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
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.
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
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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Bogen, K. T. 1997. Do U.S. county data disprove linear no-threshold predictions of lung cancer risk for residential radon?A preliminary assessment of biological plausibility. Hum. Ecol. Risk Assess. 3, 157-186.
Bogen, K.T. 1998. Mechanistic model predicts a U-shaped relation of radon exposure to lung cancer risk reflected in combined occupational and U.S. residential data. BELLE Newletter, this issue.
Cohen, B. L., 1995, Test of the linear-no threshold theory of radiation carcinogenesis for inhaled radon decay products. Health Phys., 68, 157-174.
Darby, S., Whitley, E., Silcocks, P., Thakrar, B., Green, M., Lomas, P., Miles, J., Reeves, G., Fearn, T., and Doll, R., 1998. Case-control study of lung cancer and residential radon exposure in South-west England [Abstract]. Epidemiology, 9(4 Suppl.), S108 (343 S).
Heidenreich, W. F., Luebeck, E. G., and Moolgavkar, S. H., 1997. Some properties of the hazard function of the two-mutation clonal expansion model. Risk Anal., 17, 391-399.
Hoel, D.G. 1998. Response to the reports of Andersen, Bogen and Downs. BELLE Newletter, this issue.
Létourneau, E. G., Krewski, D., Choi, N. W., Goddard, M. J., McGregor, R. G., Zielinski, J. M., and Du, J., 1994. Case-control study of residential radon and lung cancer in Winnipeg, Manitoba, Canada. Am. J. Epidemiol., 140, 310-322.
Lubin, J. H., Boice Jr., J. D., Edling, C., Hornung, R. W., Howe, G., Kunz, E., Kusiak, R. A., Morrison, H. I., Radford, E. P., Samet, J. M., Tirmarche, M., Woodward, A., Yao, S. X., and Pierce, D. A., 1994. Lung cancer and radon: A joint analysis of 11 underground miners studies, NIH Publication No. 94-3644. U.S. National Institutes of Health, Bethesda, MD.
Lubin, J. H., Boice, J. D., Edling, C., Hornung, R. W., Howe, G., Kunz, E., Kusiak, R. A., Morrison, H. I., Radford, E. P., Samet, J. M., Tirmarche, M., Woodward, A., and Yao, S. X., 1995a. Radon-exposed underground miners and inverse dose-rate (protraction enhancement) effects. Health Phys., 69, 494-500.
Lubin, J. H., Boice, J. D. J., and Samet, J. M., 1995b. Errors in exposure assessment, statistical power and the interpretation of residential radon studies. Radiat. Res., 144, 329-341.
Pershagen, G., 1998, Residential radon and lung cancerNew aspects in risk assessment [Abstract]. Epidemiology, 9(4 Suppl.), S108 (342 S).
Piantadosi, S. 1994. Invited Commentary: Ecologic Biases. Am. J. Epidemiol. 139, 761-764.
Portier, C. J., and Ye, F. 1998. Response to the reports of Andersen, Bogen and Downs. BELLE Newletter, this issue.
Wichmann, H. E., Kreuzer, M., Gerken, M., Dingerus, G., Wellmann, J., Keller, G., and Kreienbrock, L., 1998. Lung cancer risk due to radon in dwellings in Western Germany [Abstract]. Epidemiology, 9(4 Suppl.), S45 (91-O).
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