Bogen's Responses to Reviewer Comments

Moolgavkar (1998) claims that assumptions underlying the CD2 model "introduce a U-shaped exposure-response relationship on the net proliferation rate of initiated ... cells [which] is then reflected in a [similar relation] for the hazard function for lung cancer mortality," and that there is no "direct biological support" for these assumptions. As I pointed out in my accompanying paper, a U-shaped exposure-response is predicted by the CD2 model only insofar as the parameter values used imply that "(i) induced cytotoxicity is sufficient to negate a slight net proliferative advantage presumed for spontaneous premalignant clones, but (ii) induced mutations yield insufficiently many new premalignant clones to offset the latter effect on tumor likelihood." Whether the CD2 model predicts initial exposure-response patterns that are U-shaped, tilde-shaped, linear-quadratic or nearly linear depends on the ratio of cytotoxic to mutagenic potencies estimated and/or assumed (see Bogen, 1997: Fig. 3). In my accompanying paper (Bogen, 1998), the cytotoxic potency of D0 = 35cGy assumed was the average of published values for alpha-induced killing of human lung cells in vitro. There is little doubt that normal and premalignant human bronchial epithelial cells are reproductively killed by radon/daughter alpha radiation with roughly equal efficacy, because such killing is typically induced by multiple (hence often irreparable) chromosome breaks within nuclei that absorb this high linear-energy-transfer radiation. Consequently, there is direct biological support for a critical assumption that allows the CD2 model to predict a U-shaped exposure-response. That this assumption allows, yet does not require, the CD2 model to predict a U-shaped exposure response relation is illustrated in Figure 1 below, in which the CD2 fit I reported (Bogen, 1998) is compared to similar predictions obtained by varying only the assumed D0 value.

Moolgavkar's point about 2-stage model applications to hazard-rate rather than lifetime tumor-probability data is quite correct. My own earlier CD2 paper (Bogen, 1997), and not the other papers cited in Bogen (1998), was limited by a CD2-model fit to lifetime tumor-probabilities rather than hazard rates. I agree that my CD2 analysis (Bogen, 1998) would be improved considerably by taking explicit account of individual-level information for miner cohorts. Unfortunately, contrary to Moolgavkar's presumption, I could obtain from Dr. Lubin and his coauthors permission to use only person-year summary data for 5 of the 6 available cohorts of never-smoking miners worldwide, and not any of the corresponding individual-level data. The person-year data provided to me, however, were detailed and extensive, covering 83%, 89% and 88% of the total number of lung cancer cases, miners, and person years, respectively, in the combined six cohorts described by Lubin et al. (1995a). All the relative-risk estimates, associated confidence-limit estimates, and trend analyses I performed using maximum-likelihood methods required the use of person-year data. I doubt the CD2-modeling results I obtained would change appreciably if I used the corresponding individual-level data.

Moolgavkar (1998) questions the identifiability of the CD2 model I used. The editor's space constraints prevented me from including a detailed mathematical appendix. Briefly, the model was evaluated using the analytic solution to the 2-stage stochastic (MVK) model with piecewise-constant parameters described by Zheng (1995). Process-specific hazard functions, HS(t) and HR(t), corresponding to the SPM and RQM processes posited in the CD2 model, respectively, were presumed independent and each calculated as described by Zheng (1995). The latter independence implies that the hazard function for the 6-parameter CD2 model used is simply H(t) = HS(t) + HR(t). From the fact that a single MVK-type hazard function with at most three piecewise-constant parameters is identifiable (Heidenreich et al., 1997), it would thus appear that the 6-parameter CD2 model used is also identifiable in theory.

Finally, Moolgavkar (1998) emphasizes that the utility of a predictive biological model lies in the testable biological hypotheses it generates. The results I obtained certainly pose testable mechanistic hypotheses concerning the effect of subchronic or chronic exposure to relatively cytotoxic genotoxins, such as alpha radiation, on growth kinetics of premalignant foci. As mentioned above, focal resistance is not expected in the case of alpha radiation because a fraction of the damage (e.g., multiple chromosome breaks) induced is predictably misrepaired to states that are at least reproductively lethal. Verification of this prediction is needed, however. Another key CD2 hypothesis is that cell proliferation induced to compensate for normal-cell loss from low-level alpha exposure is not accompanied by the same amount of (or any) increased proliferation in surface-epithelial (P-cell) premalignant foci. Experiments that address this issue directly could also be done. Also, as I mentioned in my comments above to the paper by Andersen and Conolly (1998), to further test the CD2 model in relation to radon I am currently collaborating on a study of the effect of chronic exposure to radon-derived alpha radiation on growth kinetics of enzymatically altered foci within DEN-initiated liver.

Figure 1.

Relative risk (RR) of increased lung cancer mortality (LCM) experienced by U.S. white females during 1950-54 as a function of county-mean residential radon concentration (within six concentration ranges), based on internal comparisons to data (solid point) corresponding to the lowest exposure group (RR = 1, dashed line), replotted from Fig. 2a in Bogen (1998). These RR estimates are compared to predictions made by the 6-parameter CD2 model (using the assumed value of 35 cGy for the unestimated parameter D0, based on published in vitro data) fit to >60 age-specific LCM rates for the WF and miners corresponding to the RR estimates shown (curve labeled "35cGy"; cf. Fig. 2a in accompanying paper by Bogen), and by similar predictions obtained by using the alternative D0 values indicated. Note that the curve corresponding to a (biologically unrealistic) D0 value of 300 cGy is not U-shaped.

The coments of Hoel (1998) (see also Lubin, et al., 1995b) point to the fact that better predictions of lung-cancer risk associated with low-level radon exposures will require detailed exposure histories and lung-cancer data concerning tens of thousands of people. A coordinated effort to generate a database of large magnitude is now underway in Europe, Canada and the U.S. Initial results indicate a relative-risk pattern that is nearly linear for some data sets (e.g., those focusing on areas of relatively high residential exposure-Darby et al., 1998; Pershagen, 1998), but flat or possibly U-shaped for other data sets (e.g., those focusing on combined low and high residential-exposure areas, or on nonsmokers-Alavanja et al., 1994; Létourneau et al., 1994; Pershagen, 1998; Wichmann et al., 1998). A key assumption behind the nonlinearity predicted by the CD2 modelalpha-induced killing of premalignant cells in bronchial-surface epitheliumappears highly likely. Some (albeit perhaps negligible) nonlinearity in lung-cancer risk due to residential radon is thus indicated by current, mechanistically based multistage cancer theory. If properly designed, future analyses of expanded sets of residential case-control data will bound the magnitude and significance of any such nonlinearity.

Hoel (1998) also states that "the addition of the reservoir of unexposed cells to the CD2 model needs biological justification as it relates to lung cancer." This justification was provided by Bogen (1997: Appendix 1).

Portier and Ye (1998) point out that my analysis (Bogen, 1998) included no formal description of "the probability that the data could be explained by a monotonic curve". My previous CD2 analysis (Bogen, 1997) demonstrated clearly that a monotonically increasing MVK function is statistically inconsistent with county-level U.S. ecologic data used by Cohen (1995) relating lung-cancer rates to mean residential radon levels (p = 2.8 x 10-7). While I made no attempt to repeat this type of analysis using 1950s data for lung cancer in U.S. white women, the 1950s data are similar to Cohen's data insofar as indicating a significantly negative exposure-response trend (Bogen, 1998). I did not consider additional formal tests demonstrating statistical inadequacy of a monotonically increasing function to model U.S. ecological data to be productive, since the point of my CD2 model applications to radon have been only to demonstrate the biological plausibility of the U-shaped exposure-response for radon-associated lung cancer suggested by county-level U.S. ecologic data that have been claimed to be suspect in view of their purported biological implausibility (Piantadosi, 1995). It may be that some or most of the U-shape indicated by the ecologic data is attributable to biases that cannot be adjusted for in any ecologic analysis. As mentioned above, better case-control data will ultimately determine plausible bounds on exposure-response nonlinearity that may pertain to lung cancer risk affected by low-level radon exposures.


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