• 1
    Crump KS. A new method for determining allowable daily intakes. Fundamental and Applied Toxicology, 1984; 4(5):854871.
  • 2
    U.S. EPA. Benchmark dose technical guidance document. EPA/100/R-12/001. Washington, DC: U.S. Environmental Protection Agency, Risk Assessment Forum, 2012.
  • 3
    Akaike H. A new look at the statistical model identification. IEEE Transactions on Automatic Control, 1974; 19:716723.
  • 4
    Kang SH, Kodell RL, Chen JJ. Incorporating model uncertainties along with data uncertainties in microbial risk assessment. Regulatory Toxicology and Pharmacology, 2000; 31(1):6872.
  • 5
    Moon H, Kim HJ, Chen JJ, Kodell RL. Model averaging using the Kullback information criterion in estimating effective doses for microbial infection and illness. Risk Analysis, 2005; 25(5):11471159.
  • 6
    Morales KH, Ibrahim JG, Chen CJ, Ryan LM. Bayesian model averaging with applications to benchmark dose estimation for arsenic in drinking water. Journal of the American Statistical Association, 2006; 101(473):917.
  • 7
    Wheeler MW, Bailer AJ. Properties of model-averaged BMDLs: A study of model averaging in dichotomous response risk estimation. Risk Analysis, 2007; 27(3):659670.
  • 8
    Shao K, Small MJ. Potential uncertainty reduction in model-averaged benchmark dose estimates informed by an additional dose study. Risk Analysis, 2011; 31(10):15611575.
  • 9
    Shao K. A comparison of three methods for integrating historical information for Bayesian model averaged benchmark dose estimation. Environmental Toxicology and Pharmacology, 2012; 34(2):288296.
  • 10
    Gaylor DW, Slikker W, Jr. Risk assessment for neurotoxic effects. Neurotoxicology, 1990; 11(2):211218.
  • 11
    Crump KS. Calculation of benchmark doses from continuous data. Risk Analysis, 1995; 15(1):7989.
  • 12
    West RW, Kodell RL. A comparison of methods of benchmark-dose estimation for continuous response data. Risk Analysis, 1999; 19(3):453459.
  • 13
    Crump KS. Critical issues in benchmark calculations from continuous data. Critical Reviews in Toxicology, 2002; 32(3):133153.
  • 14
    Crump KS, Howe RB. A review of methods for calculating statistical confidence limits in low dose extrapolation. Pp. 187203 in Clayson DB, Krewski D, Munro I (eds). Toxicological Risk Assessment, Vol. I. Boca Raton, FL: CRC Press, 1985.
  • 15
    Kodell RL, West RW. Upper confidence limits on excess risk for quantitative responses. Risk Analysis, 1993; 13(2):177182.
  • 16
    West RW, Kodell RL. Statistical methods of risk assessment for continuous variables. Communications in Statistics: Theory and Methods, 1993; 22(12):33633376.
  • 17
    Budtz-Jørgensen E, Keiding N, Grandjean P. Benchmark dose calculation from epidemiological data. Biometrics, 2001; 57:698706.
  • 18
    Moerbeek M, Piersma AH, Slob W. A comparison of three methods for calculating confidence intervals for the benchmark dose. Risk Analysis, 2004; 24(1):3140.
  • 19
    Madigan D, Raftery AE. Model selection and accounting for model uncertainty in graphical models using Occams window. Journal of the American Statistical Association, 1994; 89(428):15351546.
  • 20
    Kass RE, Raftery AE. Bayes factors. Journal of the American Statistical Association, 1995; 90(430):773795.
  • 21
    Raftery AE. Approximate Bayes factors accounting for model uncertainty in generalised linear models. Biometrika, 1996; l83(2):251266.
  • 22
    Hoeting JA, Madigan D, Raftery AE, Volinsky CT. Bayesian model averaging: A tutorial. Statistical Science, 1999; 14(4):382417.
  • 23
    Montgomery JM, Nyhan B. Bayesian model averaging: Theoretical developments and practical applications. Political Analysis, 2010; 18(2):245270.
  • 24
    Kang SH, Kodell RL, Chen JJ. Incorporating model uncertainties along with data uncertainties in microbial risk assessment. Regulatory Toxicology and Pharmacology, 2000; 31(1):6872.
  • 25
    Bailer AJ, Noble RB, Wheeler MW. Model uncertainty and risk estimation for experimental studies of quantal responses. Risk Analysis, 2005; 25(2):291299.
  • 26
    Shao K, Small MJ. Statistical evaluation of toxicological experimental design for bayesian model averaged benchmark dose estimation with dichotomous data. Human and Ecological Risk Assessment, 2012; 18(5):10961119.
  • 27
    U.S. EPA. Benchmark Dose Software (BMDS). Research Triangle Park, NC: National Center for Environmental Assessment, 2011.
  • 28
    Slob W, Pieters MN. A probabilistic approach for deriving acceptable human intake limits and human health risks from toxicological studies: General framework. Risk Analysis, 1998; 18(6):787798.
  • 29
    Sand SJ, von Rosen D, Filipsson AF. Benchmark calculations in risk assessment using continuous dose-response information: The influence of variance and the determination of a cut-off value. Risk Analysis, 2003; 23(5):10591068.
  • 30
    Slob W. dose-response modeling of continuous endpoints. Toxicological Science, 2002; 66(2):298312.
  • 31
    Raftery AE. Bayesian model selection in social research. Sociological Methodology, 1995; 25:111163.
  • 32
    Wasserman L. Bayesian model selection and model averaging. Journal of Mathematical Psychology, 2000; 44(1):92107.
  • 33
    Kass RE, Wasserman L. A reference Bayesian test for nested hypotheses and its relationship to the Schwartz criterion. Journal of the American Statistical Association, 1995; 90:928934.
  • 34
    Schwarz G. Estimating the dimension of a model. Annals of Statistics, 1978; 6(2):461464.
  • 35
    Buckland ST, Burnham KP, Augustin NH. Model selection: An integral part of inference. Biometrics, 1997; 53(2):603618.
  • 36
    Burnham KP, Anderson DR. Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. New York: Springer, 2002.
  • 37
    Kullback S. Information Theory and Statistics. New York: Dover Publications, 1968.
  • 38
    Efron B. The Jackknife, the Bootstrap and Other Resampling Plans. Society for Industrial and Applied Mathematics. England: J.W. Arrowsmith Ltd, 1982.
  • 39
    Newton MA, Raftery AE. Approximate Bayesian inference with the weighted likelihood bootstrap. Journal of the Royal Statistical Society: Series B, 1994; 56(1):348.
  • 40
    Carlin BP, Chib S. Bayesian model choice via Markov-chain Monte-Carlo methods. Journal of the Royal Statistical Society: Series B, 1995; 57(3):473484.
  • 41
    Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian Data Analysis, 2nd ed. Boca Raton, FL: Chapman and Hall/CRC Press, 2003.
  • 42
    McCauley PT, Robinson M, Daniel FB, Olson GR. The effects of subacute and subchronic oral exposure to CIS-1,2-dichloroethylene in sprague-dawley rats. Drug and Chemical Toxicology, 1995; 18(2–3):171184.
  • 43
    NTP (National Toxicology Program). NTP Technical Report on the Toxicity Studies of Butanal Oxime Administered in Drinking Water and by Gavage to F344/N Rats and B6C3F1 Mice. NTP TOX 69. NC: Research Triangle Park, 2004.
  • 44
    Gelman A, Rubin DB. Inference from interative simulation using multiple sequences (with discussion). Statistical Science, 1992; 7:457511.
  • 45
    Breiman L. Bagging predictors. Machine Learning, 1996; 24(2):123140.
  • 46
    Davis JA, Gift JS, Zhao QJ. Introduction to benchmark dose methods and U.S. EPA's benchmark dose software (BMDS) version 2.1.1. Toxicology and Applied Pharmacology, 2011; 254(2):181191.