Analyses of Epidemiological Data

With few exceptions, the multistage polynomial is applied in making risk predictions from animal cancer bioassay data. Epidemiological data are typically analyzed, with empirical models of absolute or relative risk as a function of exposure. There is, however, a growing number of applications of mechanistic models, such as the two-stage clonal expansion model to epidemiological data (e.g., radon in hard rock miners [12, 46], atomic bomb survivors [47]). The estimates can be age- and time-dependent and are derived using a variety of empirical approaches. The reader is referred to the recent review of Krewski et al (21).

An example of empirical approaches to predicting risk from epidemiological data is provided for the mixed exposure case of the mycotoxin aflatoxin and hepatitis B virus (HBV). Aflatoxins are recognized carcinogens for the human liver but often occur at high levels in areas of high hepatitis B infection prevalence, another causative factor in human liver cancer. Aflatoxin B1 (AFB1) is clearly genotoxic, with DNA adduct formation increasing with dose in a linear fashion in multiple species (48) and the urinary excretion of the metabolite AFB1-N7-guanine also proportionate to human intake (46). An epidemiological study (prospective cohort) measuring both aflatoxin levels and HBV infection status (137) provides the basis for estimating cancer potency. Wu-Williams et al (15) fit various empirical models to the data corresponding to assumptions regarding (a) whether liver cancer, from aflatoxin and HBV combined, adds to or multiplies with the background of liver cancer (absent these influences), and (b) whether aflatoxin and HBV themselves add or interact (both add and multiply). A final possibility considered was a multiplicative relative risk model wherein the increases in relative risk were due to HBV multiplying the relative risk from AFB 1. The mathematical expressions corresponding to these assumptions and the results of the modeling exercise are shown in Table 2. Note that in this case, the relative and absolute risk forms of the model are mathematically equivalent (re-parameterizations of one another) and cannot be distinguished on the basis of goodness of fit to the data. However, when the models were used to make predictions for the United States, substantially different risks were predicted because the background of HBV infection in the Chinese cohort is much greater than in the United States (15). Thus, under certain assumptions regarding the prevalence of HBV in the United States, models could be distinguished in terms of the extent to which the predictions were realistic.

An obvious advantage of the use of epidemiological data for risk prediction is that no interspecies extrapolation is required. Nonetheless, there can be great uncertainty associated with such risk predictions when applied to populations different from the epidemiological study. A frequent difficulty encountered in using occupational studies to predict risk for the general population is understanding the extent to which results may predict risk from exposures of the young and el-

TABLE 2. Model Fits to Data on Daily Aflatoxin Dose (d), HBV Infection (h), and Annual Liver Cancer Incidence (y) from Guangxi, China*

Risk models

Model forms and parameters

Additive

Interactive

Multiplicative in relative risk

Excess risk form (ER) Relative risk form (RR) a, background incidence (per year, per 100,000) £>7, HBV effect (annual incidence due to HBV) b2, aflatoxin effect, (annual incidence per mg/kg-day) Goodness of fit: %2

y= a + bfh + b2cf y= a(1 + b/h + b2'd) 2.87 (7.77-22.5)

ER: 0.0055(0.0045,0.0067) RR: 191 a (NC) ER: 0.42 (0.72-1.76) RR: 14520 a (NC) 17.27 (5 df)

y = a + bfh + b2d+ b3hd y= a(1 + bi'h+ b2d+ b3'hd) 7.17(0-22.5)

ER: 0.29 (0.069 - 0.55) RR: 4690 a (369a-15681 a) ER: 0.20 (0.069, 0.55) RR: 4690 a (369a-15681 a) 6.11 (4 df)

Maximum likelihood estimates with upper and lower 95% confidence bounds given in parentheses.

NC: confidence limits infinite.

Source of data: ref. 137; analysis: ref. 15.

derly. Also, the occupational group studied can differ from the population of interest in geographical location, gender distribution, cultural habits, and other factors. Finally, the exposures for the occupational groups are often not well defined and exposure estimates correspondingly uncertain. Predictions can differ by orders of magnitude, depending on assumptions made about these factors (see, for example, the effort to examine the potency of benzidine by the International Agency for Research on Cancer [49] and the comparisons of prediction of lifetime risk of solid tumors derived from atomic bomb survivor data [47]).

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