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Public policy model for the indoor radon problem
Math1 Comput. Modelling, Vol. 10, No. 5, pp. 349-358, Printed
in Great
Britain.
1988
All rights reserved
PUBLIC
Copyright
0
0895-7177/88 $3.00 + 0.00 1988 Pergamon Press plc
POLICY MODEL FOR THE INDOOR RADON PROBLEM
M. J. SMALL and C. A. PETERS Civil Engineering and Engineering & Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. (Received September
Communicated
1987)
by E. Y. Rodin
Abstract-A model is developed that predicts the shift in distributions of indoor radon concentrations and potential risk reduction resulting from a program of homeowner sampling and remediation in a region. Indoor radon concentrations for a region are represented by a lognormal distribution. Discrete choice functions are used to describe the likelihood of homeowner sampling and remediation. The parameters of these functions are related to government policies for public information and radon risk management. A closed-form equation is derived for the shifted probability distribution function of radon, and this distribution is integrated over the lung cancer dose-response function to estimate the modified population risk in the region. Application of the model is illustrated using radon data from the Reading Prong region in Eastern Pennsylvania and the state of Washington.
INTRODUCTION
Concern about the hazard from radon gas in homes has increased significantly in recent years. Radon is an inert, radioactive element in the decay chain of 238Uwhich occurs ubiquitously in soil and rock. Radon generated in the ground enters the home through cracks and porous building materials in the substructure. Depending on underlying soil concentrations of radon and on housing construction, design and ventilation practices, indoor concentrations can be high enough to pose a significant risk of lung cancer. It is estimated that 5000-20,000 U.S. lung cancer deaths per year may result from indoor radon exposure [l, 21. Increased public awareness and the significant magnitude of the risk has placed indoor radon as a high priority problem for government officials. However, because radon is naturally occurring and exists within private homes, and because such risks are not considered by our society to be subject to direct regulatory action, the ultimate responsibility for mitigation lies largely with the individual homeowner. The policy options being considered to protect public health are thus meant to provide incentives for public action, rather than directly regulate the risk. The U.S. Environmental Protection Agency (EPA) is working with states to develop economic incentives and public education programs to induce homeowners to take mitigative action. The task facing regulators is to develop the set of programs and policies that will be most effective in reducing the public’s risk from indoor radon. This paper presents a mathematical modelling framework that quantifies the potential population risk reduction that can be achieved by alternative government policies implemented in a region. The framework incorporates the physical components of the problem by including a characterization of the probability distribution function of indoor radon concentrations in the region, a model to describe the effectiveness of remediation techniques, and a health effects model to translate radon concentration into lung cancer risk. In addition, the model includes components to describe the behavior of homeowners in dealing with radon in their homes. The behavioral components describe the relationship between policy variables, such as information dissemination and the provision of subsidies for remedial action, and the likelihood that homeowners will choose to remediate. Integrating these components into a single famework provides a mathematical tool for coordinated analysis of the physical and socioeconomic components of the radon problem. 349
M. J.
350
SMALL
MODEL
and C. A. PETERS STRUCTURE
Figure 1 shows the processes that must occur for risk reduction to take place in a region, and outlines the computational components of the model for integrated radon analysis. The indoor radon concentration, C, is defined as the spatial and temporal average of the radon concentration in a home. A region, defined as a population of homes on the scale that government actions are to be targeted; e.g. a city, county or state, is characterized by the probability density function (pdf) of indoor radon,&(c), and the cumulative distribution function (cdf), F,(c). Homeowner actions regarding sampling and remediation result in modified indoor concentrations, C’, with a shifted pdf,fc(c’), and cdf, F&c’). A suitable dose-response function is integrated overfc(c’) to compute the reduction in average population risk, and the fraction of the population with unacceptably high radon concentrations is computed directly from F&c’). These model outputs provide valuable information for radon policy decision making. Homeowner decisions on sampling and remediation are affected by factors such as the costs of sampling and remediation, the level and type of public information provided, and the severity of the problem in each home as indicated by sample results. The model relates the probability of
1 Yes .
.
Probability of remediation,
I
f-l
Sample result Cs
Effectivenessof remediation
gUn( Shifted regional pdf & cdf of indoor radon concentration after remediation
1. Reduction in average 2. Reduction in nu homes above act
Fig. 1. Components of the model for integrated radon analysis depicting the homeowner sampling and remediation processes that lead to risk reduction in a region.
351
Indoor radon problem model
sampling, Ps, and the probability of remediation given sampling, PR, to these factors by mathematical functions commonly used to model discrete-choice decisions [3,4]. For this analysis we assume that the probability of sampling within a region is the same for all homes; i.e. there is no clustering of neighboring homes with high or low values or other factors present that would result in within-region variations. The value of Ps is thus assumed to be constant. For those that sample, the decision to remediate is based on the homeowners’ perception of the risk associated with the sample result, C,, and the cost of remediation. Because indoor radon concentrations vary widely, perceptions of risk often depend on order-of-magnitude variations in Cs. Furthermore, regional distributions of indoor radon tend to be lognormal [5,6]. As such, logarithmic transformations of the indoor concentrations: X = In(C)
(1)
Xs = ln( C,) are used to compute homeowner response, and subsequent model calculations are made in terms ofXand Xs. The probability of remediation, conditioned on sampling, is given by the functional relationship: PR
=
PR(&)-
(2)
Note that there is some error inherent in different home sampling methods [7]. We could thus write: xs = x + L.
(3)
However, this error is not incorporated in the current model development, and it is assumed that X’s= X and P, = PR(X). Remediation is described in terms of the logarithm of the resulting concentration: Y = ln(C’)
(4)
and the effectiveness of remedial action is given by the functional relationship: Y=
for those who remediate
g(X);
(5) i X; for those who do not remediate. The derivation of the overall, shifted distribution, fy(y), requires consideration of the total probability of remediation. First consider the case where this probability is equal to one; that is, all homeowners sample and take action to lower their radon concentrations. Assuming that remediation effectiveness function, g(X), is monotonically increasing, the shifted pdf can be derived directly from the initial distribution by: f
r
(y)
=
dg-‘(y) dy fxk-‘(Y)l~ I I
) denotes the inverse of g( ). However, since not all homeowners are expected to where g-‘( remediate, the r.h.s. of equation (6) must be weighted by the total probability of remediation, P,P& -‘(y)], and a term added to represent the homes that are not remediated. The result is:
fxk-‘(Y)] + i1 -
pSpR(Y)lfX(Y).
(7)
Similarly, the cdf is derived as: u-g-‘09 F,(Y) = F,(Y) +
~d-‘~(~)_Mu) du.
(8)
s u=y In words, F,(y) is set equal to the probability that initial concentrations are below y, plus the probability that initial concentrations greater than y are rernediated to values less than or equal to y. The calculations in equation (7) and (8) can be referred to as probability weighted transformations. The dose-response function, D(C), is used to translate radon exposure levels into the corresponding risk of lung cancer death. The average population risk for a region with indoor
352
radon concentration
M. J.
SMALL
and C. A. PETERS
distribution &(c’)
is computed by y=rn B = “=02D (c’)&(c’) dc’ = D(Y)_&(Y) dy. s c’=0 s y= -m
The risk reduction is simply the difference between the average population fx(x) and .MY).
(9) risks calculated using
Assumed functional forms
To implement the model computations given in equations (7)-(9), particular functional forms are required for Ps, PR(X), fX(x), g(X), and D(X). As indicated previously, Ps is assumed constant, and C is assumed to be lognormally distributed, so that the pdf of X = In(C) is given by:
where pX and cX are the mean and standard deviation of X, respectively. These are related to the geometric mean of C, gm(C), and the geometric standard deviation of C, gsd(C), by: clx = lnkm(C)l
(11)
cX = ln[gsd(C)].
(12)
The probability of remediation is assumed to be related to the sampled concentration choice model [3]: PR(X) = a +
by a logit
b-a
1 + exp(a +/W)’
(13)
where a and b are limiting minimum and maximum probabilities, and a and j? are the scale and shape parameters of the relationship, respectively. The inclusion of parameters a and b, normally set equal to 0 and 1, respectively, in the logit choice model, is to account for the fact that there may be a small fraction of homeowners who remediate regardless of how low the radon concentrations in their homes are; and some who won’t remediate no matter how high the concentrations are. It is assumed that remedial action results in a fractional reduction of the indoor concentration, so that C’=RC
(14)
and Y = g(X) = In(R) + X,
(15)
where R is a fraction between 0 and 1. The value of R depends on the particular remediation method chosen and the characteristics of the home to which it is applied. In this illustration of the model, it is assumed that a single remediation method is chosen for the entire region and that variations due to differences in homes can be ignored. A constant value of R is thus used. Substituting equations (lo), (13), and (15) into equations (7) and (8), the shifted regional pdf is determined as:
and the cdf is:
Indoor
radon
problem
353
model
where @( ) denotes the cdf of the standardized normal variate. Equation (16) is in analytical form, while a numerical integration method, such as Simpson’s rule, is required to evaluate equation (17). The average population risk given by equation (9) is then determined by assuming a linear, no-threshold dose-response function: D(C)=rC
D (A’) =
r
exp(X),
where r is referred to as the carcinogenic potency factor [8]. A hermite quadrature [9] is used to evaluate the integral obtained by the substitution of equations (16) and (18) into equation (9). The integrated radon assessment model is thus specified by the two parameters of the initial regional radon distribution (pX, gX), the probability of home sampling (Ps), the four parameters of the remediation choice function (a, b, tl, p), the remedial action effectiveness (R), and the lung cancer potency factor (r).
EXAMPLE
APPLICATIONS
Test devices have been offered by both the public and private sectors and consequently a number of databases of indoor radon concentrations have been compiled. Because home radon testing is of a voluntary nature, nonrandom sampling often results. This causes difficulty in estimating the statistics of large scale distributions such as the national distribution [5, lo], but reasonable estimates of concentration distributions have been obtained on a regional scale. For illustrative purposes in this paper, we apply the model to two regions. One is the state of Washington which indicates indoor radon levels below the national average. The second is the Reading Prong region in Eastern Pennsylvania where higher than average radon levels occur due in part to high uranium concentrations in the underlying geologic formation. Current
radon distributions
The statistics for the Washington radon distribution were obtained from Nero et al. [5], who normalized the data to estimate annual average exposures. (Note that winter samples are generally higher than summer readings due to decreased air exchange during the winter.) Track-etch detector readings were taken in Washington (see [6] for information on the track-etch method), but it is unknown whether the samples were made in basements or living areas. The Reading Prong data were obtained from the Pennsylvania Department of Environmental Resources (DER) in March 1986 and analyzed by the authors. Instantaneous exposure measurements in working levels (WL) for 2500 homes in southeastern Pennsylvania were converted to radon concentration in picoCuries per liter (pCi/l) by assuming 50% radioactive equilibrium (see [l l] for a discussion of the equilibrium factor). All data were basement measurements and were converted to representative living area values by dividing by two [12]. Most measurements were made during the heating season but no adjustment was made to normalize to annual averages. In summary, the Washington and Reading Prong data sets are not strictly comparable, but they do provide representative estimates for illustrative application of the model in regions with low and high radon concentrations. The resulting statistics for the regions, along with estimates of the national distribution from Nero et al. [5], are presented in Table 1. The log probability plot of the Reading Prong data and the fitted lognormal distribution are shown in Fig. 2, indicating a good fit to the assumed lognormal shape.
Table 1. Indoor radon concentration
Reading Prong Washington United States
distribution
statistics for regional applications
Arithmetic mean am(C) (pCi/~)
Geometric mean gm(C) (pCi/l)
Geometric standard deviation gsd(C)
7.8 0.80 1.46
2.2 0.58 0.89
4.2 2.21 2.68
M. J. SMALL and C. A. PETEERS
354 2 100
5
I
10
I
20 30 llllllI
50
70 80
90 I
95 I
98
0.8
0.6
.1-f 2
11
5
,,,I,,,
10
20 30 Cumulative
0.0
11
50
70 80
90
95
98
0.1
1
4
10
loo
loo0
c (pCi/l)
Probability (96)
Fig. 2. Observed distribution (0) and fitted lognormal distribution (-) of indoor radon concentration for the Reading Prong. (Observed distribution plotted for every ;40th house.) Cumulative probability is the percentage of homes with concentrations equal to or less than the value on the y-axis.
Homeowner
j-__..c
0.01
Fig. 3. The probability
a logit function
of home remediation modelled as of the logarithm of the sample result.
choice model
The study of the way homeowners respond to risk situations in their homes is a relatively new area of research [13], though large scale studies have been initiated which should provide useful data for characterizing the homeowner choice functions, Ps and PR(X) [14, 151. At this point we can only assume parameter values and with this example demonstrate their importance, and the importance of such data collection efforts. The four parameter logit function, presented in equation (13) and shown in Fig. 3, can be used to describe the many factors that affect homeowners’ decisions to remediate, because of its flexibility in form. For example, the recommendation of an action level, a particular radon level above which remedial action should be taken, is likely to affect the horizontal location of the choice function. To illustrate this, we assume that the point of inflection occurs at the recommended action level, thus prescribing the value for ~1.For this application, a value of c( = 1.4 was calculated based on EPA’s recommended action level of 4 pCi/l [16]. The nature of the information disseminated to the public can also affect their decision mechanisms, causing variations in PR(X) which can be captured by the P-shape parameter. Reporting that risk estimates are indisputable and strongly recommending (i.e. “commanding”) that remediation be undertaken above the action level would result in a logit curve that has a steep slope near the inflection point (fi + - co). Conversely, communicating to the public the large amount of uncertainty surrounding risk estimates and using milder recommendations (i.e. “cajoling”) to induce remedial action would be reflected in a flatter PR(X) curve (/I -+ 0). The effect of these different approaches is being evaluated in the current study of New York homeowners by Smith et al. [14]. A smaller study of an information program conducted in Maine [15] indicates that homeowners’ decisions to remediate are not strongly related to radon concentration. These results would be accounted for in this model using a very small P-value, but for this application an intermediate value of p = - 1 was chosen. Variations in the cost of remediation, or conversely the level of government subsidization of remedial action, is likely to cause vertical shifts in the choice function, affecting parameters a and 6. In this application, the values a = 0.1 and b = 0.9 were assumed. Remediation
efiectiveness
Data on the effectiveness of remediation techniques are appearing from a number of research projects [e.g. 17-191. For this illustration, data from an EPA study of substructure ventilation in
Indoor
radon
problem
model 2
100.
355 5
10
20 30
50
70 SO 90 95
” “““I 1 ____-__. Initial
2
I 5
I 10
1l'll'I 20 30 50
”
70 80
I I 90 95
98
.
98
Cumulative Robability (5%)
Fig. 4. Effectiveness of substructure ventilation remediation technique. (Data from Henschel and Scott [20,21].)
Fig. 5. Original and predicted shifted indoor radon concentration distributions for the Reading Prong and Washington based on model parameters in Tables 1 and 2.
38 homes in Pennsylvania are used [20,21]. These data are shown in Fig. 4 as a plot of C’ vs C. Based on Fig. 4, an assumed value of R = 0.1 (900/, effectiveness) is used for remediation effectiveness. Note that there is considerable variation in the value of R from one application to another. This variation is not included in the current analytical model, but can be included in future Monto Carlo versions of the model described at the end of this paper. The assumed values of the parameters of the model are summarized in Table 2. These are actually baseline values since in the illustrations which follow Ps and a are varied parametrically to illustrate model sensitivity. Given these assumptions, we now compute the shifted pdf and cdf of indoor radon and the predicted risk reduction, using the numerical techniques described earlier. Results
The shifts in the predicted regional distributions of indoor radon resulting from home sampling and remediation in Washington and the Reading Prong are illustrated in Fig. 5. The change in the predicted average risk that results from varying the recommended action level and the fraction of the population that samples is illustrated in Fig. 6. Figure 6(a) shows the reduction in the average annual population risk as a function of the recommended action level. As indicated, the potential for risk reduction is much higher in the Reading Prong, where there are higher initial radon concentrations and lung cancer risks. With an action level of 4 pCi/l (a = 1.4), remedial action is likely to be undertaken such that about 90 lives per million are saved per year in the Reading Prong, while only 5 lives per million are predicted to be saved in Washington (starting, of course, from a much lower baseline). That is, given the same homeowner response functions, the potential for risk reduction in the Reading Prong is nearly an order of magnitude greater than in Washington. Figure 6(b) shows that for a given action level, the variation of risk reduction with Ps is linear; i.e. doubling the fraction of people sampling would save twice as many lives.
Table 2. Model parameters for example application Ps= 0.5
a =O.l R =O.l tl= 1.4 b = 0.9 /!?=-I r = 5.1x lO-5 per pCi/l per year (Source: [22])
M. J. 01 = 0.7
1.4
1.8
2.1
2.3
SMALL
and C. A. PETERS
2.5
1.6% CY=. 0.7 ,
3501.4 46
.
1.4
,
,
1.8
,
,
2.1 2.3 * 2.5 &ding I hong
.-----_----------------------~~~-
1.2% -
ps =0.2
1.0% Reading Rang
p =0.4
0.8 % -
ps =os
ps=0.6
0.6 C -
ps=0.8
0.4 % -
Ps=l
0.2 % -
(‘4
ps =os
Reading Prong 2
4
6
8
10
12
2
4
6
8
10
12
Suggested Action Level (pCi/l)
Suggested Action Level (pCi/l)
Fig. 6. Predicted average population risk as a function of suggested action level. Dashed lines represent initial condition and solid lines represent risk after remediation. (a) Comparison of potential risk reduction for Reading Prong and Washington (Ps = 0.5). (b) Variation of resulting risk with the extent of home sampling in the Reading Prong.
Fig. 7. Percentage of homes above (a) 50 pCi/l and (b) 4 pa/l. Dashed lines indicate initial condition and solid lines represent percent in excess after remediation.
While the reduction in the average population risk is a key result for public policy evaluation, it is not completely descriptive of the risk situation in a region, because it is says nothing about the distribution of the risk. For example, if the goal is to prevent the accumulation of high doses among a portion of the population, then we will be interested in the percentage of homes greater than some high value, such as 50 pCi/l (which is expected to result in 2550 deaths per million per year). On the other hand, our goal might be to prevent any member of the population from being exposed to levels above the action level. In this case we will be interested in the percentage of homes greater than 4 pCi/l (which is expected to result in 200 deaths per million per year). The model results for these two cases are shown in Fig. 7. Figure 7(a) shows for the Reading Prong that the percentage of homes greater than very high concentrations (in this case 50 pCi/l) is insensitive to policies regarding recommended action levels well below this value. In fact, the homeowner behavior model is structured such that at radon concentrations much greater than the action level, P R x b and the total probability of remediation is only dependent on the parameters b and Ps . This suggests that appropriate government actions to protect homeowners from very high radon levels should include extensive information dissemination to increase home sampling and subsidized remediation to persuade reluctant homeowners with high concentrations to remediate. The percentage of homes greater than 4 pCi/l for both regions is shown in Fig. 7(b) to be slightly more dependent on the recommended action level. Again, we see that there is greater potential for a reduction in the percentage of homes above the action level in the Reading Prong, which has higher initial levels. SUMMARY
AND
FUTURE
RESEARCH
This paper presents a model that integrates the physical and behavioral aspects of the indoor radon problem. It describes the shift in the indoor radon concentration distribution and the
Indoor radon problem model
357
risk reduction that can be achieved in a region with a program of home sampling and remediation. Discrete-choice models are used to describe the effect of government policies, such as the selection of a recommended action level and the subsidization of home sampling and remediation. By using this model for integrated radon analysis, government policies can be evaluated based on their effectiveness in reducing risk. The illustrative applications demonstrate the effect on lung cancer risk of lowering the recommended action level and varying the fraction of homeowners who sample. Model results also show that for identical homeowner response functions, the Reading Prong region has a much greater predicted reduction in the average population risk and fraction of homes at high levels than does Washington. This quantifies the extent to which government efforts for radon risk management can be more effectively targeted to regions with high initial indoor radon concentrations. The current model uses analytical methods to directly derive the shifted probability distribution function of regional indoor radon concentrations. The mathematical equations allow for efficient computation of the modified distribution and risk estimates. However, a number of simplifying assumptions are required to derive the mathematical expressions. In particular, errors in home sampling and variations in remedial action effectiveness must be ignored. Future development of the model will incorporate a Monte Carlo simulation to provide the capacity to deal with variability in these relationships and uncertainty in other model inputs. Also, better estimation of parameter values especially for the homeowner choice functions, should be possible in the future as more research in this area is completed. potential
Acknowledgemenrs-This research was supported in part by NSF (PYI-ECE-8552772) and a Hunter P. Wharton Scholarship from the International Union of Operating Engineers. Useful advice was offered by A. V. Nero and data were provided by C. Granlund and D. B. Henschel.
REFERENCES 1. B. L. Cohen, Radon: characteristics, natural occurrence, technological enhancement, and health effects. Prog. Nucl. Energy 4, l-24 (1978). 2. A. V. Nero, The indoor radon story. Technol. Rev., pp. 28-40 (January, 1986). 3. T. Domencich and D. McFadden, Urban Travel Demand: A Behavioral Analysis. North-Holland, Amsterdam (1975). 4. C. F. Manski and D. McFadden, Structural Analysis of Discrete Data with Econometric Applications. MIT Press, Cambridge, MA (1981). 5. A. V. Nero, M. B. Schwehr, W. W. Nazaroff and K. L. Revzan, Distribution of airborne radon-222 concentrations in U.S. homes. Science. 234, 992-997 (1986). 6. H. W. Alter and R. A. Oswald, Nationwide distribution of indoor radon measurements: a preliminary data base. J. Air Poilut. Control Ass. 31, 227-231
(1987).
7. M. Wing, The radon/radon progeny measurement proficiency program. Presented at the 2nd Int. Specialty Conf. on Indoor Radon, The Air Pollution Control Association, Cherry Hill, NJ (April, 1987). 8. E. A. C. Crouch, R. Wilson and L. Zeise, The risks of drinking water. Water Resourc. Res. 19, 1359-1375 (1983). 9. M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions. Dover, New York (1972). 10. R. F. Kohm, Statistical considerations: assessing indoor radon levels. EPA/AAAS, Environmental Science and Engineering Fellow, Office of Radiation Programs, U.S. EPA, Washington DC (August, 1986). 11. M. R. Brambley and M. Gorfien, Radon and lung cancer: incremental risks associated with residential weatherization. Energy 11, 589-605 (1986). 12. CMU, The indoor radon problem: focus on Pennsylvania. Carnegie Mellon Univ., Dept of Engineering and Public Policy, Pittsburgh, PA (April, 1986). 13. 0. Svenson and B. Fischoff, Levels of environmental decisions. J. Enuir. Psychof. 5, 55-67 (1985). 14. V. K. Smith, W. H. Desvousges, A. Fisher and F. R. Johnson, Radon risk perceptions and risk communication: preliminary results. RTI Project No. 3695-OI-IR, POB 12194, Research Triangle Institute, Research Triangle Park, NC (19087). 15. F. R. Johnson and R. A. Luken, Radon risk information and voluntary protection: evidence from a natural experiment. Risk Analysis
7, 97-107
(1987).
16. U.S. EPA, A citizen’s guide to radon; what it is and what to do about it. OPA-86-004, Office of Air and Radiation (August, 1986). 17. B. H. Turk, R. J. Prill, W. J. Fisk, D. G. Grimsrud, B. A. Moed and R. G. Sextro, Radon and remedial action in Spokane river valley residences: an interim report. LBL-21399, Lawrence Berkeley Laboratory, Berkeley, CA (March, 1986). 18. M. Osborne and T. Brennan, Radon mitigation in ten Clinton, New Jersey homes: a case history. Presented at the 2hd Inf. Speciality Co@ on Indoor Radon, The Air Pollution Control Association, Cherry Hill, NJ (April, 1987). 19. American ATCON, Demonstration of remedial techniques against radon in houses on Florida phosphate lands. Report by American ATCON for U.S. EPA, EPA 520/5-83-009 (February, 1983).
358
M. J. SMALL and C. A. PETERS
20. D. B. Henschel and A. G. Scott, Some results from the demonstration of indoor radon reduction measures in bloqk basement houses. Presented at the 4th Int. Conf. on Indoor Air Quality and Climate, Berlin, F.R. Germany (August, 1987). 21. D. B. Henschel and A. G. Scott, Testing of indoor radon reduction techniques in Eastern Pennsylvania: an update. Presented at the 2hd Int. Speciality Co& on Indoor Radon. The Air Pollution Control Association, Cherry Hill, NJ (April, 1987). 22. NCRP, Evaluation of occupational and environmental exposures to radon and radon daughters in the United States. NCRP Report No. 78, National Council on Radiation Protection and Measurements, Bethesda, MD (1985).
in Great
Britain.
1988
All rights reserved
PUBLIC
Copyright
0
0895-7177/88 $3.00 + 0.00 1988 Pergamon Press plc
POLICY MODEL FOR THE INDOOR RADON PROBLEM
M. J. SMALL and C. A. PETERS Civil Engineering and Engineering & Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213, U.S.A. (Received September
Communicated
1987)
by E. Y. Rodin
Abstract-A model is developed that predicts the shift in distributions of indoor radon concentrations and potential risk reduction resulting from a program of homeowner sampling and remediation in a region. Indoor radon concentrations for a region are represented by a lognormal distribution. Discrete choice functions are used to describe the likelihood of homeowner sampling and remediation. The parameters of these functions are related to government policies for public information and radon risk management. A closed-form equation is derived for the shifted probability distribution function of radon, and this distribution is integrated over the lung cancer dose-response function to estimate the modified population risk in the region. Application of the model is illustrated using radon data from the Reading Prong region in Eastern Pennsylvania and the state of Washington.
INTRODUCTION
Concern about the hazard from radon gas in homes has increased significantly in recent years. Radon is an inert, radioactive element in the decay chain of 238Uwhich occurs ubiquitously in soil and rock. Radon generated in the ground enters the home through cracks and porous building materials in the substructure. Depending on underlying soil concentrations of radon and on housing construction, design and ventilation practices, indoor concentrations can be high enough to pose a significant risk of lung cancer. It is estimated that 5000-20,000 U.S. lung cancer deaths per year may result from indoor radon exposure [l, 21. Increased public awareness and the significant magnitude of the risk has placed indoor radon as a high priority problem for government officials. However, because radon is naturally occurring and exists within private homes, and because such risks are not considered by our society to be subject to direct regulatory action, the ultimate responsibility for mitigation lies largely with the individual homeowner. The policy options being considered to protect public health are thus meant to provide incentives for public action, rather than directly regulate the risk. The U.S. Environmental Protection Agency (EPA) is working with states to develop economic incentives and public education programs to induce homeowners to take mitigative action. The task facing regulators is to develop the set of programs and policies that will be most effective in reducing the public’s risk from indoor radon. This paper presents a mathematical modelling framework that quantifies the potential population risk reduction that can be achieved by alternative government policies implemented in a region. The framework incorporates the physical components of the problem by including a characterization of the probability distribution function of indoor radon concentrations in the region, a model to describe the effectiveness of remediation techniques, and a health effects model to translate radon concentration into lung cancer risk. In addition, the model includes components to describe the behavior of homeowners in dealing with radon in their homes. The behavioral components describe the relationship between policy variables, such as information dissemination and the provision of subsidies for remedial action, and the likelihood that homeowners will choose to remediate. Integrating these components into a single famework provides a mathematical tool for coordinated analysis of the physical and socioeconomic components of the radon problem. 349
M. J.
350
SMALL
MODEL
and C. A. PETERS STRUCTURE
Figure 1 shows the processes that must occur for risk reduction to take place in a region, and outlines the computational components of the model for integrated radon analysis. The indoor radon concentration, C, is defined as the spatial and temporal average of the radon concentration in a home. A region, defined as a population of homes on the scale that government actions are to be targeted; e.g. a city, county or state, is characterized by the probability density function (pdf) of indoor radon,&(c), and the cumulative distribution function (cdf), F,(c). Homeowner actions regarding sampling and remediation result in modified indoor concentrations, C’, with a shifted pdf,fc(c’), and cdf, F&c’). A suitable dose-response function is integrated overfc(c’) to compute the reduction in average population risk, and the fraction of the population with unacceptably high radon concentrations is computed directly from F&c’). These model outputs provide valuable information for radon policy decision making. Homeowner decisions on sampling and remediation are affected by factors such as the costs of sampling and remediation, the level and type of public information provided, and the severity of the problem in each home as indicated by sample results. The model relates the probability of
1 Yes .
.
Probability of remediation,
I
f-l
Sample result Cs
Effectivenessof remediation
gUn( Shifted regional pdf & cdf of indoor radon concentration after remediation
1. Reduction in average 2. Reduction in nu homes above act
Fig. 1. Components of the model for integrated radon analysis depicting the homeowner sampling and remediation processes that lead to risk reduction in a region.
351
Indoor radon problem model
sampling, Ps, and the probability of remediation given sampling, PR, to these factors by mathematical functions commonly used to model discrete-choice decisions [3,4]. For this analysis we assume that the probability of sampling within a region is the same for all homes; i.e. there is no clustering of neighboring homes with high or low values or other factors present that would result in within-region variations. The value of Ps is thus assumed to be constant. For those that sample, the decision to remediate is based on the homeowners’ perception of the risk associated with the sample result, C,, and the cost of remediation. Because indoor radon concentrations vary widely, perceptions of risk often depend on order-of-magnitude variations in Cs. Furthermore, regional distributions of indoor radon tend to be lognormal [5,6]. As such, logarithmic transformations of the indoor concentrations: X = In(C)
(1)
Xs = ln( C,) are used to compute homeowner response, and subsequent model calculations are made in terms ofXand Xs. The probability of remediation, conditioned on sampling, is given by the functional relationship: PR
=
PR(&)-
(2)
Note that there is some error inherent in different home sampling methods [7]. We could thus write: xs = x + L.
(3)
However, this error is not incorporated in the current model development, and it is assumed that X’s= X and P, = PR(X). Remediation is described in terms of the logarithm of the resulting concentration: Y = ln(C’)
(4)
and the effectiveness of remedial action is given by the functional relationship: Y=
for those who remediate
g(X);
(5) i X; for those who do not remediate. The derivation of the overall, shifted distribution, fy(y), requires consideration of the total probability of remediation. First consider the case where this probability is equal to one; that is, all homeowners sample and take action to lower their radon concentrations. Assuming that remediation effectiveness function, g(X), is monotonically increasing, the shifted pdf can be derived directly from the initial distribution by: f
r
(y)
=
dg-‘(y) dy fxk-‘(Y)l~ I I
) denotes the inverse of g( ). However, since not all homeowners are expected to where g-‘( remediate, the r.h.s. of equation (6) must be weighted by the total probability of remediation, P,P& -‘(y)], and a term added to represent the homes that are not remediated. The result is:
fxk-‘(Y)] + i1 -
pSpR(Y)lfX(Y).
(7)
Similarly, the cdf is derived as: u-g-‘09 F,(Y) = F,(Y) +
~d-‘~(~)_Mu) du.
(8)
s u=y In words, F,(y) is set equal to the probability that initial concentrations are below y, plus the probability that initial concentrations greater than y are rernediated to values less than or equal to y. The calculations in equation (7) and (8) can be referred to as probability weighted transformations. The dose-response function, D(C), is used to translate radon exposure levels into the corresponding risk of lung cancer death. The average population risk for a region with indoor
352
radon concentration
M. J.
SMALL
and C. A. PETERS
distribution &(c’)
is computed by y=rn B = “=02D (c’)&(c’) dc’ = D(Y)_&(Y) dy. s c’=0 s y= -m
The risk reduction is simply the difference between the average population fx(x) and .MY).
(9) risks calculated using
Assumed functional forms
To implement the model computations given in equations (7)-(9), particular functional forms are required for Ps, PR(X), fX(x), g(X), and D(X). As indicated previously, Ps is assumed constant, and C is assumed to be lognormally distributed, so that the pdf of X = In(C) is given by:
where pX and cX are the mean and standard deviation of X, respectively. These are related to the geometric mean of C, gm(C), and the geometric standard deviation of C, gsd(C), by: clx = lnkm(C)l
(11)
cX = ln[gsd(C)].
(12)
The probability of remediation is assumed to be related to the sampled concentration choice model [3]: PR(X) = a +
by a logit
b-a
1 + exp(a +/W)’
(13)
where a and b are limiting minimum and maximum probabilities, and a and j? are the scale and shape parameters of the relationship, respectively. The inclusion of parameters a and b, normally set equal to 0 and 1, respectively, in the logit choice model, is to account for the fact that there may be a small fraction of homeowners who remediate regardless of how low the radon concentrations in their homes are; and some who won’t remediate no matter how high the concentrations are. It is assumed that remedial action results in a fractional reduction of the indoor concentration, so that C’=RC
(14)
and Y = g(X) = In(R) + X,
(15)
where R is a fraction between 0 and 1. The value of R depends on the particular remediation method chosen and the characteristics of the home to which it is applied. In this illustration of the model, it is assumed that a single remediation method is chosen for the entire region and that variations due to differences in homes can be ignored. A constant value of R is thus used. Substituting equations (lo), (13), and (15) into equations (7) and (8), the shifted regional pdf is determined as:
and the cdf is:
Indoor
radon
problem
353
model
where @( ) denotes the cdf of the standardized normal variate. Equation (16) is in analytical form, while a numerical integration method, such as Simpson’s rule, is required to evaluate equation (17). The average population risk given by equation (9) is then determined by assuming a linear, no-threshold dose-response function: D(C)=rC
D (A’) =
r
exp(X),
where r is referred to as the carcinogenic potency factor [8]. A hermite quadrature [9] is used to evaluate the integral obtained by the substitution of equations (16) and (18) into equation (9). The integrated radon assessment model is thus specified by the two parameters of the initial regional radon distribution (pX, gX), the probability of home sampling (Ps), the four parameters of the remediation choice function (a, b, tl, p), the remedial action effectiveness (R), and the lung cancer potency factor (r).
EXAMPLE
APPLICATIONS
Test devices have been offered by both the public and private sectors and consequently a number of databases of indoor radon concentrations have been compiled. Because home radon testing is of a voluntary nature, nonrandom sampling often results. This causes difficulty in estimating the statistics of large scale distributions such as the national distribution [5, lo], but reasonable estimates of concentration distributions have been obtained on a regional scale. For illustrative purposes in this paper, we apply the model to two regions. One is the state of Washington which indicates indoor radon levels below the national average. The second is the Reading Prong region in Eastern Pennsylvania where higher than average radon levels occur due in part to high uranium concentrations in the underlying geologic formation. Current
radon distributions
The statistics for the Washington radon distribution were obtained from Nero et al. [5], who normalized the data to estimate annual average exposures. (Note that winter samples are generally higher than summer readings due to decreased air exchange during the winter.) Track-etch detector readings were taken in Washington (see [6] for information on the track-etch method), but it is unknown whether the samples were made in basements or living areas. The Reading Prong data were obtained from the Pennsylvania Department of Environmental Resources (DER) in March 1986 and analyzed by the authors. Instantaneous exposure measurements in working levels (WL) for 2500 homes in southeastern Pennsylvania were converted to radon concentration in picoCuries per liter (pCi/l) by assuming 50% radioactive equilibrium (see [l l] for a discussion of the equilibrium factor). All data were basement measurements and were converted to representative living area values by dividing by two [12]. Most measurements were made during the heating season but no adjustment was made to normalize to annual averages. In summary, the Washington and Reading Prong data sets are not strictly comparable, but they do provide representative estimates for illustrative application of the model in regions with low and high radon concentrations. The resulting statistics for the regions, along with estimates of the national distribution from Nero et al. [5], are presented in Table 1. The log probability plot of the Reading Prong data and the fitted lognormal distribution are shown in Fig. 2, indicating a good fit to the assumed lognormal shape.
Table 1. Indoor radon concentration
Reading Prong Washington United States
distribution
statistics for regional applications
Arithmetic mean am(C) (pCi/~)
Geometric mean gm(C) (pCi/l)
Geometric standard deviation gsd(C)
7.8 0.80 1.46
2.2 0.58 0.89
4.2 2.21 2.68
M. J. SMALL and C. A. PETEERS
354 2 100
5
I
10
I
20 30 llllllI
50
70 80
90 I
95 I
98
0.8
0.6
.1-f 2
11
5
,,,I,,,
10
20 30 Cumulative
0.0
11
50
70 80
90
95
98
0.1
1
4
10
loo
loo0
c (pCi/l)
Probability (96)
Fig. 2. Observed distribution (0) and fitted lognormal distribution (-) of indoor radon concentration for the Reading Prong. (Observed distribution plotted for every ;40th house.) Cumulative probability is the percentage of homes with concentrations equal to or less than the value on the y-axis.
Homeowner
j-__..c
0.01
Fig. 3. The probability
a logit function
of home remediation modelled as of the logarithm of the sample result.
choice model
The study of the way homeowners respond to risk situations in their homes is a relatively new area of research [13], though large scale studies have been initiated which should provide useful data for characterizing the homeowner choice functions, Ps and PR(X) [14, 151. At this point we can only assume parameter values and with this example demonstrate their importance, and the importance of such data collection efforts. The four parameter logit function, presented in equation (13) and shown in Fig. 3, can be used to describe the many factors that affect homeowners’ decisions to remediate, because of its flexibility in form. For example, the recommendation of an action level, a particular radon level above which remedial action should be taken, is likely to affect the horizontal location of the choice function. To illustrate this, we assume that the point of inflection occurs at the recommended action level, thus prescribing the value for ~1.For this application, a value of c( = 1.4 was calculated based on EPA’s recommended action level of 4 pCi/l [16]. The nature of the information disseminated to the public can also affect their decision mechanisms, causing variations in PR(X) which can be captured by the P-shape parameter. Reporting that risk estimates are indisputable and strongly recommending (i.e. “commanding”) that remediation be undertaken above the action level would result in a logit curve that has a steep slope near the inflection point (fi + - co). Conversely, communicating to the public the large amount of uncertainty surrounding risk estimates and using milder recommendations (i.e. “cajoling”) to induce remedial action would be reflected in a flatter PR(X) curve (/I -+ 0). The effect of these different approaches is being evaluated in the current study of New York homeowners by Smith et al. [14]. A smaller study of an information program conducted in Maine [15] indicates that homeowners’ decisions to remediate are not strongly related to radon concentration. These results would be accounted for in this model using a very small P-value, but for this application an intermediate value of p = - 1 was chosen. Variations in the cost of remediation, or conversely the level of government subsidization of remedial action, is likely to cause vertical shifts in the choice function, affecting parameters a and 6. In this application, the values a = 0.1 and b = 0.9 were assumed. Remediation
efiectiveness
Data on the effectiveness of remediation techniques are appearing from a number of research projects [e.g. 17-191. For this illustration, data from an EPA study of substructure ventilation in
Indoor
radon
problem
model 2
100.
355 5
10
20 30
50
70 SO 90 95
” “““I 1 ____-__. Initial
2
I 5
I 10
1l'll'I 20 30 50
”
70 80
I I 90 95
98
.
98
Cumulative Robability (5%)
Fig. 4. Effectiveness of substructure ventilation remediation technique. (Data from Henschel and Scott [20,21].)
Fig. 5. Original and predicted shifted indoor radon concentration distributions for the Reading Prong and Washington based on model parameters in Tables 1 and 2.
38 homes in Pennsylvania are used [20,21]. These data are shown in Fig. 4 as a plot of C’ vs C. Based on Fig. 4, an assumed value of R = 0.1 (900/, effectiveness) is used for remediation effectiveness. Note that there is considerable variation in the value of R from one application to another. This variation is not included in the current analytical model, but can be included in future Monto Carlo versions of the model described at the end of this paper. The assumed values of the parameters of the model are summarized in Table 2. These are actually baseline values since in the illustrations which follow Ps and a are varied parametrically to illustrate model sensitivity. Given these assumptions, we now compute the shifted pdf and cdf of indoor radon and the predicted risk reduction, using the numerical techniques described earlier. Results
The shifts in the predicted regional distributions of indoor radon resulting from home sampling and remediation in Washington and the Reading Prong are illustrated in Fig. 5. The change in the predicted average risk that results from varying the recommended action level and the fraction of the population that samples is illustrated in Fig. 6. Figure 6(a) shows the reduction in the average annual population risk as a function of the recommended action level. As indicated, the potential for risk reduction is much higher in the Reading Prong, where there are higher initial radon concentrations and lung cancer risks. With an action level of 4 pCi/l (a = 1.4), remedial action is likely to be undertaken such that about 90 lives per million are saved per year in the Reading Prong, while only 5 lives per million are predicted to be saved in Washington (starting, of course, from a much lower baseline). That is, given the same homeowner response functions, the potential for risk reduction in the Reading Prong is nearly an order of magnitude greater than in Washington. Figure 6(b) shows that for a given action level, the variation of risk reduction with Ps is linear; i.e. doubling the fraction of people sampling would save twice as many lives.
Table 2. Model parameters for example application Ps= 0.5
a =O.l R =O.l tl= 1.4 b = 0.9 /!?=-I r = 5.1x lO-5 per pCi/l per year (Source: [22])
M. J. 01 = 0.7
1.4
1.8
2.1
2.3
SMALL
and C. A. PETERS
2.5
1.6% CY=. 0.7 ,
3501.4 46
.
1.4
,
,
1.8
,
,
2.1 2.3 * 2.5 &ding I hong
.-----_----------------------~~~-
1.2% -
ps =0.2
1.0% Reading Rang
p =0.4
0.8 % -
ps =os
ps=0.6
0.6 C -
ps=0.8
0.4 % -
Ps=l
0.2 % -
(‘4
ps =os
Reading Prong 2
4
6
8
10
12
2
4
6
8
10
12
Suggested Action Level (pCi/l)
Suggested Action Level (pCi/l)
Fig. 6. Predicted average population risk as a function of suggested action level. Dashed lines represent initial condition and solid lines represent risk after remediation. (a) Comparison of potential risk reduction for Reading Prong and Washington (Ps = 0.5). (b) Variation of resulting risk with the extent of home sampling in the Reading Prong.
Fig. 7. Percentage of homes above (a) 50 pCi/l and (b) 4 pa/l. Dashed lines indicate initial condition and solid lines represent percent in excess after remediation.
While the reduction in the average population risk is a key result for public policy evaluation, it is not completely descriptive of the risk situation in a region, because it is says nothing about the distribution of the risk. For example, if the goal is to prevent the accumulation of high doses among a portion of the population, then we will be interested in the percentage of homes greater than some high value, such as 50 pCi/l (which is expected to result in 2550 deaths per million per year). On the other hand, our goal might be to prevent any member of the population from being exposed to levels above the action level. In this case we will be interested in the percentage of homes greater than 4 pCi/l (which is expected to result in 200 deaths per million per year). The model results for these two cases are shown in Fig. 7. Figure 7(a) shows for the Reading Prong that the percentage of homes greater than very high concentrations (in this case 50 pCi/l) is insensitive to policies regarding recommended action levels well below this value. In fact, the homeowner behavior model is structured such that at radon concentrations much greater than the action level, P R x b and the total probability of remediation is only dependent on the parameters b and Ps . This suggests that appropriate government actions to protect homeowners from very high radon levels should include extensive information dissemination to increase home sampling and subsidized remediation to persuade reluctant homeowners with high concentrations to remediate. The percentage of homes greater than 4 pCi/l for both regions is shown in Fig. 7(b) to be slightly more dependent on the recommended action level. Again, we see that there is greater potential for a reduction in the percentage of homes above the action level in the Reading Prong, which has higher initial levels. SUMMARY
AND
FUTURE
RESEARCH
This paper presents a model that integrates the physical and behavioral aspects of the indoor radon problem. It describes the shift in the indoor radon concentration distribution and the
Indoor radon problem model
357
risk reduction that can be achieved in a region with a program of home sampling and remediation. Discrete-choice models are used to describe the effect of government policies, such as the selection of a recommended action level and the subsidization of home sampling and remediation. By using this model for integrated radon analysis, government policies can be evaluated based on their effectiveness in reducing risk. The illustrative applications demonstrate the effect on lung cancer risk of lowering the recommended action level and varying the fraction of homeowners who sample. Model results also show that for identical homeowner response functions, the Reading Prong region has a much greater predicted reduction in the average population risk and fraction of homes at high levels than does Washington. This quantifies the extent to which government efforts for radon risk management can be more effectively targeted to regions with high initial indoor radon concentrations. The current model uses analytical methods to directly derive the shifted probability distribution function of regional indoor radon concentrations. The mathematical equations allow for efficient computation of the modified distribution and risk estimates. However, a number of simplifying assumptions are required to derive the mathematical expressions. In particular, errors in home sampling and variations in remedial action effectiveness must be ignored. Future development of the model will incorporate a Monte Carlo simulation to provide the capacity to deal with variability in these relationships and uncertainty in other model inputs. Also, better estimation of parameter values especially for the homeowner choice functions, should be possible in the future as more research in this area is completed. potential
Acknowledgemenrs-This research was supported in part by NSF (PYI-ECE-8552772) and a Hunter P. Wharton Scholarship from the International Union of Operating Engineers. Useful advice was offered by A. V. Nero and data were provided by C. Granlund and D. B. Henschel.
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(1987).
7. M. Wing, The radon/radon progeny measurement proficiency program. Presented at the 2nd Int. Specialty Conf. on Indoor Radon, The Air Pollution Control Association, Cherry Hill, NJ (April, 1987). 8. E. A. C. Crouch, R. Wilson and L. Zeise, The risks of drinking water. Water Resourc. Res. 19, 1359-1375 (1983). 9. M. Abramowitz and I. A. Stegun (Eds), Handbook of Mathematical Functions. Dover, New York (1972). 10. R. F. Kohm, Statistical considerations: assessing indoor radon levels. EPA/AAAS, Environmental Science and Engineering Fellow, Office of Radiation Programs, U.S. EPA, Washington DC (August, 1986). 11. M. R. Brambley and M. Gorfien, Radon and lung cancer: incremental risks associated with residential weatherization. Energy 11, 589-605 (1986). 12. CMU, The indoor radon problem: focus on Pennsylvania. Carnegie Mellon Univ., Dept of Engineering and Public Policy, Pittsburgh, PA (April, 1986). 13. 0. Svenson and B. Fischoff, Levels of environmental decisions. J. Enuir. Psychof. 5, 55-67 (1985). 14. V. K. Smith, W. H. Desvousges, A. Fisher and F. R. Johnson, Radon risk perceptions and risk communication: preliminary results. RTI Project No. 3695-OI-IR, POB 12194, Research Triangle Institute, Research Triangle Park, NC (19087). 15. F. R. Johnson and R. A. Luken, Radon risk information and voluntary protection: evidence from a natural experiment. Risk Analysis
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(1987).
16. U.S. EPA, A citizen’s guide to radon; what it is and what to do about it. OPA-86-004, Office of Air and Radiation (August, 1986). 17. B. H. Turk, R. J. Prill, W. J. Fisk, D. G. Grimsrud, B. A. Moed and R. G. Sextro, Radon and remedial action in Spokane river valley residences: an interim report. LBL-21399, Lawrence Berkeley Laboratory, Berkeley, CA (March, 1986). 18. M. Osborne and T. Brennan, Radon mitigation in ten Clinton, New Jersey homes: a case history. Presented at the 2hd Inf. Speciality Co@ on Indoor Radon, The Air Pollution Control Association, Cherry Hill, NJ (April, 1987). 19. American ATCON, Demonstration of remedial techniques against radon in houses on Florida phosphate lands. Report by American ATCON for U.S. EPA, EPA 520/5-83-009 (February, 1983).
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M. J. SMALL and C. A. PETERS
20. D. B. Henschel and A. G. Scott, Some results from the demonstration of indoor radon reduction measures in bloqk basement houses. Presented at the 4th Int. Conf. on Indoor Air Quality and Climate, Berlin, F.R. Germany (August, 1987). 21. D. B. Henschel and A. G. Scott, Testing of indoor radon reduction techniques in Eastern Pennsylvania: an update. Presented at the 2hd Int. Speciality Co& on Indoor Radon. The Air Pollution Control Association, Cherry Hill, NJ (April, 1987). 22. NCRP, Evaluation of occupational and environmental exposures to radon and radon daughters in the United States. NCRP Report No. 78, National Council on Radiation Protection and Measurements, Bethesda, MD (1985).