Information‐theoretic model‐averaged benchmark dose analysis in environmental risk assessment

An important objective in environmental risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a pre-specified Benchmark Response (BMR) in a dose-response experiment. In such settings, representations of the risk are traditionally based on a specified parametric model. It is a well-known concern, however, that existing parametric estimation techniques are sensitive to the form employed for modeling the dose response. If the chosen parametric model is in fact misspecified, this can lead to inaccurate low-dose inferences. Indeed, avoiding the impact of model selection was one early motivating issue behind development of the BMD technology. Here, we apply a frequentist model averaging approach for estimating benchmark doses, based on information-theoretic weights. We explore how the strategy can be used to build one-sided lower confidence limits on the BMD, and we study the confidence limits' small-sample properties via a simulation study. An example from environmental carcinogenicity testing illustrates the calculations. It is seen that application of this information-theoretic, model averaging methodology to benchmark analysis can improve environmental health planning and risk regulation when dealing with low-level exposures to hazardous agents.

[1]  Matthew W Wheeler,et al.  Properties of Model‐Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[2]  Joseph G. Ibrahim,et al.  Bayesian Model Averaging With Applications to Benchmark Dose Estimation for Arsenic in Drinking Water , 2006 .

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  Ralph L. Kodell,et al.  Replace the NOAEL and LOAEL with the BMDL01 and BMDL10 , 2009, Environmental and Ecological Statistics.

[5]  Elaine M. Faustman,et al.  Review of noncancer risk assessment: Applications of benchmark dose methods , 1997 .

[6]  Matthew W Wheeler,et al.  Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses , 2005, Risk analysis : an official publication of the Society for Risk Analysis.

[7]  K S Crump,et al.  A new method for determining allowable daily intakes. , 1984, Fundamental and applied toxicology : official journal of the Society of Toxicology.

[8]  R L Kodell,et al.  Incorporating model uncertainties along with data uncertainties in microbial risk assessment. , 2000, Regulatory toxicology and pharmacology : RTP.

[9]  A. John Bailer,et al.  Comparing model averaging with other model selection strategies for benchmark dose estimation , 2009, Environmental and Ecological Statistics.

[10]  Clifford M. Hurvich,et al.  Regression and time series model selection in small samples , 1989 .

[11]  K. Burnham,et al.  Model selection: An integral part of inference , 1997 .

[12]  Robert B Noble,et al.  Model‐Averaged Benchmark Concentration Estimates for Continuous Response Data Arising from Epidemiological Studies , 2009, Risk analysis : an official publication of the Society for Risk Analysis.

[13]  Ralph L Kodell,et al.  Model Uncertainty and Model Averaging in the Estimation of Infectious Doses for Microbial Pathogens , 2013, Risk analysis : an official publication of the Society for Risk Analysis.

[14]  Walter W Piegorsch,et al.  Simultaneous Confidence Bands for Abbott-Adjusted Quantal Response Models. , 2008, Statistical methodology.

[15]  G. Molenberghs,et al.  Model Averaging Using Fractional Polynomials to Estimate a Safe Level of Exposure , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[16]  Walter W Piegorsch,et al.  Nonparametric estimation of benchmark doses in environmental risk assessment , 2012, Environmetrics.

[17]  D. Madigan,et al.  Bayesian Model Averaging for Linear Regression Models , 1997 .

[18]  Haiying Wang,et al.  Frequentist model averaging estimation: a review , 2009, J. Syst. Sci. Complex..

[19]  A. John Bailer,et al.  Model Averaging Software for Dichotomous Dose Response Risk Estimation , 2008 .

[20]  Wout Slob,et al.  A Comparison of Three Methods for Calculating Confidence Intervals for the Benchmark Dose , 2004, Risk analysis : an official publication of the Society for Risk Analysis.

[21]  Kenny S. Crump,et al.  Calculation of Benchmark Doses from Continuous Data , 1995 .

[22]  C J Portier,et al.  Biostatistical issues in the design and analysis of animal carcinogenicity experiments. , 1994, Environmental health perspectives.

[23]  Mattias Öberg.  Benchmark dose approaches in chemical health risk assessment in relation to number and distress of laboratory animals , 2010 .

[24]  Ralph L. Kodell.  Managing uncertainty in health risk assessment , 2005 .

[25]  Keming Yu,et al.  Bayesian Mode Regression , 2012, 1208.0579.

[26]  Nils Lid Hjort,et al.  Model Selection and Model Averaging: Contents , 2008 .

[27]  Anthony C. Davison,et al.  A note on model uncertainty in linear regression , 2003 .

[28]  James J. Chen,et al.  Model Averaging Using the Kullback Information Criterion in Estimating Effective Doses for Microbial Infection and Illness , 2005, Risk analysis : an official publication of the Society for Risk Analysis.

[29]  Roland C Deutsch,et al.  Maximum likelihood estimation with binary-data regression models: small-sample and large-sample features. , 2010, Advances and applications in statistics.

[30]  David Fletcher,et al.  Model-averaged confidence intervals for factorial experiments , 2011, Comput. Stat. Data Anal..

[31]  Lingling An,et al.  The impact of model uncertainty on benchmark dose estimation , 2012, Environmetrics.

[32]  Jeffrey S Gift,et al.  Introduction to benchmark dose methods and U.S. EPA's benchmark dose software (BMDS) version 2.1.1. , 2011, Toxicology and applied pharmacology.

[33]  Stefan D Muri,et al.  The benchmark dose approach in food risk assessment: is it applicable and worthwhile? , 2009, Food and chemical toxicology : an international journal published for the British Industrial Biological Research Association.

[34]  Adrian E. Raftery,et al.  Bayesian model averaging: a tutorial (with comments by M. Clyde, David Draper and E. I. George, and a rejoinder by the authors , 1999 .

[35]  Salomon Sand,et al.  The current state of knowledge on the use of the benchmark dose concept in risk assessment , 2008, Journal of applied toxicology : JAT.

[36]  Alan T. K. Wan,et al.  Optimal Weight Choice for Frequentist Model Average Estimators , 2011 .

[37]  I. Jamieson,et al.  Multimodel inference in ecology and evolution: challenges and solutions , 2011, Journal of evolutionary biology.

[38]  David R. Anderson,et al.  Model selection bias and Freedman’s paradox , 2010 .

[39]  J. Cavanaugh.  A large-sample model selection criterion based on Kullback's symmetric divergence , 1999 .

[40]  Jens C. Streibig,et al.  Bioassay analysis using R , 2005 .

[41]  Eileen Kuempel,et al.  An Approach to Risk Assessment for TiO2 , 2007, Inhalation toxicology.

[42]  Christel Faes,et al.  Model Averaging in Microbial Risk Assessment Using Fractional Polynomials , 2008, Risk analysis : an official publication of the Society for Risk Analysis.