Hazard Index Explained: How to Combine Multiple Metals into One Risk Number
THQ tells you the risk from one metal. The Hazard Index (HI) adds them up — but only when the additivity assumption holds. Formulas, a worked example, and common pitfalls.
Introduction
People don't eat cadmium. They eat fish — and that fish contains cadmium, lead, mercury, and arsenic at the same time. Assessing each metal separately and stopping there misses the point of dietary risk assessment: the consumer is exposed to the mixture, not to individual elements.
The Hazard Index (HI) is the standard way to combine non-carcinogenic risks across metals. It is built into Labreador's Risk Assessment module, and this post explains what it does, when the math is defensible, and where people go wrong.
From THQ to HI
You already know the single-metal chain (see our post on THQ):
EDI = (C × IR) / BW
THQ = EDI / RfD
The Hazard Index is simply the sum of the target hazard quotients across all metals in the exposure scenario:
HI = THQ_1 + THQ_2 + ... + THQ_n
Interpretation mirrors THQ:
| HI value | Interpretation |
|---|---|
| HI < 1 | Combined exposure unlikely to cause adverse non-carcinogenic effects |
| HI ≥ 1 | Combined exposure exceeds the threshold; further investigation warranted |
A worked example
Fish consumption scenario: IR = 0.0546 kg/day, BW = 70 kg, concentrations on a wet-weight basis, US EPA reference doses.
| Metal | C (mg/kg) | RfD (mg/kg/day) | THQ |
|---|---|---|---|
| Cd | 0.30 | 0.001 | 0.234 |
| Pb | 0.15 | 0.0035 | 0.033 |
| As | 0.80 | 0.0003 | 2.080 |
THQ_Cd = (0.30 × 0.0546) / (70 × 0.001) = 0.234
THQ_Pb = (0.15 × 0.0546) / (70 × 0.0035) = 0.033
THQ_As = (0.80 × 0.0546) / (70 × 0.0003) = 2.080
HI = 0.234 + 0.033 + 2.080 = 2.347
Two lessons from this table:
- HI > 1 even though two of three metals look harmless alone. If you had assessed only Cd and Pb, you would have reported "no concern" — and been wrong about the mixture.
- One metal dominates. Arsenic contributes 89% of the HI. That is actionable information: mitigation efforts should target As, not Cd.
The additivity assumption — and its limits
Summing THQs assumes the metals act on the same target organ or mechanism in an additive way. That is a simplification:
- Metals with different target organs (e.g., a nephrotoxin and a neurotoxin) arguably shouldn't be summed at all. US EPA guidance recommends segregating HI by effect when the data allow it.
- Real mixtures can be synergistic or antagonistic — HI captures neither.
In practice, the conservative full sum is the accepted screening approach: if the summed HI is below 1, you are done; if it exceeds 1, a refined, effect-specific analysis is the next step. Report the per-metal THQs alongside the HI so readers can see which metal drives the total.
Complete panels only
This is the pitfall we see most often. If a sample was measured for Cd and Pb but not for As, its HI is not "lower" — it is undefined for the full panel. Summing the available THQs would silently underestimate the mixture risk.
The correct rule: compute HI only for samples with a complete set of the selected metals. Samples with missing measurements are reported separately as partial panels, and the summary statistics (mean HI, P(HI > 1)) use the complete panels as the denominator — while the total sample count still reflects everything you imported. Labreador's batch mode enforces exactly this: partial panels are labeled (e.g., "partial 2/3") and excluded from HI summaries, never silently zero-filled.
Connecting to Monte Carlo
A deterministic HI has the same weakness as a deterministic THQ: it describes the mean consumer. The probabilistic extension sums the per-metal THQ distributions iteration by iteration:
for each iteration i:
HI_i = THQ_Cd,i + THQ_Pb,i + THQ_As,i
P(HI > 1) = (iterations with HI > 1) / N
Because the metals are drawn independently, the HI distribution is wider than any single-metal distribution — the probability of exceeding 1 is driven by whichever metal's tail is heaviest, plus the chance of several metals being high at once. See our Monte Carlo post for the full method.
Common mistakes to avoid
- Summing across different exposure scenarios. HI assumes one consumer, one ingestion rate, one body weight. Don't sum an adult-fish THQ with a child-drinking-water THQ.
- Mixing bases. All concentrations must be on the same (wet-weight) basis before THQs are computed — see dry weight vs wet weight.
- Zero-filling non-detects. A metal measured but below the LOD is not zero; resolve it explicitly (non-detects and LOD/2) before it enters the sum.
- Reporting HI without the components. Always show the per-metal THQ table. "HI = 1.8" alone hides whether the risk is spread evenly or driven by a single metal.
Try it yourself
The Risk Assessment module computes per-metal THQs and the Hazard Index for single samples or batch datasets, handles partial panels transparently, and extends the analysis to Monte Carlo exceedance probabilities — all in your browser, with your data never leaving your device.
References
- US EPA (1989). Risk Assessment Guidance for Superfund, Volume I: Human Health Evaluation Manual (Part A). EPA/540/1-89/002.
- US EPA IRIS — Integrated Risk Information System.