On the MVK stochastic carcinogenesis model with Erlang distributed cell life lengths

An adjustment factor for mode-of-action uncertainty with dual-mode carcinogens: the case of naphthalene-induced nasal tumors in rats

The U.S. Environmental Protection Agency (USEPA) guidelines for cancer risk assessment recognize that some chemical carcinogens may have a site-specific mode of action (MOA) involving mutation and cell-killing-induced hyperplasia. The guidelines recommend that for such dual MOA (DMOA) carcinogens, judgment should be used to compare and assess results using separate "linear" (genotoxic) versus "nonlinear" (nongenotoxic) approaches to low-level risk extrapolation. Because the guidelines allow this only when evidence supports reliable risk extrapolation using a validated mechanistic model, they effectively prevent addressing MOA uncertainty when data do not fully validate such a model but otherwise clearly support a DMOA. An adjustment-factor approach is proposed to address this gap, analogous to reference-dose procedures used for classic toxicity endpoints. By this method, even when a "nonlinear" toxicokinetic model cannot be fully validated, the effect of DMOA uncertainty on low-dose risk can be addressed. Application of the proposed approach was illustrated for the case of risk extrapolation from bioassay data on rat nasal tumors induced by chronic lifetime exposure to naphthalene. Bioassay data, toxicokinetic data, and pharmacokinetic analyses were determined to indicate that naphthalene is almost certainly a DMOA carcinogen. Plausibility bounds on rat-tumor-type-specific DMOA-related uncertainty were obtained using a mechanistic two-stage cancer risk model adapted to reflect the empirical link between genotoxic and cytotoxic effects of the most potent identified genotoxic naphthalene metabolites, 1,2- and 1,4-naphthoquinone. Bound-specific adjustment factors were then used to reduce naphthalene risk estimated by linear extrapolation (under the default genotoxic MOA assumption), to account for the DMOA exhibited by this compound.

Computer algebra in the life sciences

This note (1) provides references to recent work that applies computer algebra (CA) to the life sciences, (2) cites literature that explains the biological background of each application, (3) states the mathematical methods that are used, (4) mentions the benefits of CA, and (5) suggests some topics for future work.

Testing goodness of fit for stochastic models of carcinogenesis

This paper considers the utility of statistical goodness of fit testing in the context of mechanistic models of carcinogenesis. Two stochastic models of carcinogenesis were tested with several sets of experimental and epidemiological data using a formal goodness of fit test specially designed to accommodate censored observations: these were the two-stage model allowing for clonal expansion of initiated cells and its simpler version with gamma distributed promotion time. The results of this application, supplemented by visual examination of local likelihood kernel estimates of the hazard function and the corresponding model-based estimates, show that mechanistic models of carcinogenesis provide a good fit to the data in the majority of cases under study.

Modeling radioprotective mechanisms in the dose effect relation at low doses and low dose rates of ionizing radiation

A new model (Random Coincidence Model--Radiation Adapted (RCM-RA)) is proposed which explains a possible pseudo threshold for stochastic radiation effects. It describes the formation of cancer in the case of multistep fixation of lesions in the critical regions of tumor associated genes such as proto-oncogenes or tumor-suppressor genes. The RCM-RA contains two different possibilities of DNA damage to complementary nucleotides. The damage may be caused either by radiation or by natural processes such as cellular radicals or thermal damage or by chemical cytotoxins. The model is based on the premise that radiation initially is bionegative, damaging organisms at their different levels of organization. The radiation, however, also induces various cellular radioprotective mechanisms which decrease the damage by natural processes. Considering both effects together, the theory explains apparent thresholds in the dose-response relation for radiation carcinogenesis without contradiction to the classical assumption that radiation is predominantly bionegative at doses typically found in occupational exposures.

A unified approach to a class of stochastic carcinogenesis models

Survival and hazard functions play a pivotal role in carcinogenesis modeling. This paper provides a unified approach to computing these two quantities by classifying a large class of carcinogenesis models from a computational point of view, and prescribes specific computational recipes according to this classification.

A carcinogenesis model describing mutational events at the DNA adduct level

A stochastic carcinogenesis model is proposed to describe a sequence of component mutational changes that constitute the G:C-->A:T base substitution. This paper provides the biological basis and mathematical formulation underlying the proposed model. In addition, the paper elaborates on a numerical approach for studying the cumulant functions, survival functions, and hazard functions of the model. Several numerical examples are given of potential applications of the model.