Aggregate Cancer Risk

Aggregate compatible route-specific linear cancer-risk estimates across chemicals under additive low-risk screening assumptions; not independent-action probability union and not a validated high-risk probability.

Description

Sum route-specific dose–slope-factor products within chemicals and across an entered chemical matrix.

A linear cancer-risk calculation multiplies an exposure dose by a compatible cancer slope factor. The dose usually has a lifetime-average basis, and the factor must match the route and dose definition. An assessment must justify those inputs and the use of a linear approximation.^[1]

This calculator places chemicals in rows and exposure routes in columns. It returns one summed estimate per chemical, an overall additive estimate, and a flag if that total exceeds one. Doses and slope factors must have reciprocal units so each product is dimensionless.

When to use Aggregate Cancer Risk

Use it to audit a chemical-by-route risk worksheet after exposure estimates and assessment factors have been prepared.

How to use Aggregate Cancer Risk and understand its results

Enter nonempty routeLifetimeDosesByChemical and routeSlopeFactorsByChemical arrays with equal row counts and equally long paired rows. Match chemical and route order.
Use nonnegative entries and check the lifetime averaging, route-specific factor, and administered-versus-absorbed dose basis for every pair.
Run the calculation and inspect chemicalRiskEstimates, aggregateLinearRiskEstimate, and exceedsUnitRisk. Keep the row and column labels in your assessment record.

risk_i = Σ_j (dose_ij × slopeFactor_ij); aggregate = Σ_i risk_i; exceedsUnitRisk = aggregate > 1

This is an arithmetic additive model. Values above one are preserved, not clipped to one or combined by an independent-probability formula.

json

{
  "input": {
    "routeLifetimeDosesByChemical": [
      [
        0.1,
        0.2
      ],
      [
        0.3,
        0.1
      ]
    ],
    "routeSlopeFactorsByChemical": [
      [
        0.1,
        0.2
      ],
      [
        0.3,
        0.2
      ]
    ]
  },
  "output": {
    "chemicalRiskEstimates": [
      0.05000000000000001,
      0.11
    ],
    "aggregateLinearRiskEstimate": 0.16,
    "exceedsUnitRisk": false
  }
}

Zero doses or factors are accepted and contribute zero. A total exactly one has exceedsUnitRisk false; 1.1 has it true. Negative entries, empty rows, and missing paired cells are rejected. Different chemicals may have different row lengths if their dose and factor rows match; document their route order explicitly.

Limitations and assumptions

No factor lookup, route adjustment, exposure fitting, interaction analysis, or uncertainty propagation is performed. An inhalation unit risk per air concentration cannot be substituted directly for a dose-based slope factor.

The tool cannot detect duplicated exposure contributions or validate additive cancer-risk assumptions. Large totals indicate a limitation of the linear approximation rather than a literal probability above 100%.

Alternative or Complementary methods

Prepare lifetime-average doses first. Noncancer hazard indices use benchmark ratios and endpoint grouping, rather than these cancer slope-factor products.

References

EPA’s Approach for Assessing the Risks Associated with Chronic Exposure to Carcinogens — U.S. Environmental Protection Agency

Similar or alternative tools

Lifetime Average Daily Dose
Average an ordered exposure calendar over a supplied lifetime.
Hazard Index
Sum compatible noncancer hazard quotients within caller-defined groups.