14.1 Non-Cancer Risk Characterization: Hazard Quotient (HQ), Hazard Index (HI) & Margin of Exposure (MoE)

Risk characterization is the decision document

Handbook III.D.1 is risk characterization: combining hazard, dose–response, and exposure into a statement a risk manager can use. Domain III is 38% of the DABT examination; risk characterization and management is 9%. Independent OpenExamPrep teaching in this section covers hazard quotients (HQ), hazard indices (HI), margins of exposure (MOE) and pharmaceutical margins of safety (MOS), aggregate versus cumulative combination, World Health Organization (WHO) toxic equivalency factors (TEFs) for dioxin-like compounds, and mixture models (dose additivity, response additivity, independent action, synergism). It is not an ABT product and does not claim official approval, review, or partnership with ABT, EPA, EFSA, WHO, or FDA.

A characterization is not a second hazard-identification essay. Hazard asked whether an adverse effect can occur. Dose–response asked how much. Exposure asked who gets how much. Characterization answers: for this receptor, this duration, and this set of chemicals, is the ratio of concern under a named decision rule? It also states the assumptions that produced the number. Chapter 11 already distinguished aggregate from cumulative at the conceptual-site-model stage; this section supplies the arithmetic and the combination rules.

Hazard quotient: exposure divided by a reference value

For threshold (noncancer) effects, the usual EPA Superfund and IRIS comparison is:

HQ = exposure / RfD

when the toxicity value is an oral reference dose (RfD) in mg/kg-day and exposure is an average daily dose (ADD) in the same units. For air:

HQ = exposure concentration / RfC

with both terms in mg/m³ (or both in µg/m³). Ecological and industrial-chemical programs use the same ratio with different names:

• Predicted environmental concentration / predicted no-effect concentration (PEC/PNEC) in REACH-style environmental risk (sometimes called a risk quotient)
• Risk characterization ratio (RCR) = exposure / derived no-effect level (DNEL) in REACH human-health characterization

An HQ equal to 1 means estimated exposure equals the reference value. An HQ below 1 is typically read as not exceeding that chemical’s noncancer reference for that route and duration. An HQ above 1 is a flag for refinement or management, not a probability that 30% of people will be ill if HQ = 1.30. The RfD already contains uncertainty factors (Chapter 13); HQ does not add those factors a second time.

Worked HQ. Oral ADD = 0.024 mg/kg-day, chronic RfD = 0.03 mg/kg-day. HQ_oral = 0.024 / 0.03 = 0.80.

Inhalation exposure concentration = 0.018 mg/m³, RfC = 0.02 mg/m³. HQ_inh = 0.018 / 0.02 = 0.90.

Worked PEC/PNEC. Surface-water PEC = 2.4 µg/L, aquatic PNEC = 8.0 µg/L. PEC/PNEC = 2.4 / 8.0 = 0.30. Same ratio logic as HQ; different receptor (an ecosystem, not a 70 kg adult).

If the oral 0.80 and inhalation 0.90 describe the same chemical in the same person, they are aggregate (below), not two cumulative chemicals.

Hazard index: add HQs only when the combination rule allows it

HI = Σ HQ_i for chemicals (or routes) that share a common mode of action (MOA) or a common target organ or system you have actually justified. EPA mixture guidance and pesticide cumulative assessment groups are built on that idea. Adding every HQ in a laboratory package because the samples arrived in one cooler is not a cumulative assessment.

Worked HI. Three groundwater chemicals:

HI_liver = 0.45 + 0.35 = 0.80 (below 1).
Blind sum = 0.45 + 0.35 + 0.90 = 1.70 (above 1).

Calling 1.70 “the site HI” treats a kidney toxicant as if it were another CAR liver agonist. That overstates liver risk and hides that chemical C’s own HQ is already 0.90—a single-chemical story that should stay visible. If A, B, and C truly shared one MOA, dose addition to 1.70 would be the correct HI and would warrant refinement.

HI greater than 1 does not prove clinical disease. It means the sum of fractions of the reference values exceeds the screening line, so you segregate by target, refine exposure, use relative potency factors (RPFs), or move to a fuller mixture model.

Margin of exposure and margin of safety

MOE = PoD / exposure

The point of departure (PoD) is often a BMDL10 or a NOAEL. Exposure is the same ADD or dietary intake used in an HQ. MOE is the reciprocal family of HQ when the “reference” has not already been divided by uncertainty factors: a large MOE means exposure sits far below the PoD. If HQ were built from that same PoD without UFs, HQ ≈ 1 / MOE only after you apply the same factor set; once the RfD exists, HQ and MOE are different documents.

Worked MOE. BMDL10 = 0.36 mg/kg-day, dietary exposure = 0.0036 mg/kg-day. MOE = 0.36 / 0.0036 = 100.

If exposure were 0.000036 mg/kg-day, MOE = 0.36 / 0.000036 = 10,000.

Named frameworks, not a universal constant.

• For many threshold endpoints, an MOE of 100 (10-fold interspecies × 10-fold human variability) is a common starting comparison when the PoD is a chronic NOAEL or BMDL10. Extra factors for LOAEL-to-NOAEL or database gaps raise the MOE you would want; a chemical-specific adjustment factor can lower it. 100 is not a law of biology.
• The European Food Safety Authority (EFSA) Scientific Committee MOE approach for substances that are both genotoxic and carcinogenic in food (opinions 2005 and 2012) treats an MOE of 10,000 or larger, calculated from a rodent BMDL10, as low concern from a public-health point of view. An MOE below 10,000 is a priority for risk management, not a proof of human tumors. That 10,000 belongs to that EFSA food-contaminant framework. ICH M7 often uses the same numerical margin for mutagenic pharmaceutical impurities—a different named program already taught with slope-factor math in Chapter 12. EPA linear cancer slope factors (section 14.2) do not convert every carcinogen into an MOE of 10,000.

MOS in drug development. Pharmaceutical margin of safety compares a nonclinical exposure at a NOAEL or, in oncology, a highest non-severely toxic dose (HNSTD) with the clinical exposure, usually as area under the concentration–time curve (AUC) in matching matrices (sometimes Cmax):

MOS = AUC_animal,NOAEL (or HNSTD) / AUC_clinical

Worked MOS. Rat NOAEL AUC0–24 = 15,000 ng·h/mL; intended human AUC0–24 = 2,500 ng·h/mL. MOS = 15,000 / 2,500 = 6.0.

A MOS of 6 on AUC is a clinical-development statement. It is not an EPA HQ, and it is not an EFSA food MOE of 10,000. Mixing MOS, MOE, and HQ on one slide is a Domain III error.

Aggregate versus cumulative

Aggregate: one chemical, all routes and pathways that operate for that receptor. Food plus water plus indoor air of the same insecticide is aggregate. In HQ language, HI_aggregate = HQ_oral + HQ_dermal + HQ_inhalation for that active ingredient when the toxicity values represent the same systemic effect.

Using the oral 0.80 and inhalation 0.90 above: HI_aggregate = 0.80 + 0.90 = 1.70. Each route was under 1; together they are not. That is the pedagogical point of aggregation.

Cumulative: multiple chemicals that share a common mechanism. Organophosphate acetylcholinesterase inhibitors in one diet are the teaching class. TEFs/TEQs and RPFs are cumulative tools. Cumulative is not a synonym for “we added several numbers.”

WHO TEFs and toxic equivalency

For dioxin-like polychlorinated dibenzo-p-dioxins (PCDDs), dibenzofurans (PCDFs), and dioxin-like polychlorinated biphenyls (PCBs) that act through the aryl hydrocarbon receptor (AhR), WHO assigns TEFs relative to 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) = 1. EPA Superfund and many residue programs still use the WHO 2005 TEF table; WHO convened a later expert re-evaluation (2022), so live work must cite which TEF year was used. This section teaches the method, not a claim that one table is frozen forever.

TEQ = Σ (C_i × TEF_i)

Worked TEQ (WHO 2005 teaching TEFs). Fish fillet:

Convert the intake units first: 0.020 kg fish/day = 20 g fish/day. Intake is 33 pg TEQ/g × 20 g/day = 660 pg TEQ/day. For a 70 kg adult that is 660 / 70 = 9.4 pg TEQ/kg-day. Comparing that ADD with EPA IRIS’s oral RfD for TCDD of 0.7 pg/kg-day (7 × 10^−10 mg/kg-day, 2012) gives HQ = 9.4 / 0.7 = 13.4—a cumulative dioxin-like HQ, not three unrelated congener HQs. Non-dioxin-like PCBs are not in this TEQ; they need a different toxicology.

Mixture combination rules

Independent-action arithmetic. Two dissimilar agents, each producing a 0.10 extra risk of the same apical effect if they acted alone: P_mix = 1 − (1 − 0.10) × (1 − 0.10) = 1 − 0.90 × 0.90 = 1 − 0.81 = 0.19. Naive addition of probabilities gives 0.20. At low risk the two numbers almost match; at P_i = 0.40 each, independent action gives 1 − 0.60 × 0.60 = 0.64, while naive addition gives 0.80. Dose addition is the wrong equation if the chemicals do not share an MOA—but independent action is also not automatic synergism. Synergism means the observed mixture response exceeds the additive (dose or response) prediction. Environmental-dose synergy is uncommon as a default; EPA and EFSA mixture guidance start with dose addition for similarly acting chemicals unless data show otherwise.

The diagram in this section is the decision path: compute HQ or MOE for each matched pair, then ask whether dose addition (HI or TEQ) is justified before you add.

Scenario

A pesticide file lists three organophosphates in food (common AChE mechanism) and a pyrethroid (voltage-gated sodium channel). The correct cumulative HI or RPF sum is the three organophosphates. The pyrethroid is a separate assessment unless a documented interaction study exists. A second file adds oral and dermal HQs for one fumigant: that is aggregate, and an oral HQ of 0.80 plus a dermal HQ of 0.40 is an aggregate 1.20 even though each route looked “fine.” A third file reports MOS = 6 from HNSTD AUC versus Phase 1 AUC and labels it “EFSA MOE 10,000 equivalent.” It is not.

Traps

• Adding every HQ on a laboratory report into one HI without a shared MOA or target.
• Treating HQ = 2 as “twice the people will be affected.”
• Using MOE, MOS, and HQ as interchangeable words.
• Applying the EFSA 10,000 food-genotoxic-carcinogen MOE to a threshold liver-enzyme change, or treating 10,000 as an ABT or EPA universal constant.
• Putting non-dioxin-like PCBs into a WHO TEQ.
• Calling several routes of one chemical “cumulative.”