Introduction

Everything we have covered so far — EDI, THQ, the Hazard Index — answers one question: is the dose below the level expected to cause non-carcinogenic harm? But some metals are also carcinogens, and for carcinogens the logic is different. There is no safe threshold assumed; instead, every dose carries a small probability of causing cancer over a lifetime, and the job of the assessment is to estimate that probability.

That is what the cancer risk (CR) calculation does, and it is built into Labreador's Risk Assessment module alongside THQ and HI. This post explains the two ingredients — the lifetime average daily dose (LADD) and the cancer slope factor (CSF) — and shows why the same dataset can give two different, both defensible, answers.

The two ingredients

Cancer slope factor (CSF). A CSF is the upper-bound estimate of cancer probability per unit of lifetime-averaged dose, expressed in (mg/kg/day)⁻¹. It comes from dose-response modeling of epidemiological or animal data. A larger CSF means a more potent carcinogen. In Labreador the defaults come from US EPA IRIS:

Metal	Oral CSF (mg/kg/day)⁻¹	Source
As	32	US EPA IRIS, final 2025
Cr(VI)	0.27	US EPA IRIS, final 2024
Pb	0.0085	Legacy screening assumption (not an IRIS benchmark)

Note what is not in the table: Cd, Hg, Ni, Zn and most other elements have no oral CSF. A missing CSF is not evidence of zero carcinogenic hazard — it means no quantitative slope factor is available, and the metal simply does not enter the CR total.

Lifetime average daily dose (LADD). Carcinogenic risk is about lifetime probability, so the dose is averaged over a conventional 70-year lifetime — not over the exposure period:

LADD = (C × IR × EF × ED) / (BW × ATc)

C   = concentration in food (mg/kg, wet weight)
IR  = ingestion rate (kg/day)
EF  = exposure frequency (days/year)
ED  = exposure duration (years)
BW  = body weight (kg)
ATc = averaging time for carcinogens = 70 × 365 = 25,550 days

Then:

CR = LADD × CSF

CR is a unitless probability: CR = 1e-4 means an estimated upper-bound excess lifetime cancer risk of 1 in 10,000.

Simple vs advanced: the same data, two answers

The module offers two modes, and the difference matters:

Simple CR assumes daily exposure for the entire lifetime: LADD = EDI. This is the conservative screening default.
Advanced CR uses your explicit exposure scenario (EF, ED) and averages over the 70-year lifetime separately from the chronic EDI used for THQ.

Worked example — arsenic in fish at C = 0.01 mg/kg wet weight, IR = 0.0546 kg/day, BW = 70 kg, EF = 365 days/year, ED = 30 years:

EDI  = (0.01 × 0.0546) / 70 = 7.8e-6 mg/kg/day

Simple:   CR = 7.8e-6 × 32 = 2.5e-4

Advanced: LADD = (0.01 × 0.0546 × 365 × 30) / (70 × 25,550)
               = 3.34e-6 mg/kg/day
          CR   = 3.34e-6 × 32 = 1.1e-4

Same sample, same consumer — and the two estimates differ by a factor of 2.3. Neither is wrong: the simple mode answers "what if this person eats this fish every day for life?", the advanced mode answers "what if they eat it daily for 30 years?". Report which mode you used, with EF and ED stated explicitly.

Interpreting the number

The conventional decision framework:

CR value	Interpretation
CR < 1e-6	Below the de minimis level; negligible
1e-6 ≤ CR ≤ 1e-4	Generally treated as acceptable/tolerable range
CR > 1e-4	Above de manifestis; risk reduction warranted

Our example sits right at the upper boundary (1.1e-4 advanced, 2.5e-4 simple) — a textbook case of why the exposure scenario must be reported alongside the number. A reviewer reading "CR = 1.1e-4, acceptable" deserves to know that the daily-lifetime assumption would push the same data to 2.5e-4.

Two more rules the module enforces:

CR totals cover supplied CSFs only. If your panel is Cd + Pb + As, the total CR sums Pb and As; Cd contributes nothing because it has no oral CSF. The total is labeled accordingly — never read it as "total carcinogenic risk of the sample."
Non-detects are resolved before CR, not after. A substituted LOD/2 value flows through LADD exactly like a measured concentration (see non-detects and LOD/2).

Connecting to Monte Carlo

Like THQ, a deterministic CR describes the mean consumer. The Monte Carlo extension propagates the concentration, ingestion rate and body weight distributions through the same CR = LADD × CSF chain, giving you a distribution of lifetime risks and the probability of exceeding 1e-4 — far more informative than a single point estimate when you report to a regulator.

Common mistakes to avoid

Using EDI where LADD belongs. For a 30-year exposure, EDI overstates the lifetime-averaged dose by 70/30 ≈ 2.3×. Know which mode your number came from.
Treating CR > 1e-4 as "cancer will occur." CR is an upper-bound probability estimate built on conservative assumptions; it is a screening signal, not a diagnosis.
Mixing up the averaging times. THQ averages over the exposure duration (AT = ED × 365); CR averages over the whole lifetime (ATc = 70 × 365). Using AT for both silently inflates cancer risk.
Reporting a CR total without listing which metals have CSFs. An incomplete CSF panel understates the mixture, and the reader cannot see it.
Forgetting the weight basis. Like every dose calculation, C must be on a wet-weight basis to match IR — see dry weight vs wet weight.

Try it yourself

The Risk Assessment module computes Simple and Advanced CR next to THQ and HI, applies the 2025 IRIS arsenic and 2024 chromium(VI) slope factors by default, labels CR totals with their CSF coverage, and extends to Monte Carlo exceedance probabilities — all locally in your browser.

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: Arsenic, inorganic (final 2025); Chromium(VI) (final 2024).