Table of Contents
Risk Management for Plausibly Hormetic Environmental Carcinogens: The Case of Radon

Kenneth T. Bogen, Dr. P.H. and David W. Layton, Ph.D.

Lawrence Livermore National Laboratory, University of California, Livermore, CA*

*Health and Ecological Assessment Div. (L-396), Lawrence Livermore National Laboratory, Livermore, CA 94550, USA, Tel: (510) 422-0902, Fax: (510) 424-3255, NET:

Abbreviations: BEIR = Biological Effects of Ionizing Radiations, CD2 = cytodynamic 2-stage, LCM = lung cancer mortality, LN = linear no-threshold, NRC = National Research Council, RR = relative risk.


Risk management typically involves efforts to reduce human exposures by establishing regulations that limit the concentration of the substance in environmental media. In cases where a substance is widely used in commerce or is naturally occurring in the environment, compliance costs can be substantial because of nationwide requirements to add expensive control technologies. Uncertainties in a dose-response function further impact risk management decisions because they may correspond to large differences in health benefit per unit exposure reduction. These problems are highlighted in the case of plausibly hormetic environmental carcinogens, for which a linear-no-threshold (LNT) dose-response model has been the traditional regulatory default assumption. In this case, model uncertainty is pivotal, and risk management is consequently inherently controversial. However, marginal cost functions that arise for plausibly hormetic carcinogens are expected to possess a common analytic feature that may be particularly useful for this type of risk management problem. Specifically, marginal cost functions in this context are expected to have roots reflecting contaminant concentration values above which regulatory goals may be optimally placed subject to cost constraints. Here we illustrate this heuristic feature in the case of residential radon, using both a LNT model and a biologically plausible hormetic model to predict associated risks of lung cancer mortality.

Key Words: Alpha, dose-response model, epidemiology, hormesis, linear-no-threshold, radiation, risk management.


U.S. regulatory agencies typically use linear-no-threshold (LNT) risk extrapolation for environmental carcinogens, particularly for agents that damage DNA or chromosomes in approximate LNT fashion over a large dose range (NRC, 1994). Risk management under the LNT assumption involves minimizing a monotonically increasing risk-vs.-dose function and/or some function involving corresponding marginal costs, subject to uncertainties constrained by the assumption that exposure reductions will never increase risk. In contrast, by definition, a reduction in exposure to a hormetic environmental carcinogen will increase risk over a limited range of low-level exposure. Risk management for a plausibly hormetic environmental carcinogen thus inevitably involves a tradeoff between alternative­indeed, mutually exclusive­risk predictions.

While quantitative uncertainty analysis should play an important role in risk-tradeoff decisions, methods to quantify model uncertainty remain controversial (NRC, 1994). Because model uncertainty is pivotal in the case of plausibly hormetic environmental carcinogens, related risk management will be inherently controversial, but a common analytic feature that arises may be useful in this context. Here we illustrate this heuristic feature in the case of residential radon.

Radioactive radon gas (222Rn) diffuses through rocks and soil, accumulating in enclosed areas such as underground mines and homes. Inhaled radon and its decay progeny emit alpha radiation that is genotoxic and cytotoxic, even at very low doses, and such respiratory exposure has been observed to cause lung cancer in experimental animals and in underground miners (NRC, 1988). Lung cancer risk due to residential exposure is currently estimated by linear-no-threshold (LNT) extrapolation from underground miner data, and is thought to pose the greatest threat from indoor air pollution in the U.S.­responsible for about 10% of all lung cancer, and about 20-30% of all lung cancer in nonsmokers (Kerr, 1988; Lubin and Boice, 1989; Nazaroff and Teichman, 1990; Oge and Farland, 1992; Lubin and Steindorf, 1995; Lubin et al., 1995). In contrast, U.S. county-level data reflect an apparent negative correlation between lung cancer mortality (LCM) and residential radon levels, inconsistent with LNT predictions (Cohen, 1995). Moreover, just such a negative association (or “hormesis”) at typical residential levels of radon exposure, together with increased LCM risks at much higher levels of radon exposure, were shown recently to be jointly predicted by a biologically plausible, mechanistic “cytodynamic 2-stage” (CD2) model of radon's effect on lung carcinogenesis (Bogen, 1997). Notably, while the CD2 model realistically assumes LNT dose-response models for both alpha-induced cell killing and alpha-induced critical mutations, it nevertheless predicts reduced LCM risk (“hormesis”) at alpha exposures that are large enough to negate a slight net proliferative advantage presumed for unexposed premalignant clones, but small enough not to offset the latter effect via induction of new premalignant clones (Bogen, 1997).

Below we describe methods we used to assess residential radon exposure in the U.S., to predict associated LCM risks using LNT and CD2 models, and to calculate model-specific marginal costs of risk reduction and their weighted average values as functions of radon remediation level and remediation efficiency. Implications for risk management are then discussed.


Exposure Assessment. Radon concentrations in household indoor air vary according to housing properties (air exchange rates with outdoor air, cracks in basement walls and slab floors, types of heating and cooling systems, etc.), the emanation of radon from the radioactive decay of 226Ra present in soils, and properties of adjacent soils. Radon levels are highest in basements and decline in each story above the basement (e.g., radon in basement air is usually ~2-fold higher than in first-floor air). Inhalation exposures are therefore controlled by the time spent in different indoor environments with different radon concentrations. Marcinowski et al. (1994) placed alpha track detectors for measuring radon in 4658 single-family detached houses throughout the U.S. Houses were selected using stratified random sampling to ensure that sampled residences were representative of the general housing stock. Data from radon detectors placed on each floor for 1 y, and from residents asked to provide information on time spent on different floors, were used to develop an aggregate U.S. distribution of exposure-weighted radon concentrations. The resulting distribution is approximately lognormal with a geometric mean of 27.4 Bq/m3 and a geometric standard deviation of 2.92 (Marcinowski et al., 1994). For the present study, we assume this distribution pertains to a total stock of H = 58.9 million detached U.S. residences, housing a total of N = 2.3H people based on a median family occupancy of 2.3 persons per residence (U.S. Census Bureau, 1993).

Control Technologies and Costs. Efforts to reduce residential radon exposure have focused primarily on techniques for reducing radon entry into indoor air from soil via cracks in basement walls and floor slabs. Radon flow through such cracks is controlled in part by depressurization of building air due to indoor heating, wind flow over the building shell, and other factors creating a pressure gradient between soil gas (containing radon) and indoor air (Riley et al., 1996). One way to reduce radon inflow is to collect it in soil adjacent to a basement wall or floor slab prior to entry. In subslab depressurization, pipes are inserted in holes drilled through a floor slab, and a fan is used to pull air through the pipes leading to the subslab soil. Extraction of soil air results in subsurface depressurization that draws in radon-bearing soil air. Radon collected during depressurization is then vented to outdoor air. For new home construction, membranes can be placed below a subslab gravel layer to inhibit radon transport by isolating this layer so that it serves as a conduit for radon capture and subsequent venting, which has been shown to reduce indoor radon levels by factors of 4 to 15 (Fisk et al., 1995). Installed costs of active soil-depressurization methods range from $800 to $2500, annual operating costs vary from $40 to $300, and corresponding control efficiencies range from 80 to 99% (Henschel, 1994). In our analysis, we assumed that control efficiencies (f) were functionally related to the total of capital expenditures plus discounted operating costs as follows: $5000 for f = 100%, $2000 for f =93.3%, $1500 for f = 75%, and $1000 for f = 50%.

Cancer Risk Models. Two alternative functions were considered relating RR for LCM to lifetime residential exposure to radon at concentration c (Bq m-3) in the presence of other causes of death. Both have the form: RRi(c) = (h(t)(1+ERRi(t,c))/r0, where h(t) = LCM hazard specific to age t, ERRi(t,c) = age-specific excess relative hazard at concentration c, = a life table function using 1980-4 rates for U.S. males (NRC, 1988; Eq. 2A-22 and Table 2A-10, implying r0 = 0.067), and i specifies model type. The LNT model (i = 1) used was the BEIR IV model specifying ERR1(t,c) (NRC, 1988; Eq. 2A-17), as adapted by Puskin (1992) to account for a relatively lower effectiveness of residential radon concentrations at exposing critical target cells in the lung, compared to similar levels experienced by underground miners (NRC, 1991). The hormesis model (i = 2) used was based on the CD2 model (Bogen, 1997), which originally was fit jointly to RR data for U.S. males and Colorado Plateau data miners (Cohen, 1995; NRC, 1988). For the present study, the CD2 model was refitted to the combined RR data accounting for competing risks of death as described

in which the survival function S(c,t) is the CD2-model quantity SSSR (Bogen, 1997; Appendix 2). The LNT and refitted CD2 models for residential exposure-scenarios are shown in Fig. 1a.

Values of population-average RR attributable to radon remediation with efficiency f of all residential radon concentrations C above a specified concentration c were calculated as

where p is the lognormal density function reflecting variation in mean radon concentrations among U.S. homes (see above). Corresponding mean percent excess relative risks, calculated as %ERR i (c) = 100% (RR i (c,f) 1), are shown in Fig 1b where % ERR 1(,0) = 8.32% and % ERR 2 (,0) = 4.74% are shown as horizontal dashed lines (reflecting no remediation).

Marginal Risk-Reduction Costs. Excess cases for a stationary population were estimated assuming a background LCM rate of r 0* = 0.046 for U.S. males + females (NRC, 1988). LCM risks attributable specifically to radon were estimated as r i* = r 0*[1 RR i (,0) ¯1], and corresponding cases as r i * N = 2.3 r i * H. Corresponding marginal remediation costs MC(c,f) (in $K) per life saved (or, taken, as the case may be) were then calculated as

where Kf ($K) is unit remediation cost conditional on alternative values of f as specified above, and wi are model-specific subjective probabilities that add to 1. Three weight sets, { w 1 .w 2} = {1, 0}, {0, 1}, and {0.5, 0.5}, were considered. Marginal cost estimates using the first two weight sets correspond to assumptions that the LNT and CD2 models are true, respectively (Figs. 2a-b), while those using the last set of weights presume that both models are equally likely to be true (Fig. 3b, compared to corresponding values of %ERR plotted in Fig. 3a). The present analysis thus focused on implications of model uncertainty. While model-specific parameter uncertainty was not considered explicitly, insofar as each model was fit to the same occupational data, LNT and CD2 parameter uncertainties would be rather correlated, which implies a deminished impact of this source of uncertainty on cost-risk comparisons.


From a risk-management standpoint, the skewness of the lognormal distribution of radon concentrations in detached U.S. residences has a significant impact on the number of homes needing remediation to achieve a given level of indoor radon. For example, realization of the U.S. EPA's current action level for mitigating indoor radon of 150 Bq/m3 (developed using LNT assumptions) would require that nearly 3.4 million (or ~6% of) detached U.S. residences would require remediation. If the action level were raised by a factor of 3 (to 450 Bq/m 3), the number of residences targeted for remediation would drop by a factor of 12, or to <0.5% of all detached houses. Using assumptions described above, the higher action level would imply a total remediation cost reduction of $5 to $6.5 billion, assuming remediation efficiencies between 75% and 93%. However, analysis of the marginal cost-effectiveness of remediation are better suited to identifying regulatory goals having efficiencies consistent with those of other societal efforts to improve environmental health.

Using the CD2 (hormesis) model, a striking feature of marginal costs calculated as functions of target action levels, c, corresponding to four different remediation efficiencies considered are the portions that descend vertically through the abscissa, reflecting the concentrations at which this model predicts the costs of additional remediation to be associated with increased rather than decreased mortality (Fig. 2b). A similar feature also appears in marginal cost plots that reflect both models equally (Fig. 3b), and indeed would be expected using any model weights that reflect nontrivial likelihoods for both LNT and hormetic predictions. Thus, for plausibly hormetic environmental carcinogens, the roots of the function representing marginal costs of exposure reduction provide heuristic guides to the selection of remediation or exposure-reduction goals. Note that these roots indicate only minimal target concentrations for this purpose, since predicted marginal costs may become quite large at concentrations that exceed these minima. For example, if the CD2 model is true and a remediation efficiency of 93% is assumed, then costs exceeding $100K per averted LCM are predicted for remediation of all homes in which the average radon concentration exceeds ~450 Bq m-3 (~3 times the current EPA guideline) (Fig. 2b). If f = 93% and the LNT and CD2 models are presumed equally likely, the same marginal cost is realized at ~300 Bq m-3 (~2 times the current EPA guideline) (Fig. 3b). The differential cost in remediating to the alternative concentrations is about one billion dollars.

The recent National Research Council (NRC) report on risk assessment for environmental carcinogens (NRC, 1994) specifically recommends against quantitative combinations of model uncertainty (e.g., the weighted analysis reflected in Fig. 3b), preferring instead that model uncertainty be considered using narrative/qualitative comparisons of model-specific analyses (such as that given in Fig. 2a-b). Effective management of imminent public health threats clearly requires some method of triage calculus, including formal quantitative treatment of model uncertainty if applicable. The NRC recommendation, on the other hand, pertains specifically to environmental carcinogens, which pose relatively delayed and distributed risks that we are urged to manage in some more subtle and less accountable fashion. The distinction between the two contexts hardly justifies a suppression of analytic clarity. Anyway, there is little logical merit to the distinction between model and parameter uncertainty, since discrepant models may always be represented by alternative parameter values of some more generally defined model (NRC, 1994; Note 4, p. 187). This is particularly true in the case of the LNT vs. CD2 models, since the former reduces to the latter in the absence of (e.g., cytotoxicity caused) cell-kinetic changes (Bogen, 1989; 1997).

Finally, our analyses demonstrate that uncertainties in the dose-response function for radon can have significant risk-management implications. Specifically, we show that the costs expended per life saved increase with decreasing concentrations of radon in indoor air for the LNT model, and for the CD2 model we show that the marginal costs can actually become negative because of the shape of the dose-response function. Despite the dramatic risk-management implications of the hormetic CD2 dose-response model, the existing regulatory/research framework provides no formal mechanism for balancing the costs of implementing a given regulation (which in the case of radon is based on a linear dose-response model that is assumed to be true or certain) with the potential benefits of reducing the uncertainties in the dose-response relationship by expending additional research dollars.


This work was performed under the auspices of the U.S. Department of Energy at Lawrence Livermore National Laboratory under contract W-7405-ENG-48.


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