Do 2-amino-3,8-dimethylimidazo[4,5-f] quinoxaline data support the conclusion of threshold carcinogenic effects?

Abstract

The objectives of this paper are to (1) reexamine the data that were used to support the conclusion of a threshold effect for 2-amino-3,8-dimethylimidazo[4,5-f] quinoxaline (MeIQx)-induced initiation and carcinogenicity at low doses in the rat liver, and (2) discuss issues and uncertainties about assessing cancer risk at low doses. Our analysis is part of an effort to understand proper interpretation and modeling of data related to cancer mechanisms and is not an effort to develop a risk assessment for this compound. The data reanalysis presented herein shows that the low-dose initiation activity of MeIQx, which can be found in cooked meat, cannot be dismissed. It is argued that the threshold effect for carcinogenic agents cannot be determined by statistical non-significance alone; more relevant biological information is required. A biologically motivated procedure is proposed for data analyses. The concept and procedure that are appropriate for analyzing MeIQx data are equally applicable to other compounds with comparable data.

Appendix

The following brief derivation is taken from Chen et al. (1991) for modeling initiation–promotion data. A generalization of the same tumor development concept can be found in Chen and Farland (1991). This approach uses the same concept of carcinogenesis modeling in Cohen and Ellwein (1990) in which mitotic rate is explicitly introduced in the model. The advantage of modeling by mitotic rate is that some information on mitotic rate is available; these data can be used as prior information in the Bayesian analysis.

1.1 Basic assumptions

(1) At time t = 0, a normal cell has a probability μ ₁ of being initiated to become an I-cell;

(2) Each I-cell has a random lifetime (i.e., time to mitosis) with a probability density function f(t);

(3) At mitosis, an I-cell is subjected to a homogenous birth and death process with probability of birth and death, given respectively by b and d with b + d = 1; and

(4) All I-cells go through this process independently of each other.

Under the assumption that cell lifetime is exponentially distributed with parameter λ [i.e., f(t) = λexp(−λt)], the probability that a focus has size k at time t is given by

$$ P_{k} (t) = [1 - P_{0} (t)][1 - A(t)][A(t)]^{{k - 1}} ,\quad k \ge 1 $$

(3)

where

$$ B(t) = \frac{{1 - \exp (gt)}} {{1 - r\exp (gt)}};\quad g = \lambda (b - d);\;r = b/d; $$

and A(t) = rB(t).

The reciprocal, 1/λ, of the parameter λ can be interpreted as the mean time to mitosis, or equivalently, λ can be interpreted as mean mitotic rate.

If we assume that a focus becomes detectable when it contains at least s cells, then the probability for a focus to be countable is

$$ D_{s} (t) = {\sum\limits_{k = s} {P_{k} (t)} } = [1 - B(t)][A(t)]^{{s - 1}} $$

(4)

Eq. (4) is the basic formula to construct a time dependent piece-wise constant model used in the simulation.

The advantage of considering random cell-lifetime in formulating the initiation and growing process of foci is that available biological information, as discussed above, can be readily incorporated and it is more realistic to assume that cell lifespan is random, rather than assuming that all cells enter the mitotic phase at the same time; this is a feature particularly suitable for Bayesian analysis.

1.2 Piece-wise constant model

To allow for partial lifetime exposure, we divide the animal lifetime in the IP study into three subintervals: (0, 20), (21, 49), and (50, 133) in days. This represents the experimental conditions that animals were 3 weeks (21 days) old when they were first received MeIQx for 4 weeks followed by PB for 11 weeks. The general concept to construct a model with piece-wise constant parameters for Bayesian analysis is based on the fact that the number of initiated cells, I(t), at any giving time t, is a Poisson process (Chen and Moini 1990), and the fact that the expected number of I-cells at any time t, getting initiated at t ₀, is I(t) = I(t ₀) exp(g(t − t ₀)) where g = b − d is the net growth rate for an I-cell. In the piece-wise constant model g is allowed to vary over different time intervals. Using this concept, the number of I-cells available at the beginning of the last sub-interval (50, 133) can be calculated. The number of foci of a particular size can be computed using Eqs. (3) and (4).

The model can be computed using the free software WinBugs as described in the text. In this model, the number of normal cells per cm² is assumed to be N = 600,000. It should be noted that accuracy of N is not required because Nμ ₁ occurred as a term in the model and μ ₁ is estimated from data; under-specification of N will be compensated for by the higher estimated value μ ₁ and vice versa. For the dose group k at age t, as specified in the model, the parameter μ ₁ is assumed to be linearly related to dose μ ₁[k, t] = μ ₁₀ + μ ₁₁ dose_MQ[k, t] and the mean mitotic rate is given by mt[k, t] = (1 − exp[−(mt ₀ + mt ₁ dose 1[k, t] + mt ₂ dose 2[t])]) where mt ₀ is the background mitotic rate, mt ₁ and mt ₂ are, respectively, coefficients for the MeIQx (dose 1) and the PB (dose 2) doses. In order to assign a reasonable non-informative, some knowledge about these parameters are needed. Some mitosis data can be found in Cohen and Ellwein (1990) and others. A wide range, from 1.0E-5 to 1.0E-2, of mitotic rate for the normal cells is also reported in Dolijanski (1960). Although the precise magnitude of mitotic rate for the MeIQX-induced initiated cells is not known, this information is useful for setting the upper bound for the non-informative prior in the Bayesian analysis. In all of the calculations, b ₀ = 0.501 is used. The value for b ₀ is obtained by perturbation of its value upward from 0.50 to find the best fit of data from the non-IP data in Table 1. Note that this is considered part of the process of using the non-IP data for summarizing and synthesizing information coming from various sources with different quality; the objective is to find a set of parameters that adequately fit the data. Ultimately, the conclusion comes from the more rigorous analysis of the IP-data.