TERA has expertise in the mathematical modeling of complex biological processes
using physiological‐based pharmacokinetic (PBPK) models and pharmacodynamic
(PD) or biologically‐based dose‐response (BBDR) modeling. PBPK models predict
target tissue doses in response to chemical exposure allowing more accurate
extrapolation across species, age groups, dose routes, or exposure durations. BBDR
models are a mathematical description of the cellular mechanisms of toxicity that
can improve low‐dose and interspecies extrapolation. TERA scientists have recent
experience with models for trichloroethylene (https://tera.org/news), nickel,
methylene chloride, ethylene dichloride, warfarin, parathion, and others.

TERA staff are proficient with Bayesian statistical techniques for analyzing
uncertainty in mathematical models and population variability. Bayesian
population analysis using Markov chain Monte Carlo (MCMC) simulation is a
technique that is well suited for analysis of pharmacokinetic data using PBPK
models and can enhance our understanding of interspecies and human variability
using these highly parameterized models. TERA scientists recently performed
Bayesian analysis of the harmonized PBPK models for trichloroethylene
(https://tera.org/news), as well as other models for methylene chloride,
ethylene dichloride, and methylene chloride. TERA staff have also played a
significant role in identifying and addressing key uncertainties and issues that need
to be addressed in order to more extensively incorporate the results of MCMC
simulation into risk assessment.

TERA scientists are currently developing methodology for validating biomarkers
and performing biomarker‐based dose‐response for use in risk assessment using
Bayesian networks. Network models are developed that link exposure, biomarkers
of exposure and effects, and disease outcomes. This approach incorporates data
spanning the exposure‐early effects‐disease continuum are analyzed, integrating
complex data from emerging technologies (e.g., gene expression assays) with
traditional toxicity data. This approach will reduce the need to early time points
and low doses.

The benchmark dose (BMD) approach has a number of advantages over the traditional NOAEL/LOAEL approach. The greatest advantage is that the BMD approach responds appropriately to sample size, reflecting increased uncertainty in smaller sample sizes and yielding a lower point of departure. TERA scientists have conducted BMD analyses for numerous chemicals, published on issues related to the application of BMD methods, served on the peer review panel for the most recent BMD guidance, and participated in workshops on future development and issues of the BMD approach. TERA also offers training courses on the BMD approach. See https://tera.org/Global/Training/index.html.

Categorical regression is a dose‐response technique that incorporates not only information on how the incidence of response increases with dose, but also information on how the severity of response increases with dose. Categorical regression is a powerful tool for combining sparse data across studies or endpoints, for quantitative
analysis of qualitative toxic severity data, and for integrating concentration‐duration‐response data for development of acute exposure guidelines, particularly for the inhalation route. TERA scientists have performed several categorical regression analyses, including the risk characterization of non‐lethal weapons and have
published on the subject in the scientific literature.

TERA scientists have experience conducting dose‐response analysis of occupational exposure‐response and epidemiological data. For example, in a published analysis of the lung cancer risk from inhalation exposure to hexavalent chromium, TERA staff used Poisson and Cox regression analysis of job‐exposure matrix data to estimate cancer potency, and lifetable analysis to refine the extrapolation from the occupational data to environmental exposure scenarios and compute additional lifetime risks. As further examples, TERA staff have developed models to analyze odds ratios associated with occupations involving diesel exhaust and asbestos exposure.