Bayesian model averaging for benchmark dose estimation

Environmental and Ecological Statistics - Tập 22 - Trang 5-16 - 2014
Susan J. Simmons1, Cuixian Chen1, Xiaosong Li1, Yishi Wang1, Walter W. Piegorsch2, Qijun Fang2, Bonnie Hu1, G. Eddie Dunn3
1Department of Mathematics and Statistics, University of North Carolina Wilmington, Wilmington, USA
2Graduate Interdisciplinary Program in Statistics, University of Arizona, Tucson, USA
3Department of Computer Science, University of North Carolina Wilmington, Wilmington, USA

Tóm tắt

Benchmark dose estimation is widely used in various regulatory and industrial settings to estimate acceptable exposure levels to hazardous or toxic agents by predefining a level of excess risk (US EPA in Benchmark dose technical guidance document. Technical Report #EPA/100/R-12/001. U.S. Environmental Protection Agency, Washington, DC, 2012). Although benchmark dose estimation is a popular method for identifying exposure levels of agents, there are some limitations and cautions on use of this methodology. One such concern is choice of the underlying risk model. Recently, advances have been made using Bayesian model averaging to improve benchmark dose estimation in the face of model uncertainty. Herein we employ the strategies of Bayesian model averaging to build model averaged estimates for the benchmark dose. The methodology is demonstrated via a simulation study and with real data.

Tài liệu tham khảo

Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki B (eds) Proceedings of the second international symposium on information theory. Akademial Kiado, Budapest, pp 267–281 Bailer AJ, Noble RB, Wheeler MW (2005) Model uncertainty and risk estimation for experimental studies of quantal responses. Risk Anal 25(2):291–299 Crump KS (1984) A new method for determining allowable daily intake. Fundam Appl Toxicol 4(5):854–871 Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis, 2nd edn. Chapman and Hall/CRC, Boca Raton, FL Hamon NW (1990) Goldenseal. Can Pharm J 123(11):508–510 Kendall MG (1955) Rank correlation methods. Hafner Publishing Co, New York Litzkow M, Livny M, Mutka M (1988) Condor—a hunter of idle workstations. In: Proceedings of the 8th international conference distributed computing system, pp 104–111 Morales KH, Ibrahim JG, Chen C-J, Ryan LM (2006) Bayesian model averaging with applications to benchmark does estimation for arsenic in drinking water. J Am Stat Assoc 101(473):9–17 Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33(3):1065–1076 Piegorsch WW, Bailer AJ (2005) Analyzing environmental data. Wiley, England Piegorsch WW, An L, Wickens AA, West RW, Peña E, Wu W (2013) Information-theoretic model-averaged benchmark dose analysis in environmental risk assessment. Environmetrics 24(3):143–157 R Development Core Team (2012) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria Raftery AE, Madigan D, Hoeting J (1997) Bayesian model averaging for linear regression models. J Am Stat Assoc 92(437):179–191 Rosenblatt M (1956) Remarks on some nonparametric estimates of a density function. Ann Math Stat 27(3):832–837 Schwarz G (1978) Estimating the dimension of a model. Ann Stat 6:461–464 Shao K, Gift JS (2014) Model uncertainty and Bayesian model averaged benchmark dose estimation for continuous data. Risk Anal 34(1):101–120 Shao K, Small MJ (2011) Potential uncertainty reduction in model-averaged benchmark dose estimates informed by an addition dose study. Risk Anal 31(10):1561–1575 Shao K (2012a) A comparison of three methods for integrating historical information for Bayesian model averaged benchmark dose estimation. Environ Toxicol Pharmacol 34(2):288–296 Shao K, Small MJ (2012) Statistical evaluation of toxicological experimental design for Bayesian model averaged benchmark dose estimation with dichotomous data. Hum Ecol Risk Assess 18(5):1096–1119 Silverman BW (1998) Density estimation for statistics and data analysis. Chapman & Hall/CRC, London Tierney L (1994) Markov chains for exploring posterior distributions. Ann Stat 22:1701–1762 (with discussion) US EPA (2012) Benchmark dose technical guidance document. Technical Report #EPA/100/R-12/001. U.S. Environmental Protection Agency, Washington, DC US National Toxicology Program (2010) Toxicology and carcinogenesis studies of goldenseal root powder (Hydrastis Canadensis) in F344/N Rats and B6C3F1 Mice (Feed studies). Technical Report #562: U.S. Department of Health and Human Services, Public Health Service, Research Triangle Park, NC West W, Piegorsch WW, Peña E, An L, Wu W, Wickens A, Xiong H, Chen W (2012) The impact of model uncertainty on benchmark dose estimation. Environmetrics 23(8):706–716 Wheeler MW, Bailer AJ (2007) Properties of model-averaged BMDLs: a study of model averaging in dichotomous response risk estimation. Risk Anal 27(3):659–670 Wheeler MW, Bailer AJ (2008) Model averaging software for dichotomous dose response risk estimation. J Stat Softw 26(5). http://www.jstatsoft.org/v26/i05/paper Wheeler MW, Bailer AJ (2009) Comparing model averaging with other model selection strategies for benchmark dose estimation. Environ Ecol Stat 16(1):37–51