Dose-response Modeling

Exponent scientists have conducted a broad range of dose-response analyses and modeling to support important decisions. Our team includes nationally recognized specialists key to developing the dose-response modeling methodology used today, and who are uniquely poised to provide highly effective technical support in the areas of:

  • Analyses of complex data in epidemiology and toxicology
  • Regulatory limits 
  • Product registration 
  • Risk/Safety assessment 
  • Site-specific modeling

Dose-Response Modeling in Epidemiology

The dose makes the poison,” commonly attributed to Paracelsus1 is a cornerstone of our understanding of how our bodies respond to chemical, biological, and radiological agents found in food, consumer and industrial products, and the environment. Dose-response modeling in modern epidemiology and toxicology plays a key role to support scientifically sound public health and environmental policies.

Dose-response and exposure-response modeling provide a basis for the setting of regulatory limits, such as air quality, drinking water, and food tolerance standards by providing approaches to extrapolation from observed data at high exposure levels to the exposures of regulatory interest. These models can also be used to investigate and understand complex temporal patterns of risk of disease following exposure to a putative toxic agent.

Dose-Response Modeling in Quantitative Risk Assessment

For non-cancer endpoints, traditional quantitative risk assessment methods involve dividing a no-observed-adverse effect level (NOAEL) or point of departure (POD) for the critical toxic response by appropriate uncertainty or safety factors. However, such an approach does not take into account the shape of the dose-response curve. Therefore, it may be more informative to fit the observed dose-response data to mathematical forms using regression methods. The Benchmark Dose (BMD) approach formalizes the application of regression methods for the purposes of quantitative risk assessment. Using this method, the BMD, which is the maximum likelihood estimate of the dose associated with a specific effect above the background rate of the response and the lower confidence limit on the BMD are determined and uncertainty factors then applied. In contrast, for cancer end-points, both statistical and biologically-based dose-response (BBDR) models can be used for dose-response or exposure-response analyses. BBDR models combine the best available mechanistic knowledge to define mathematical functions used to fit the dose-response data, allowing analysis of datasets with complex patterns of exposure to multiple carcinogens.

BBDR approaches include Physiologically Based Pharmacokinetic (PBPK) models that link administered dose to biologically effective target-tissue concentrations; mutation/clonal-proliferation models (such as the two-stage or multistage Moolgavkar-Venzon-Knudson or MVK model) that link tissue concentrations to tumor-occurrence data; and combinations of these approaches, suchas Physiologically Based Pharmacodynamic (PBPD) modeling. Because model selection can profoundly influence the dose-response predictions associated with data in the low-dose region, care must be taken to select the most appropriate modeling methods. Mode-of-action (MOA) understanding is especially important in developing dose-response models for carcinogens.

Exponent scientists have expertise in both traditional statistical techniques, such as logistic regression, and Cox proportional hazards regression, and BBDR models to support dose-response evaluation and modeling.

Examples of our work include:

  • Analysis of a large epidemiological data set of Chinese tin miners exposed to three lung carcinogens, tobacco smoke, arsenic, and radon to estimate the fraction of lung cancers attributable to each of these carcinogens in the cohort 
  • Analyses of a large epidemiological data on exposure to diesel engine exhaust and lung cancer using both traditional statistical approaches and BBDR models
  • BBDR modeling for quantitative risk analyses of coke oven emissions and of refractory ceramic fibers 
  • Combined PPBK and MOA-specific MVK modeling to evaluate cancer risks posed by exposures to methyl tert-butyl ether (MTBE) and naphthalene
  • Modeling allergic contact dermatitis elicitation risks associated with exposures to sensitizing agents such as nickel (Ni), chromium (III and VI), acrylates, and methacrylates
  • Dose-response modeling using EPA’s “R” modeling codes and BMDS to support risk assessments for pesticide registration 
  • Development of PBPK/PD models for organophosphate insecticides to link exposure to response of concern (cholinesterase inhibition)


Bogen, KT. Linear-no-threshold default assumptions for noncancer and nongenotoxic-cancer risks: A mathematical and biological critique. Risk Anal 2015; doi.10.1111/risa.12460 (in press).

Bogen, KT, Heilman J. Reassessment of MTBE cancer potency considering modes of action for MTBE and its metabolites. Crit Rev Toxicol 2015 doi.10.3109/10408444.2015.1052367 (in press).

Bogen KT, Garry MR, Volberg V. Risks of allergic contact dermatitis elicited by nickel, chromium, and (meth)acrylates: Modeled comparisons of published patch-test data on ~5,000 sensitive individuals. Presented at the Society of Toxicology 54th Annual Meeting, San Diego CA, March 22–26, 2015. The Toxicologist 2015; 144(1):139.

Moolgavkar SH, Chang ET, Luebeck G, Lau EC, Watson HN, Crump KS, Boffetta P, McClellan R. Diesel engine exhaust and lung cancer mortality: Time-related factors in exposure and risk. Risk Anal 2015; 35(4):663–675.

1 The phrase “the dose makes the poison” is attributed to Paracelsus (Swiss, 1493-1541), who wrote “Alle Ding sind Gift, und nichts ohn Gift; allein die Dosis macht, daß ein Ding kein Gift ist.” [“All things are poison, and nothing is without poison; the dose alone allows something not to be a poison.”].