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Should you measure the radon concentration in your home?

Phillip N. Price

∗

Andrew Gelman

†

January 23, 2004

Introduction

Radon, a naturally occurring radioactive element, was discovered in the year 1900, and high lung

cancer rates among miners were recognized hundreds of years before that, but it wasn’t until the

1950s that researchers accepted that exposure to radon decay products was one of the major causes

of the very high lung cancer rate among miners. Risks to the general population weren’t recognized

until the early 1980s, when it was discovered that even homes can have high concentrations of

radon—indeed, the airborne radioactivity in some (very rare) homes is higher than is allowed in

uranium mines!

Once a risk from radon was recognized, the U.S. Environmental Protection Agency, and other

organizations including the Department of Energy, launched research efforts to help assess risks and

remediation options: what is the statistical and spatial distribution of indoor radon, what methods

can be used to reduce radon concentrations in homes, what is the risk as a function of exposure,

and so on. In this chapter, we summarize some of the data on radon distributions and some of the

risk estimates, and then discuss how the available information can be used in a decision analysis to

make recommendations on who should perform radon measuremnents or remediation. This chapter

focuses on the decision analysis itself (originally discussed in Lin et al., 1999), and not on the

statistical model, based on Bayesian hierarchical regression, that fed into the decision analysis. For

more information about hierarchical regression, see Gelman et al. (2003, section 22.4).

The home radon problem

Radon is a naturally occurring radioactive gas produced by decay of the element radium, which is

present in small quantities in rocks and soil. Since radon is a gas, it can flow through the soil and

into homes. Radon’s decay products, which are themselves radioactive, are known to cause lung

∗

Energy and Environment Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 USA.

pnprice@lbl.gov

†

Department of Statistics, Columbia University, New York, NY 10027 USA.

gelman@stat.columbia.edu

0.00

0.10

0.20

Home radon exposure (pCi/L)

Probability of lung cancer

Male smokers

Male non−smokers

0.00

0.10

0.20

Home radon exposure (pCi/L)

Probability of lung cancer

Female smokers

Female non−smokers

Figure 1: Lifetime added risk of lung cancer, as a function of average radon exposure in picoCuries
per liter (pCi/L). The median and mean radon levels in ground-contact houses in the U.S. are 0.7
and 1.5 pCi/L, respectively (see Figure 3), and over 50,000 homes have levels above 20 pCi/L.

cancer if high concentrations are inhaled for a long time. When we speak of risk from radon, we

really mean the risk from radon decay products.

What is the risk from radon? Studies have been carried out for uranium miners, many of whom

had extended exposures at a high concentration of 20 picoCuries per liter, abbreviated 20 pCi/L,

or more. Those studies, and others, suggest that life-long exposures of this magnitude increase the

risk of lung cancer to about .06 for male non-smokers (from a risk of less than .006 for those not

exposed to radon) and 0.32 for male smokers (from an unexposed risk of .07); estimates for women

are comparable but slightly lower (National Research Council, 1998).

Figure 1 shows the estimated additional lifetime risk of lung cancer death for male and female

smokers and nonsmokers, as a function of average radon exposure over 30 years, under the assumption

that observed risks at the concentrations faced by uranium miners can be extrapolated linearly to

lower concentrations that occur in homes (typically below 5 pCi/L). The miners were exposed to

much higher radon concentrations than

typically

found in homes, but more than 50,000 of the U.S.’s

70 million houses have levels above 20 pCi/L; people who live in these houses receive a radiation dose

that exceeds the occupational safety limit for uranium miners. For almost everyone else, the risk

of lung cancer is much lower than for uranium miners, but there are millions of people facing this

risk. Assuming the linear dose-response assumption is accurate, between 5,000 and 25,000 people

die annually in the U.S. due to lung cancer caused by inhaling radon decay products in their homes,

with most of these deaths being among smokers. The estimated number of annual deaths from radon

far surpasses that from other chemical or radiological exposures. However, these estimates of radon

deaths (including the uncertainties) are based on linear extrapolation, and there is no guarantee

that the risk from radon is actually linear in exposure; the actual risk could be lower (or somewhat

higher) than these estimates suggest.

The EPA’s recommendations

The Environmental Protection Agency (EPA) recommends that all homeowners in the United States

test for radon and, if the radon level exceeds a 4 picoCuries per liter (4 pCi/L) “action level,”

remediate the house to reduce the radon exposure to an acceptable level. Remediation costs about

$2000, including maintenance and energy costs for operating the system. The action level was

originally set based on the “annual living-area average” concentration in U.S. homes, which is the

mean concentration in the living areas of a home, averaged over a year.

However, the EPA’s

recommended testing methods don’t measure the average concentration of the living areas of a

home: the EPA recommends testing only on the lowest level of the home that is used as living

space. Some state health departments, and many radon testing companies, recommend testing on

the lowest level of the home that

can

be used as living space, rather than the lowest level that

used as living space, so in practice most homes are monitored in basements, whether or not the

basement is frequently occupied. Testing on the lowest level of the home that is (or can be) used

as living space almost always leads to a measurement that is higher than the living-area average

radon concentration, since concentrations are typically highest on the lowest level of the home. The

concentration in the basement is often two to three times higher than the concentration on the upper

floors.

There are two types of inexpensive radon measuring devices; one measuring the average concen-

tration over just a few days, the other averaging over several or many months. Unfortunately, a

short-term measurement gives very little information about a home’s long-term average concentra-

tion, which is believed to be the important parameter for radon risk: indoor radon concentrations

vary substantially from day to day and from season to season, primarily due to changes in weather

that affect the amount of soil gas that is drawn into the house.

The EPA recommends either a long-term test, or a short-term test plan that has two tiers: make

a short-term test, and if the concentration exceeds 4 pCi/L then make another short-term test,

taking the average of the two tests to see if remediation is recommended. In practice, relatively

few people make long-term tests, and many people fail to follow the short-term protocol, especially

when testing is performed as part of a real estate transaction and a rapid test is desired: the de

facto testing plan for many homeowners who test for radon is to make a single short-term test on

the lowest level of the home, and use that test as the basis for a decision. We will refer to this

one-measurement decision plan as the “standard” plan even though it differs somewhat from the

EPA’s recommendation. Analyzing the EPA’s actual recommended short-term testing plan would

complicate our work without changing the results very much.

The standard decision plan has two notable features: first, the measurements on which it is based

are biased (because they are taken on a low floor) and highly variable (because they are taken over

only a few days) if interpreted as estimates of the average annual living area concentration; and

second, the same testing procedure is recommended for all homes, even though some areas of the

country and some types of homes tend to have much higher radon concentrations than others do.

Performing a single short-term test in every house in the country would cost nearly 2 billion

dollars just for the measurements, and if those measurements are used to make remediation decisions

based on the 4 pCi/L action level, many billion dollars more will be spent on remediations, most of

them in homes that do not in fact have substantially elevated radon concentrations. We estimate

that use of this decision plan in every house would cost $21 billion ($25 for each measurement and

$2000 for each remediation) and save 55,000 lives over a thirty-year period. It is natural to wonder if

we can do better using area- and house-specific information to develop an alternative decision plan.

Towards a better decision plan

Collecting and analyzing area- and house-specific information about radon risk is the key to finding

optimal homeowner-specific recommendations about what action to take. This can be done through

a formal decision analysis which considers the possible homeowner decisions (test, remediate, do

nothing) as part of a statistical analysis. The decision analysis requires that we determine the

predicted outcomes for each possible decision, namely how much money would be spent and how

many people would die, including some measure of the uncertainty in these predictions. Including

the uncertainty is crucial so that decisions take into account the full range of possible outcomes.

One must also develop a quantitative measure of the desirability of each outcome. In this decision

problem that amounts to attaching a dollar value to each live saved (or lost). We return to this

important but hard question later. Based on the predicted outcomes and the relative desirability of

each outcome, the decisions are analyzed to choose the one that has the best expected outcome.

Data and estimation of radon exposure

The first step in building a decision plan is to obtain information about the distribution of radon

exposure across different homes in different regions of the country. There are several sources of

residential radon data. In terms of the number of measurements, by far the largest data sets simply

summarize all of the radon measurements performed by radon testing companies; often these are

available by state, county, or even by zip code. Unfortunately, there are some serious problems

with these data, most importantly that they overrepresent homes with high radon levels, and often

include multiple measurements from such homes. High-radon homes are more likely to be included

Annual−average radon concentration, pCi/L

Fraction of homes

0.00

0.10

0.20

>10

Figure 2: Distribution of average annual living area radon concentrations in U.S. residences; bin
heights show fraction of homes in each bin, and the last bin shows the fraction of homes with
concentrations exceeding 10 pCi/L. A superimposed curve shows a lognormal distribution with
geometric mean (GM) of 0.67 pCi/L and geometric standard deviation (GSD) of 3.1; that is, the
logarithms of the radon levels have mean log(0.67) and standard deviation log(3.1). The nationwide
distribution is very close to lognormal.

because people who suspect their houses have high radon levels—perhaps because a neighbor has

obtained a high measurement—are more likely to take measurements, and those who obtain a high

measurement are more likely to measure again and this measurement will also be included in the

database. Because of this large and unpredictable bias in “volunteer” data, we instead work with

data collected by the government from random samples of houses. This is an illustration of the

importance of using chance in the collection of data to avoid having systematic biases enter the

data.

The EPA worked with most of the state health departments to perform radon testing in repre-

sentative random samples of homes in each state. Taken together, these “EPA/State Residential

Radon Surveys” contain about 55,000 radon measurements (Wirth, 1992). These are short-term

measurements on the lowest level of the home but at least they use a standard protocol and are not

subject to the selection bias (favoring high radon homes) that affects the commercial data.

Additionally, the EPA conducted a “National Residential Radon Survey,” which measured an-

nual living-area average concentrations (using long-term detectors on every floor of each home) in

about 5700 homes across the country (Marcinowski et al., 1994). Figure 2 shows the distribution of

annual living-area average radon concentrations as determined by that survey. It is common when

working with quantities like concentrations, which are greater than or equal to zero, to work with

the logarithm of the measurement. The logarithms tend to more readily allow the use of tradi-

tional statistical tools. For example, the logarithms of the radon levels follow a normal distribution

> 4 pCi/L
3−4 pCi/L
2−3 pCi/L
1−2 pCi/L
< 1 pCi/L

Figure 3: (a) Observed geometric mean indoor radon concentration by county, from the EPA/State
Residential Radon Surveys. Measurements in these surveys are strongly biased estimates of annual-
average living-area concentrations. Some states did not participate in these surveys but did collect
data in different surveys; these data, using different measurement protocols, are not displayed but
were used in our full analysis. (b) County geometric mean indoor radon concentration estimated
from a hierarchical Bayes regression model, which corrects for systematic measurement biases, uses
geologic and other information, and reduces small-sample variation, to predict long-term living-area
concentrations.

with mean log(0.67) and standard deviation log(3.1); in standard terminology, the distribution is

“lognormal” with a “geometric mean” (GM) of 0.67 pCi/L and a “geometric standard deviation”

(GSD) of 3.1. Among other things, this implies that 6% of the homes have radon levels exceeding

the EPA’s threshold level of 4 pCi/L. To see this note that a radon level of 4 pCi/L is (log(4)-

log(0.67))/log(3.1) = 1.58 standard deviations from the mean, and the probability that a sample

from a standard normal distribution exceeds 1.58 is 6%.

The state radon surveys contain measurements in about 55,000 homes, and there are about

3000 counties in the U.S. The geometric mean measurements by county are shown in Figure 5a.

Some of the counties were heavily sampled by the surveys, while others were missed altogether or

included only a few houses. Radon concentrations vary a lot within a county, so a small number of

measurements isn’t enough to estimate accurately the distribution of radon concentrations within

any given county. Also, as mentioned above, the measurement protocol for these surveys leads to

measurements that are biased (because they are from the lowest level of the house only) and that

are subject to a lot of variation (because they are short-term measurements).

The National and EPA/State survey data can be used to form a predictive model that allows

us to draw inferences about the radon concentration in a house. For the moment we ignore the

known weaknesses (bias, variability) of the state survey data. Our approach to learning about

radon concentrations from the state survey data is to provide a statistical model linking the survey

measurements to house and county factors (Price et al., 1996, and Price, 1997). This is a traditional

survey inference approach, learning about the population from a limited number of sampled units.

We analyzed the radon data used a technique known as Bayesian hierarchical modeling (some-

times called “multilevel modeling”). The key idea underyling this method is that information about

one data sampling unit (for example, a county) also tells you something about other units (other

counties). For example, suppose we were to make a lot of radon measurements in 86 out of the

87 counties in Minnesota using the state survey protocol, and that we find that almost all of the

counties have geometric mean concentrations in the range 2–5 pCi/L. Even with no samples at all

from the missing county, we would think that it’s very likely that its geometric mean would also be

somewhere between 2 and 5 pCi/L. As this example illustrates, knowing the distribution of county

geometric means can help in estimating the geometric mean for a specific county, even if that county

is sparsely sampled or isn’t sampled at all.

This concept can be applied even in more complicated cases that involve predictor variables.

In our case, the state survey measurements are found to correlate with a number of home and

county characteristics: the county’s average surface radium concentration as measured with airborne

detectors by the National Uranium Resource Evaluation; whether the home has a basement; the

“geologic province” containing the county; and the county’s heating degree-days (a measure of

winter climate severity that is related to the convective forces that draw soil gas into homes). Even

when all of these variables are taken into account, however, there remains considerable variation

in radon concentrations, both within and between counties. Homes in some counties tend to have

higher radon levels than expected given the county and home characteristics, while homes in other

counties tend to have lower levels than expected. These tendencies are probably related to county

characteristics that we have not measured or included in the study. We use a regression modeling

approach to estimate the effects of all of the variables listed above on radon measurements, and

we also include parameters to allow for the “county effects” that quantify the extent to which

radon levels in a county are higher or lower than would be predicted from the other variables. We

estimated the regression model separately in each of 10 regions of the U.S., yielding predictions (and

uncertainties) of what every county’s measured radon distribution would have been if they had all

made very large numbers of measurements in the (biased) state surveys.

By comparing the state survey data to the national radon survey data it is possible to estimate

the degree to which the state survey data are biased. This can be thought of as a calibration step,

relating the biased state survey data to the more accurate annual living area average concentration

from the national survey data. One way to think about this step is that we take the data from

the national survey and compare each home’s measurement to the prediction that would be made

for that home using the regression model that was developed with the

state

survey data; if the

national data differ systematically from the state survey prediction, we can figure out how to adust

the prediction to remove the systematic error. (In practice the adjustment is done through a more

sophisticated statistical model that looks at both data sources simultaneously (Price and Nero,

1996)). Once the bias is removed, we have a predicted radon distribution for almost every county

in the United States; in some counties the distribution can be estimated rather precisely, but in

the ones that were sparsely sampled the uncertainties are large. The estimated geometric mean

living-area-average radon concentration in each county is displayed in Figure 5b.

We shall use these estimated distributions to make decision recommendations for homeowners

living in each of the 3000 counties in the U.S., but first we must lay out the decision options and

their costs and benefits.

Decision analysis, balancing dollars and lives

As with many public health decisions, radon measurement and remediation involves a balance be-

tween dollars and lives—or, more precisely, between resources spent on reducing radon risks and

resources spent otherwise. Mathematically, the balance of dollars and lives is expressed as a

loss

function

measuring the combined cost of measurements, remediation, and lives lost. For this problem

a natural way to express the loss is to start with the cost of measurements and remediation (which

are measured in dollars) and add to that a constant times the expected number of lives lost in the

next thirty years (a reasonable guess at the time that a remediation system will be effective). The

constant assigns a dollar value to saving a life. An approach for choosing a value for that parameter

is described below.

Consider a home with an average living-area radon concentration of 4 pCi/L, which is the EPA’s

recommended “action level.” Suppose the home has the average U.S. household mix of .30 male

and .27 female smokers and 1.07 male and 1.16 female nonsmokers. (It may seem odd to consider a

household containing fractional people but this allows us to discuss an average case that addresses

all of the types of people of interest.) For such a household, a 4 pCi/L concentration represents an

expected .02 radon-induced lung cancer deaths over a thirty-year period. Let

represent the dollar

value of a life. If this household does nothing about radon, then the expected loss is

. Assume

remediation costs about $2000 and reduces the average radon level to 2 pCi/L for thirty years (thus

cutting the radon risk in half). For this household, the expected loss if remediation is performed is

$2000 +

. The fact that 4 pCi/L is the EPA’s recommended action level means that this is the

radon level for which the EPA thinks the above two expected losses are about the same. If true this

would tell us that the value of saving a life is

= $200,000/life. Though $200

000 can buy a lot, it is

actually low compared to the value of life assumed in most public health decisions in rich countries;

if the linear dose-response is true, then remediating your 4 pCi/L home for $2000 is something we

should consider a good investment! Setting the threshold at other levels yields different implicit

values of a life. For example, a threshold of 20 pCi/L, as used by Canada, corresponds to only

$22,000 per life saved under our assumptions. The fact that such a low value is implied for a human

life suggests that if the dose-response relationship is linear then the Canadian threshold is way too

high and puts too many people at risk.

Using the same action level in every house will actually lead to a wide variation in the dollars

spent per life saved: for a household with several inhabitants who smoke, reducing radon would save

more lives than would the same reduction in a home with one, non-smoking, inhabitant. Conversely,

if the trade-off between lives and dollars is the same for every

person

, as seems reasonable, then it

is the action level that should vary among households. We assume that each household assigns the

same dollar value ($200

000 as implied by the EPA recommendation) to a life, compute the number

of lives that would be saved by remediation based on the predicted or measured radon level and the

composition of the household, and combine these estimates to calculate the expected loss with and

without remediation. This allows the homeowner to select the strategy that minimizes the expected

loss.

Advice for homeowners

We perform two separate decision analyses, one of them geared towards individuals (Should you

measure the radon in your home?) and one geared towards public policy-makers such as the Envi-

ronmental Protection Agency (Should we recommend that everyone in a particular county perform

a measurement?).

The decision tree is shown in Figure 5. At the first stage a homeowner must choose between doing

nothing, remediating immediately, or making a long-term measurement and then deciding whether

to remediate or not. (A short-term measurement is also possible but turns out not to be the optimal

decision for almost everyone.) The second stage of the decision tree covers the case where we measure

first and then decide. Remediating has the highest cost in dollars but the lowest expected loss of

life; doing nothing costs zero dollars but has the highest expected loss of life, and measurement

potentially followed by remediation is somewhere in between in terms of dollars spent and lives

saved. Our analysis chooses the decision option with the lowest expect loss (combining dollars spent

and lives saved as described earlier). Remember that each household will make decisions based on

the number of males/females and smokers/nonsmokers in the house, whereas we discussed only the

remediate: cost = $2000,

lives lost = min(r,2 pCi/L)*s

make a long-term

measurement

remediate: cost = $2050,

lives lost = min(r,2)*s

do nothing:
cost = $50,

lives lost = r*s

do nothing:

cost = $0,

lives lost = r*s

Figure 4: Decision tree for radon measurement and remediation. The first decision (whether to
remediate, do nothing, or take a (long-term) measurement) depends on estimates from the county-
level model displayed in Figure 5b. If a measurement is taken, the second decision depends on the
value of the measurement. The expected loss of life depends on the radon concentration

, the

post-remediation radon concentration (which we assume to be 2 pCi/L or

, whichever is lower),

and on the risk per unit concentration for the household, which we call

. We assume that making

a long-term measurement on each living area of the home costs $50.

average case earlier.

The decision tree must be evaluated from right to left, starting with the final decision. That is

we first figure out what each homeowner should do if they do take a measurement. This is the only

way to compare the measurement option to the other possible first stage decisions. In detail then

we proceed as follows:

•

We must decide whether the homeowner should remediate the house, given a measurement of

the average living-area airborn radon concentration. We assume the homeowner would reme-

diate if the home’s indoor radon concentration exceeds a household-specific action level, where

the action level is set by equating the expected loss (given the measured radon concentration

and the makeup of the household) under remediation and under no action using the value of

$200

000

life that is implicit in the EPA’s current recommendation. There is a slight differ-

ence between remediating if the home’s

long-term measurement

exceeds the action level and

remediating if the home’s

long-term average concentration

exceeds the action level, because

even long-term measurements do not exactly match the personal exposure of the people in the

home, but this is not crucial for the discussion here.

•

Given the rule for the inner decision, the homeowner must decide whether to remediate im-

county, state

house

hhold

GSD

Pr(remed)

Expected

(pCi/L)

cost ($)

lives saved

Lebanon, Pa.

avg

3.7

2.2

0.47

990

0.013

avg

6.4

2.2

0.74

1530

0.030

Montgomery, Md.

BNL

FS, MS

0.8

2.1

0.02

001

FS, MS

1.4

2.1

0.08

210

0.003

avg

1.4

2.1

0.08

210

0.001

Sacramento, Cal.

avg

0.4

2.1

0.00

0.000

BNL

avg

0.6

2.1

0.01

0.000

avg

0.8

2.1

0.02

0.000

Table 1: Estimated costs and benefits of making a long-term measurement and then deciding whether
or not to perform remediation, for houses in a few different counties. House type can be B =
Basement is a living area, BNL = Basement is not a living area, or NB = No basement. The variable

hhold

represents household makeup; in the table we consider the average household (.27 female

smokers, .30 male smokers, 1.16 female nonsmokers, and 1.07 male nonsmokers) and a household
with 1 female smoker (FS) and 1 male smoker (MS). The column labeled Pr(remed) shows the
probability that remediation will be recommended if the “action level” is set at 4 pCi/L, independent
of household composition. Expected lives saved are over a thirty-year period.

mediately, do nothing, or make a measurement, in the initial (outer) decision. The value

of the measurement depends on the probability that it will affect the decision of whether to

remediate, which is why we first had to evaluate the measurement/remediation decision.

The inputs to the decision problem for any household include the predicted radon concentration

from our statistical model which is based on the county and the house type; the number of male

and female nonsmokers; the costs of monitoring and remediation; and the value of

, the “dollar

value of a life” (which mathematically determines, or is determined by, the radon concentration at

which the owners would remediate). The inputs allows us to compute the expected cost of each

action, including “do nothing” (which costs nothing and saves no lives). Table 1 shows the expected

costs and benefits for one possible action: carry out a strategy of making a long-term living-area

measurement and then deciding whether or not to perform remediation. The table shows the costs

and benefits for different types of homes and households in several different counties.

For example, the first line of the table shows that for a home in Lebanon County, Pennsylvania—

one of the highest-radon counties in the country—following this approach in a non-basement house

will lead to a 47% chance of performing remediation. If remediation costs $2000 (including energy

and maintenance costs for the system), then the expected total cost of following this plan is about

$990, including the cost of measurements, and for a home with the national-average mix of female

and male smokers and nonsmokers this plan is expected to save about .013 lives. Both the cost

and the life savings presented in the table are for the entire decision plan: there’s some chance that

remediation will not be performed (because the radon measurement will not be high) and thus no

expected lives will be saved, and some chance that remediation will be performed and there will be

some expected life savings, and the values of expected dollar cost and of expected lives saved include

both of these possibilities.

For a home in Lebanon County that has a basement that is used as living space, the expected

cost is higher than for a non-basement house because there’s even higher likelihood of remediating

due to the higher expected radon concentration, but the number of lives saved is also much higher

because of the larger radon reduction that would be provided by remediation. For such a home,

using this decision plan has an expected dollar cost of $1530 but is expected to save almost .03 lives.

That’s quite a bargain: there aren’t many other opportunities to have a 3% chance of saving a life

for under $1600.

For a home in Sacramento, California—a low-radon county—the expected lives saved would be

of the order of .0003 if this measurement plan if followed in an average house (rounded to .000 in the

table). There’s a 99% chance that the long-term living-area measurement will fall below the 4 pCi/L

action level, and even if it does exceed the action level it is likely to do so by only a small amount (in

contrast to the situation in Lebanon County, where many houses will be far above the action level).

In Sacramento County, if the “value of a life” is set to $200,000 as implied by the 4 pCi/L action

level under a linear dose-response relationship, making measurements in a non-basement house isn’t

worth the cost.

Montgomery County, Maryland, has a radon distribution that is fairly typical for the northern

half of the continental U.S., with radon concentrations generally higher than in Sacramento but

lower than in Lebanon County. Table 1 also shows the difference in risk for different households:

even though an “average” household contains about 3 people, remediation would actually save more

lives on average in a household consisting of two smokers because of their higher risk for a given

exposure.

The analysis described above is the analysis that a homeowner might carry out, given only

some basic information about a home’s location and the makeup of the household. Additional

information can be used as well, as long as the relationship to radon concentrations can be estimated.

For example, suppose you have knowledge of a neighbor’s measurement. Such information can

be included to improve predictive distribution for the radon concentration in your house. Using

information concerning the spatial correlation of radon—that is, the degree to which nearby homes

have similar radon concentrations—we modified the decision analysis to incorporate information on

measurements in nearby houses if they are available. You can try out the process at the web site

http://www.stat.columbia.edu/radon/

(Gelman and Price, 1999).

A public health official has a different decision problem to work on. Such a person would need

0
0-20%
20%-40%
40%-60%
60%-80%
80%-100%
100%

Figure 5: Maps showing (a) fraction of houses in each county for which measurement is recommended,
given the perfect-information action level of

action

= 4 pCi/L; (b) expected fraction of houses in

each county for which remediation will be recommended, once the measurement

has been taken.

In some counties no measurements would be recommended; these counties do have some high-radon
home, but for any individual home the odds of an elevated concentration are so low that it’s not
worth the paying for a measurement. Apparent discontinuities across the boundaries of Utah and
South Carolina arise from irregularities in the radon measurements from the radon surveys conducted
by those states, an issue we ignore here.

to see the effect of different public policies/recommendations on all of the homeowners they serve.

Individual decisions can be combined to determine nationwide costs and benefits for various public

policies that could be implemented at the county level. For example, the maps in Figure 7 display,

for each county, the fraction of houses that would measure, and the estimated fraction of houses that

would remediate, if the recommended decision strategy were followed everywhere with an action level

of 4 pCi/L (and if we treat all households as if they have the country-average number of male and

female smokers and non-smokers ). About 26% of the 70 million ground-contact houses in the U.S.

would monitor. The total monetary cost is estimated at $7.3 billion: $1 billion for measurement and

$6.3 billion for remediation, and would be expected to save the lives of 49,000 smokers and 35,000

nonsmokers over a 30-year period. This compares quite favorably with the current strategy of having

everyone make a remediation decision based on a short-term measurement: that plan would cost

almost three times as much and save fewer lives.

Discussion

The standard dose-response model for radon—which we have used—is that risk is linear with dose

even at low concentrations, but there’s no strong evidence that this is true. The Canadian gov-

ernment assumes that the risk per dose is less at low doses and, consequently, they recommend

remediation at 20 pCi/L rather than 4 pCi/L. Several studies have tried to estimate radon risk from

concentrations below 10 pCi/L, but the studies aren’t conclusive about even the presence of risk

at, say, 4 pCi/L, much less the exact magnitude. Our analysis could of course be re-done using

different risk-dose assumptions. and in the paper on which this chapter is based (Lin et al., 1999),

we considered how the costs and benefits would change if there is a threshold below which there is

no health effect. Of course, we could also keep the same dose-response assumptions but try different

“action levels” (or different quantities for the “value of a life saved.”)

Many people are uncomfortable with setting a dollar value for saving a life, and may even think

it’s immoral to do so, but actually, there’s no avoiding it—if a expenditure of $

is considered

worthwhile because because it will save

lives, then that implies a value per life. It is impossible

to spend an infinite amount of money to reduce risks, so $

D/N

will always be finite. Nobody should

be ashamed at choosing a dollar value, although there are plenty of other opportunities for shameful

choices in risk-related decisions (a common one is failing to distinguish between

who

bears the costs

and

who

reaps the benefits, but that’s not an issue here, because the risks of radon exposure and

the costs of remediation are borne by the same people). In our analysis we have set the “dollar

value of saving a life” at a very low level, but this is the level that is implied by current radon

policy and standard dose-response assumptions. Another value could be used instead, which would

lead to different recommendations for which homes should be monitored for radon. The key is

that whatever “value of a life saved” you select, you want to choose the optimal monitoring and

remediation strategy for that value; otherwise, you’re wasting lives by saving fewer people than you

could for the same money.

Setting a radon policy involves many considerations other than those discussed here, including

issues of practicality and politics that are very difficult to formalize (so we didn’t try).

What

we have illustrated is how statistical methods can be used to help inform a difficult public health

decision in which exposures are both spatially variable and have variable uncertainty. We have

used a statistical model to estimate the distribution of home radon levels within U.S. counties using

data from national and state radon surveys. The estimated radon distributions can be used for

individual-level decisions and can be aggregated to test the costs and radon reductions if various

radon policies are implemented. The individual decisions can be modified to take into account

additional information such as available measurements on neighboring houses. Our calculations

suggest that simple modifications to the EPA’s monitoring recommendations could save more lives

for less money than the current policy, assuming, of course, that people would actually follow the

recommendations.

References

Carlin, B. P., and Louis, T. A. (2000).

Bayes and Empirical Bayes Methods for Data Analysis

second edition. London: CRC Press.

Clemen, R. T. (1996).

Making Hard Decisions

, second edition. Belmont, Calif.: Duxbury Press.

Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2003).

Bayesian Data Analysis

, second

edition. London: CRC Press.

Gelman, A., and Price, P. N. (1999). Radon risk page.

http://www.stat.columbia.edu/radon/

Lin, C., Gelman, A., Price, P. N., and Krantz, D. H. (1999). Analysis of local decisions using

hierarchical modeling, applied to home radon measurement and remediation (with discussion).

Statistical Science

, 305–337.

Marcinowski, F., Lucas, R. M., and Yeager, W. M. (1994). National and regional distributions of

airborne radon concentrations in U.S. homes.

Health Physics

, 699–706.

National Research Council, Committee on the Biological Effects of Ionizing Radiation (BEIR VI)

(1998).

Health Risks of Radon and Other Internally Deposited Alpha-Emitters

. Washington,

D.C.: National Academy Press.

Price, P. N., Gelman, A., and Nero, A. V. (1996).

Bayesian prediction of mean indoor radon

concentrations for Minnesota counties.

Health Physics

, 922–936.

Price, P. N., and Nero, A. V. (1996). Joint analysis of long- and short-term radon monitoring data

from the Northern U.S.

Environment International

, S699–S714.

Price, P. N. (1997).

Predictions and maps of county mean indoor radon concentrations in the

mid-Atlantic states.

Health Physics

, 893–906.

Wirth, S. (1992). National Radon Database documentation: The EPA/State Residential Radon

Surveys. Washington, D.C.: U.S. Environmental Protection Agency.