Hazard Index
Sum compatible hazard quotients within caller-assigned common endpoint groups instead of indiscriminately summing unrelated toxic endpoints; additivity is an assumption.
Description
Sum supplied hazard quotients within numeric endpoint groups and flag group totals strictly above one.
A hazard index combines compatible noncancer hazard quotients under an additive screening interpretation. Endpoint or target-organ grouping can help avoid combining unrelated toxicological comparisons, but deciding which components belong together requires assessment of the evidence and dose basis.1
This tool receives hazard quotients already calculated and numeric group IDs already assigned. It sums quotients only within matching groups and returns the groups in ascending numeric order. Group numbers are labels; they do not encode toxicity severity.
The outputs are dimensionless group sums and numeric 0-or-1 flags. A flag of one means the group index exceeds one. An index is a screening ratio sum rather than a probability of harm or a measured mixture response.
When to use Hazard Index
Use it to reproduce an endpoint-grouped hazard-index worksheet after validating the constituent quotients and the rationale for grouping them.
How to use Hazard Index and interpret its calculation
- Enter aligned, nonempty hazardQuotients and endpointGroupIds lists, with nonnegative quotients and nonnegative safe-integer group IDs.
- Confirm the route, duration, benchmark, and endpoint assumptions supporting each group, then run the sum.
- Read uniqueEndpointGroups beside groupHazardIndices and aboveUnitFlags. Pair outputs by their sorted group order rather than the original component order.
HI_g = Σ HQ_i where group_i = g; flag_g = 1 if HI_g > 1, otherwise 0 Equality to one gives flag zero; groups are sorted numerically, not by first appearance.
The implementation deduplicates group IDs, sorts them ascending, and sums the matched quotients for each ID. It does not compute the input quotients, assign endpoints, or return a single all-endpoint total.
{
"input": {
"hazardQuotients": [
0.5,
0.7,
0.2
],
"endpointGroupIds": [
1,
1,
2
]
},
"output": {
"uniqueEndpointGroups": [
1,
2
],
"groupHazardIndices": [
1.2,
0.2
],
"aboveUnitFlags": [
1,
0
]
}
}Group ID zero is allowed. Zero quotients contribute nothing but their groups remain in the output. A group sum exactly one has flag zero. Negative quotients, fractional group IDs, empty lists, and mismatched lengths are rejected.
Limitations and assumptions
The calculator cannot validate grouping, identify duplicate exposure contributions, or determine that an additive interpretation is appropriate. Similar target organs alone do not verify a shared toxicity model.
No benchmark selection, interaction adjustment, uncertainty analysis, causal attribution, or clinical interpretation is included. An index above or below one does not independently prove the presence or absence of adverse effects.
Alternative or Complementary methods
Calculate compatible component hazard quotients first. Use a separately justified concentration-addition or independent-action response model when the question is a predicted effect rather than a benchmark-ratio sum.
References
-
Supplementary Guidance for Conducting Health Risk Assessment of Chemical Mixtures (2000) — U.S. Environmental Protection Agency
Similar or alternative tools
- Hazard Quotient
Calculate a component daily-dose quotient against a supplied compatible reference dose.
- Concentration Addition Mixture
Predict a normalized mixture effect from EC50s and a common Hill slope.