.
•Comparing cancer risk to $1.0$ or hazard index to $10^{-6}$ . The thresholds are not interchangeable: cancer risk is judged against $10^{-6}$ – $10^{-4}$ , hazard index against $1.0$ .
•Carrying stray units. CSF has inverse-dose units so $\text{Risk}$ is unitless; RfD shares CDI's units so $\text{HQ}$ is unitless. A leftover unit means the wrong factor was used.
•Overstating precision. Slope factors, reference doses, and intakes usually carry two significant figures, so a computed risk or hazard quotient should be reported to two as well—writing $0.420$ or $1.65\times10^{-5}$ as a headline implies digits the data do not support.
•Confusing NOAEL with LOAEL: NOAEL is the highest no-effect dose, LOAEL the lowest effect dose. The RfD is built from the NOAEL (or a benchmark dose), never the LOAEL directly.

References

NCEES FE Reference Handbook — Safety (Risk Assessment/Toxicology)
EPA, Risk Assessment Guidance for Superfund, Vol. I (Human Health Evaluation Manual, Part A)
Davis & Cornwell, Introduction to Environmental Engineering — risk assessment chapter

B. Exposure routes and pathways

Exposure Pathways and Chronic Daily Intake

Build the chronic daily intake from concentration, intake rate, and exposure factors across ingestion, inhalation, and dermal routes, and pick the averaging time splitting cancer from noncancer dose.

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C. Occupational health

Occupational Health: PPE and Noise Exposure

OSHA permissible exposure limits and time-weighted averages, the noise dose with its 5-dB exchange rate and hearing-conservation triggers, PPE selection, and the hierarchy of controls.

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