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## Risk Assessment of Radon in Drinking Water (1999) Commission on Life Sciences (CLS)

### Citation Manager

. "F EPA Approach to Analyzing Uncertainty and Variability." Risk Assessment of Radon in Drinking Water. Washington, DC: The National Academies Press, 1999.

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### FEPA Approach to Analyzing Uncertainty and Variability

In the EPA (1995) risk assessment, the risk posed by exposure to radon by each pathway (that is, ingestion, inhalation of radon, and inhalation of progeny) is calculated by multiplying a series of terms that describe the link between radon concentration in water and the risk to the population using that water. The terms in this link include the radon concentration in water, human exposure levels per unit concentration, radiation dose per unit exposure, and cancer risk per unit radiation dose. On the basis of the best available data, EPA developed for each of these terms probability distributions that account for the value range of a parameter and the likelihood of exceeding any value within that range. Both uncertainty and variability are accounted for in these distributions. Monte Carlo simulations were used to propagate variance in the product of the terms.

#### Uncertainty and Variability in the Risk Posed by Ingested Radon Gas

In the EPA (1995) analysis, a cancer death risk was calculated for ingestion of radon gas in drinking water with a Monte Carlo analysis and the following formula:

where

R = risk of fatal cancer (per person per year) associated with ingestion of radon gas in water.

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 Front Matter (R1-R14) Public Summary (1-7) Executive Summary (8-22) 1 Introduction (23-31) 2 Baseline Information on Indoor Radon and Radon in Water in the United States (32-49) 3 Transfer of Radon from Water to Indoor Air (50-58) 4 Dosimetry of Ingested Radon and its Associated Risk (59-81) 5 Dosimetry of Inhaled Radon and its Associated Risks (82-104) 6 Molecular and Cellular Mechanisms of Radon Induced Carcinogenesis (105-123) 7 Defining Key Variabilities and Uncertainties (124-140) 8 Mitigation (141-179) 9 Multimedia Approach to Risk Reduction (180-197) 10 Research Recommendations (198-199) References (200-222) Glossary (223-230) A Behavior of Radon and Its Decay Products in the Body (231-240) B A Model for Diffusion of Radon Through the Stomach Wall (241-248) C Water-Mitigation Techniques (249-253) D Risks Associated with Disinfection By-products Formed by Water Chlorination Related to Trihalomethanes (THMs) (254-256) E Gamma Radiation Dose from Granular-Activated Carbon (GAC) Water Treatment Units (257-259) F EPA Approach to Analyzing Uncertainty and Variability (260-268) Index (269-279)

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--> Table F.1 Probability Density Functions Used in the Calculation of Risk of Cancer Posed by Ingestion of Radon Gas in Water (following notation of EPA 1995)   Variability Uncertainty Parameter Distribution Type Distribution Values Distribution Type Distribution Values C (concentration of radon in water, pCi/L[water]) Lognormal distribution, LN(µ) C = LN(µ,σ) µ = TS(m,s,n) (σ)2=IChi(s,n) Student t, distribution, TS(m,s,n) Inverse chi-squared distribution, IChi(s,n) n= 10 m = ln(200) s = ln(1.85) V (volume of water ingested, L/d) Lognormal distribution, LN(µ,σ) V = LN(µ,σ) µ=TS(m,s,n) (σ)2=IChi(s,n) Student t distribution, TS(m,s,n) Inverse chi-squared distribution, IChi(s,n) n=100 m = ln(0.526) s = ln(1.922) F (fraction remaining) Beta distribution, B(m,md,min,max) F=B(m,md,min,max) min=0.5 max=1 m=U(a,b) md=U(m,max) or U(min,m) Uniform distributions U(a,b) U(m,max) a=0.7 b=0.9 min = 0.5 max=1 RF (risk factor, cancer-death risk per person per pCi ingested) This factor has uncertainty only   RF=LN(µ,σ) µ= ln(1.24 × 10-11 σ = ln(2.42) Calculated individual risk Uncertainty==> Variability 5th percentile mean 95th percentile 5th percentile 1.7 × 10-8 1.3 × 10-7 4.0 × 10-7 median 8.3 × 10-8 6.2 × 10-7 1.9 × 10-6 95th percentile 3.4 × 10-7 2.6 × 10-6 7.9 × 10-6 m=mean value derived from a sample s=standard deviation of a sample n=sample size md=mode of a sample µ=mean value of ln(x) in a lognormal distribution µ=standard deviation of ln(x) in a lognormal distribution

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--> Table F.2 Probability Density Functions Used by EPA (1995) in Calculation of Unit Dose of Radon Gas Inhaled after Transfer from Water (following notation of EPA 1995)   Variability Uncertainty Parameter Distribution Type Distribution Values Distribution Type Distribution Values TF (transfer factor, pCi/L[air] per pCi/L[water]) Truncated lognormal TLN(µ, σ,min,max) TF = TLN(µ, σ, min,max) µ = TS(m,s,n) (σ=2=IChi(s,n) min=6. × 10-6 max=8. × 10-4 Student t distribution, TS(m,s,n) Inverse chi-squared distribution, IChi(s,n) n= 25 m = ln(6.57 × 10-5) s = ln(2.88) BR (breathing rate, L/day) Truncated normal TN(m,s,min, max) BR = TN(µσ min.max) µ = TS(m,s,n) σ2=IChi(s,n) min=3700 max=66,000 (Student t distribution, TS(m,s,n) Inverse chi-squared distribution, IChi(s,n) n=10 m = 13,000 s = 2880 OF (occupancy factor) Beta distribution B(m,md,min,max) OF=B(m,md,min,max) Min=0.17 Max=0.95 m=U(a,b) md=U(min,m) U(m,max) Uniform distributions U(a,b) U(min,m) U(m,max) a=0.65 b= 0.80 min = 0.17 max = 0.95 UD pCi inhaled per(unit dose, year per pCi/L) Uncertainty==> Variability 5th percentile 17 mean 95th percentile 5th percentile 32 250 800 median 57 380 1300 95th percentile 540 2400 m=mean value derived from a sample s=standard deviation of a sample n=sample size md=mode of a sample µ=mean value of In(x) in a lognormal distribution σ=standard deviation of ln(x) in a lognormal distribution µ=mean value of x in a normal distribution µ=standard deviation of x in a normal distribution

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