×

zbMATH — the first resource for mathematics

Bayesian model-averaged benchmark dose analysis via reparameterized quantal-response models. (English) Zbl 1395.62337
Summary: An important objective in biomedical and environmental risk assessment is estimation of minimum exposure levels that induce a pre-specified adverse response in a target population. The exposure points in such settings are typically referred to as benchmark doses (BMDs). Parametric Bayesian estimation for finding BMDs has grown in popularity, and a large variety of candidate dose-response models is available for applying these methods. Each model can possess potentially different parametric interpretation(s), however. We present reparameterized dose-response models that allow for explicit use of prior information on the target parameter of interest, the BMD. We also enhance our Bayesian estimation technique for BMD analysis by applying Bayesian model averaging to produce point estimates and (lower) credible bounds, overcoming associated questions of model adequacy when multimodel uncertainty is present. An example from carcinogenicity testing illustrates the calculations.
MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
BMDS; R; tsbridge
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Akaike, Proceedings of the Second International Symposium on Information Theory pp 267– (1973)
[2] Andrieu, A tutorial on adaptive MCMC, Statistics and Computing 18 pp 343– (2008) · doi:10.1007/s11222-008-9110-y
[3] Armitage, The age distribution of cancer and a multi-stage theory of carcinogenesis, British Journal of Cancer 8 pp 1– (1954) · doi:10.1038/bjc.1954.1
[4] Bailer, Model uncertainty and risk estimation for experimental studies of quantal responses, Risk Analysis 25 pp 291– (2005) · doi:10.1111/j.1539-6924.2005.00590.x
[5] Bedrick, A new perspective on priors for generalized linear models, Journal of the American Statistical Association 91 pp 1450– (1996) · Zbl 0882.62057 · doi:10.1080/01621459.1996.10476713
[6] Casella, Statistical Inference (2002)
[7] Crump, A new method for determining allowable daily intake, Fundamental and Applied Toxicology 4 pp 854– (1984) · doi:10.1016/0272-0590(84)90107-6
[8] Crump, Calculation of benchmark doses from continuous data, Risk Analysis 15 pp 79– (1995) · doi:10.1111/j.1539-6924.1995.tb00095.x
[9] Davis, Introduction to benchmark dose methods and U.S. EPA’s Benchmark Dose Software (BMDS) version 2.1.1, Toxicology and Applied Pharmacology 254 pp 181– (2012) · doi:10.1016/j.taap.2010.10.016
[10] Fang, Hierarchical Bayesian Benchmark Risk Analysis (2014)
[11] Faustman, Review of noncancer risk assessment: Applications of benchmark dose methods, Human and Ecological Risk Assessment 3 pp 893– (1997) · doi:10.1080/10807039709383733
[12] Gelman, Prior distributions for variance parameters in hierarchical models, Bayesian Analysis 1 pp 515– (2006) · Zbl 1331.62139 · doi:10.1214/06-BA117A
[13] Geweke, Bayesian Statistics 4 pp 169– (1992) · Zbl 1093.62107
[14] Guha, Nonparametric Bayesian methods for benchmark dose estimation, Risk Analysis 33 pp 1608– (2013) · doi:10.1111/risa.12004
[15] Hoeting, Bayesian model averaging: A tutorial, Statistical Science 14 pp 382– (1999) · Zbl 1059.62525
[16] Kang, Incorporating model uncertainties along with data uncertainties in microbial risk assessment, Regulatory Toxicology and Pharmacology 32 pp 68– (2000) · doi:10.1006/rtph.2000.1404
[17] Kodell, Managing uncertainty in health risk assessment, International Journal of Risk Assessment and Management 14 pp 193– (2005) · doi:10.1504/IJRAM.2005.007167
[18] Lopes, Bayesian model assessment in factor analysis, Statistica Sinica 14 pp 41– (2004) · Zbl 1035.62060
[19] Meng, Simulating ratios of normalizing constants via a simple identity: A theoretical exploration, Statistica Sinica 6 pp 831– (1996) · Zbl 0857.62017
[20] Morales, Bayesian model averaging with applications to benchmark dose estimation for arsenic in drinking water, Journal of the American Statistical Association 101 pp 9– (2006) · Zbl 1118.62373 · doi:10.1198/016214505000000961
[21] Piegorsch, Analyzing Environmental Data (2005) · doi:10.1002/0470012234
[22] Piegorsch, Information-theoretic model-averaged benchmark dose analysis in environmental risk assessment, Environmetrics 24 pp 143– (2013) · doi:10.1002/env.2201
[23] Piegorsch, Nonparametric estimation of benchmark doses in quantitative risk analysis, Environmetrics 23 pp 717– (2012) · doi:10.1002/env.2175
[24] Polson, On the half-Cauchy prior for a global scale parameter, Bayesian Analysis 7 pp 887– (2012) · Zbl 1330.62148 · doi:10.1214/12-BA730
[25] Portier, Biostatistical issues in the design and analysis of animal carcinogenicity experiments, Environmental Health Perspectives 102 pp 5– (1994) · doi:10.1289/ehp.94102s15
[26] R: A Language and Environment for Statistical Computing (2012)
[27] Ringblom, Current modeling practice may lead to falsely high benchmark dose estimates, Regulatory Toxicology and Pharmacology 69 pp 171– (2014) · doi:10.1016/j.yrtph.2014.03.004
[28] Schlosser, Benchmark dose risk assessment for formaldehyde using airflow modeling and a single-compartment, DNA-protein cross-link dosimetry model to estimate human equivalent doses, Risk Analysis 23 pp 473– (2003) · doi:10.1111/1539-6924.00328
[29] Shao, A comparison of three methods for integrating historical information for Bayesian model averaged benchmark dose estimation, Environmental Toxicology and Pharmacology 34 pp 288– (2012) · doi:10.1016/j.etap.2012.05.002
[30] Shao, Model uncertainty and Bayesian model averaged benchmark dose estimation for continuous data, Risk Analysis 34 pp 101– (2014) · doi:10.1111/risa.12078
[31] Shao, Potential uncertainty reduction in model-averaged benchmark dose estimates informed by an additional dose study, Risk Analysis 31 pp 1561– (2011) · doi:10.1111/j.1539-6924.2011.01595.x
[32] Stern, Encyclopedia of Quantitative Risk Analysis and Assessment 2 pp 580– (2008)
[33] Benchmark Dose Technical Guidance Document (2012)
[34] U.S. National Toxicology Program 2009 Toxicology and Carcinogenesis Studies of Cumene (CAS NO. 98-82-8) in F344/N Rats and B6C3F 1 Mice
[35] West, The impact of model uncertainty on benchmark dose estimation, Environmetrics 23 pp 706– (2012) · doi:10.1002/env.2180
[36] Wheeler, Comparing model averaging with other model selection strategies for benchmark dose estimation, Environmental and Ecological Statistics 16 pp 37– (2009) · doi:10.1007/s10651-007-0071-7
[37] Wheeler, Benchmark dose estimation incorporating multiple data sources, Risk Analysis 29 pp 249– (2009) · doi:10.1111/j.1539-6924.2008.01144.x
[38] Wheeler, Monotonic Bayesian semiparametric benchmark dose analysis, Risk Analysis 32 pp 1207– (2012) · doi:10.1111/j.1539-6924.2011.01786.x
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.