12.3 Low-Dose Extrapolation, Cancer Slope Factors (CSF), Unit Risk & First-in-Human Dose
Key Takeaways
- In linear mutagenic cancer assessment, CSF = BMR / BMDL with units of 1/(mg/kg-day). Example: BMR 0.10 and BMDL10 2.5 mg/kg-day give CSF = 0.040 per (mg/kg-day).
- Inhalation unit risk (IUR) is extra cancer risk per unit air concentration (for example per µg/m³). Do not mix IUR units with oral CSF units without a dosimetry conversion.
- ICH M7 compound-specific assessment often uses a lifetime margin of exposure of 10,000 from a rodent BMDL10. Worked example: 0.50 mg/kg/day × 50 kg / 10,000 = 2.5 µg/day acceptable intake.
- FDA 2005 healthy-volunteer FIH: convert animal NOAEL to HED with body-surface-area scaling (body weight^0.67; rat factor often 0.16), then divide by a safety factor often equal to 10 to obtain the MRSD.
- Worked HED: rat NOAEL 50 mg/kg/day × 0.16 = 8.0 mg/kg/day; MRSD = 0.80 mg/kg/day; 60 kg volunteer → 48 mg/day. PBPK can replace BSA scaling when internal dose differs. Below the PoD, slopes and factors are model/policy choices, not observed incidences.
Below the PoD and into humans
Once a PoD exists, Domain III.C.1–2 asks how you travel below it (cancer slope, unit risk, margin of exposure) and how drug developers pick a first-in-human (FIH) dose. Independent OpenExamPrep teaching covers cancer slope factors (CSF), inhalation unit risk (IUR), ICH M7 margins for mutagenic impurities, FDA 2005 conversion of NOAEL to human equivalent dose (HED) and maximum recommended starting dose (MRSD), PBPK for interspecies internal dose, and why all of this is uncertain once you leave the observed range. This section is not an ABT product and does not claim official approval, review, or partnership with ABT, EPA, FDA, or ICH.
Chapter 13 will layer uncertainty factors onto noncancer PoDs to make RfD/RfC values. Here the jobs are linear cancer math, impurity MOE, and FIH arithmetic.
Cancer slope factor: CSF = BMR / BMDL
For a linear cancer assessment (EPA 2005 default when the mode of action is mutagenic), extra risk at low dose is modeled as a straight line from the origin to the PoD on the extra-risk versus dose plot.
If the BMR is 0.10 (10% extra risk) and the PoD is BMDL10, then
CSF = 0.10 / BMDL10
Units: (mg/kg-day)^−1, spoken “per milligram per kilogram per day.”
Worked CSF. BMDL10 = 2.5 mg/kg-day.
CSF = 0.10 / 2.5 = 0.040 per (mg/kg-day)
Linear extra risk at an oral lifetime average dose of 0.001 mg/kg-day:
Risk = 0.040 × 0.001 = 4.0 × 10^−5 (4 in 100,000)
Check by similar triangles: 0.001 is 2.5 / 2500 of the BMDL; 0.10 / 2500 = 0.00004. Same result.
If someone inverts the ratio (2.5 / 0.10 = 25), they have built a dose at 10% risk, not a slope. If they multiply 0.10 × 2.5 = 0.25, the units are nonsense. If they use the central BMD instead of the BMDL, they have ignored the conservative bound that risk assessment treats as the PoD.
Inhalation unit risk (IUR) is the same linear idea for air: extra risk per µg/m³. If IUR = 2.0 × 10^−6 per µg/m³ and lifetime exposure is 5 µg/m³, extra risk = 2.0 × 10^−6 × 5 = 1.0 × 10^−5. Do not multiply an oral CSF (per mg/kg-day) by an air concentration (µg/m³) without a dosimetry conversion (Chapter 11: HEC, RGDR, ventilation). Oral slope factors and IURs are population cancer-potency slopes for risk characterization. They are not FIH starting doses.
| Construct | Formula / meaning | Units | Playbook |
|---|---|---|---|
| CSF | BMR / BMDL for linear oral cancer | 1/(mg/kg-day) | EPA mutagenic cancer |
| IUR | Extra risk per air concentration | per µg/m³ (typical) | EPA inhalation cancer |
| MOE (ICH M7) | BMDL10 / human impurity dose | dimensionless | Mutagenic impurities |
| HED then MRSD | NOAEL × BSA factor, then ÷ safety factor | mg/kg/day then mg/day | FDA 2005 healthy volunteers |
ICH M7: margin of exposure for genotoxic impurities
ICH M7 addresses mutagenic impurities in pharmaceuticals. When a compound-specific carcinogenicity PoD exists, a common teaching construction is
MOE = BMDL10 / human exposure (same dose units).
A lifetime MOE of 10,000 from a rodent BMDL10 is a widely cited ICH M7-style basis for a compound-specific acceptable intake (AI).
Worked AI. BMDL10 = 0.50 mg/kg/day. Adult body weight 50 kg (a round impurity-example mass):
0.50 mg/kg/day × 50 kg = 25 mg/day = 25,000 µg/day
AI = 25,000 µg/day / 10,000 = 2.5 µg/day
If no compound-specific data exist, ICH M7 also provides a threshold of toxicological concern (TTC) of 1.5 µg/day for lifetime daily intake of a mutagenic impurity, with higher staged values for less-than-lifetime clinical exposure. The TTC is a default when you lack a BMDL; it does not forbid using a BMDL when you have one. MOE 10,000 and TTC 1.5 µg/day are different tools. Applying a drug-substance CSF to an impurity milligram dose without converting units and without the M7 framework is a category error.
FDA 2005 FIH: NOAEL → HED → safety factor → MRSD
The 2005 FDA guidance Estimating the Maximum Safe Starting Dose in Initial Clinical Trials for Therapeutics in Adult Healthy Volunteers is the healthy-volunteer playbook.
Steps:
- Identify the NOAEL in the most appropriate species (toxicity biology, not automatically the species with the numerically lowest mg/kg).
- Convert to HED using body-surface-area scaling. Dose in mg/m² scales with body weight^0.67. Equivalently, mg/kg HED = animal mg/kg × (W_animal / W_human)^0.33, because 1 − 0.67 = 0.33. FDA tables implement this with Km factors (human Km 37; rat 6; mouse 3; dog 20). Rat conversion: 6/37 ≈ 0.16.
- Divide HED by a safety factor, often 10, to obtain the MRSD in mg/kg. Increase the factor for steep dose–response, nonmonitorable toxicity, or a thin nonclinical package. Pharmacology may justify a different start (MABEL, section 12.2) instead of this NOAEL path.
- Multiply by human body weight (FDA often uses 60 kg) to get a milligram starting dose.
Worked HED with round numbers. Rat oral NOAEL = 50 mg/kg/day. Human body weight = 60 kg. Rat body weight for the exponent illustration = 0.25 kg.
Table method (FDA rat factor 0.16):
HED = 50 × 0.16 = 8.0 mg/kg/day
Km method: HED = 50 × (6 / 37) = 300 / 37 = 8.1 mg/kg/day
Exponent method: (0.25 / 60)^0.33 = 0.004167^0.33 ≈ 0.164
HED = 50 × 0.164 = 8.2 mg/kg/day
All three cluster near 8 mg/kg/day. Using the table value 8.0:
MRSD = 8.0 / 10 = 0.80 mg/kg/day
For a 60 kg volunteer: 0.80 × 60 = 48 mg/day starting dose. That is an FIH hedge, not a chronic RfD and not a cancer PoD.
Failure modes you should be able to compute. Skip the 0.16 step and only divide 50 by 10: 5 mg/kg/day = 300 mg/day at 60 kg, which is 300 / 48 = 6.25 times too high. Divide by 0.16 instead of multiplying: HED = 50 / 0.16 = 312.5 mg/kg/day, scaling in the wrong direction (human dose larger than rat mg/kg, the opposite of BSA logic for a smaller animal).
Oncology STD10/HNSTD fractions and MABEL starts are not this 10-fold healthy-volunteer recipe.
PBPK for interspecies conversion
BSA scaling assumes similar mg/m² exposure produces similar systemic exposure. That fails when clearance, protein binding, or metabolic pathways differ. PBPK replaces the exponent with physiology: scale organ blood flows and volumes, insert species-specific clearance, and match internal metrics (AUC, Cmax, amount metabolized) as in section 12.1. FIH then uses a human simulated internal dose at the animal NOAEL (or BMDL), not 50 × 0.16 by default. PBPK is stronger when the model is calibrated to kinetic data; it is not automatic permission to drop a safety factor. It is also the honest way to move a reactive-metabolite toxicant across species when mg/kg of parent is the wrong x-axis.
Uncertainty of extrapolation below the PoD
Every step past the lowest informative data is an extrapolation:
- Linear cancer: the straight line below BMDL10 is a default for mutagenic MOA, not a measured incidence at 0.001 mg/kg-day. A nonlinear cancer MOA, if accepted, would not use this CSF at all.
- Noncancer RfD (preview): dividing a BMDL by 100 does not prove a threshold at PoD/100.
- FIH: 10-fold on HED is a starting-dose hedge, not a guarantee that 48 mg is the highest safe dose or that 49 mg is toxic.
- Impurity MOE 10,000 is a consensus margin, not a personalized cancer probability.
The honest statement on a DABT item is: the PoD is constrained by data; below the PoD you are choosing a model and a policy factor. Sensitivity to BMR, to linear versus nonlinear cancer MOA, and to 0.67 BSA scaling versus PBPK should be discussed, not hidden.
Scenario
A mutagenic rodent liver carcinogen has BMDL10 = 2.5 mg/kg-day. CSF = 0.04 per (mg/kg-day). At a food-related lifetime average daily dose of 0.001 mg/kg-day, linear extra risk is 4 × 10^−5. Separately, a mutagenic impurity in a tablet has BMDL10 = 0.50 mg/kg/day; the ICH M7-style AI at 50 kg and MOE 10,000 is 2.5 µg/day—not the oral CSF applied to the active ingredient. Separately, a non-mutagenic small molecule with rat NOAEL 50 mg/kg/day enters healthy-volunteer FIH: HED 8 mg/kg, MRSD 0.8 mg/kg, 48 mg/day. Using the CSF as the FIH dose, or using 48 mg/day as a lifetime cancer PoD, mixes the three playbooks. A fourth file is an inhalation mutagenic carcinogen with IUR 2.0 × 10^−6 per µg/m³ at 5 µg/m³: extra risk 1 × 10^−5, still not an MRSD.
Traps
- Writing CSF = BMDL / BMR, or using BMD in the denominator when BMDL is the PoD.
- Mixing IUR per µg/m³ with oral mg/kg-day CSF without dosimetry.
- Applying TTC 1.5 µg/day when a compound-specific BMDL10 AI was already derived, as if TTC overrode data—or ignoring TTC when no compound-specific PoD exists.
- Scaling FIH by 10-fold on animal mg/kg without BSA/HED, or converting with the factor inverted.
- Treating linear extrapolation below the PoD as if it were observed bioassay incidence at environmental doses.
- Using FDA 2005 MRSD logic for a CD28 superagonist that needs a MABEL, or using MABEL logic as a substitute for an EPA oral CSF.
A mutagenic carcinogen has BMDL10 = 2.5 mg/kg-day for a 10% extra-risk BMR. What is the oral cancer slope factor, and what excess risk does linear extrapolation predict at 0.001 mg/kg-day?
A rat oral NOAEL is 50 mg/kg/day. Using the FDA 2005 body-surface-area factor of 0.16 for rat-to-human mg/kg conversion and a 10-fold safety factor, what is the maximum recommended starting dose in mg/kg/day for a healthy adult volunteer?
For a mutagenic impurity with a rodent BMDL10 of 0.50 mg/kg/day, ICH M7-style compound-specific assessment often applies a 10,000-fold margin of exposure. For a 50 kg person, what lifetime acceptable intake does that arithmetic yield?