Introduction

If you work with trace-element data — heavy metals in fish, crops, drinking water, or soil — sooner or later a reviewer, a client, or a regulator will ask the same question: is it safe to eat? Concentrations in mg/kg alone don't answer that. The bridge between a measured concentration and a human-health statement is the target hazard quotient (THQ), the non-carcinogenic risk metric used throughout the US EPA risk-assessment framework and thousands of food-safety papers.

This guide walks through the full calculation chain — EDI → THQ → HI — explains every input parameter, shows a worked example, and covers the interpretation pitfalls that get papers desk-rejected.

The calculation chain

1. Estimated daily intake (EDI)

EDI = (C × IR) / BW

C — measured metal concentration in the food (mg/kg, wet weight)
IR — ingestion rate (kg/day), e.g. daily fish consumption
BW — body weight of the exposed population (kg)

EDI is expressed in mg/kg body weight/day. Getting the units right is the most common source of errors: if your lab reports µg/g, that is numerically equal to mg/kg — but µg/kg (dry weight vs wet weight) is a different story.

2. Target hazard quotient (THQ)

THQ = EDI / RfD = (C × IR) / (RfD × BW)

The reference dose (RfD) is the estimated daily oral exposure that is unlikely to cause adverse effects over a lifetime, published by US EPA IRIS and other bodies. The Pb entry below is a retained legacy screening assumption, not an EPA IRIS RfD:

Element	Oral RfD (mg/kg/day)
As (inorganic)	0.0003
Cd	0.001
Pb*	0.0035 (legacy assumption, not an IRIS RfD)
Hg (methylmercury)	0.0001
Cr (III)	1.5
Zn	0.3
Cu	0.04
Ni	0.02

* Labreador retains Pb 0.0035 mg/kg/day as a legacy screening assumption. Its historical rationale refers to WHO/JECFA PTWI 25 µg/kg/week (approximately 0.003571 mg/kg/day), withdrawn in 2010 as insufficiently protective. EPA IRIS provides no numerical oral RfD or oral CSF for lead. The application's retained Pb CSF 0.0085 (mg/kg/day)^-1 has an unverified authoritative source. These Pb assumptions do not establish safe exposure or a validated cancer-risk estimate, and must be disclosed when reporting results. See the EPA IRIS lead assessment and WHO/JECFA lead evaluation.

3. Hazard index (HI)

Metals rarely occur alone. The hazard index sums the individual quotients:

HI = THQ(1) + THQ(2) + ... + THQ(n)

How to interpret the numbers

THQ < 1 — the exposure is below the reference dose; non-carcinogenic risk from that single element is considered negligible.
THQ ≥ 1 — exposure exceeds the reference dose; adverse effects cannot be ruled out and further assessment is warranted.
HI < 1 — combined exposure to all assessed metals is acceptable.
HI ≥ 1 — the mixture may pose a risk even when every individual THQ is below 1. This is the scenario most often missed in manuscripts.

THQ is a screening metric, not a probability of illness. It does not mean "a person will get sick at THQ = 1.2"; it means exposure sits above the level considered safe with built-in uncertainty factors.

Worked example

A study measures Cd = 0.08 mg/kg in carp muscle. Local consumption is IR = 0.03 kg/day, adult BW = 70 kg, RfD(Cd) = 0.001 mg/kg/day.

EDI = (0.08 × 0.03) / 70 = 3.43e-5 mg/kg/day
THQ = 3.43e-5 / 0.001 = 0.034

Well below 1 — acceptable for a typical adult. Repeat for Pb, Hg and As in the same samples, sum them into HI, and you have a complete non-carcinogenic risk statement. For carcinogens (e.g. inorganic As), target cancer risk CR = LADD × CSF uses lifetime-average daily dose, not chronic EDI for a shorter exposure. Advanced Labreador uses LADD = (C × IR × EF × ED) / (BW × 70 × 365); simple CR explicitly assumes daily lifetime exposure.

Advanced THQ uses the same kg/day ingestion unit as simple THQ; there is no extra 10^-3 conversion. With daily exposure and AT = ED × 365, simple and advanced THQ agree.

Common mistakes that undermine the analysis

Mixing wet-weight and dry-weight concentrations. RfD values assume the food as consumed. Convert or state your basis clearly.
Using mean concentration with worst-case IR without saying so. Mixing conservative and central-tendency assumptions in one calculation inflates or hides risk inconsistently. Better: run a Monte Carlo analysis over the distributions.
Reporting THQ per element but never the HI. Reviewers increasingly demand the cumulative index.
Copying RfD values without citing the source. EPA IRIS values are periodically revised — record which database and year you used.
Treating non-detects or missing cells as zero. Preserve censoring and justify a documented handling method; risk imports do not automatically impute. HI requires the full selected panel, and missing inputs or references make totals unavailable.

Speed it up

The full chain — EDI, THQ per element, HI, target cancer risk, plus batch processing of many samples at once — is implemented in the Labreador Risk Assessment module. Paste your concentrations, pick ingestion rate and body weight (an adult 70 kg screening default is provided; child-specific inputs must be chosen and justified by the user), and you get THQ tables, a colour-coded heatmap across elements and samples, and an optional Monte Carlo probabilistic analysis. Everything runs locally in your browser; no data is uploaded.

Related guides

If Labreador helps your work, please cite it: Helczman, M. (2026). Labreador - Bioassay Analysis Platform (Version 1.7.0) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.23537408