×

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

References:

[1] Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Proceedings of the Second International Symposium on Information Theory, PetrovB. N. and CsakiB., (eds), 267-281. Akademiai Kiado, Budapest. · Zbl 0283.62006
[2] Andrieu, C. and Thoms, J. (2008). A tutorial on adaptive MCMC. Statistics and Computing18, 343-383.
[3] Armitage, P. and Doll, R. (1954). The age distribution of cancer and a multi‐stage theory of carcinogenesis. British Journal of Cancer8, 1-12.
[4] Bailer, A. J., Noble, R. B., and Wheeler, M. W. (2005). Model uncertainty and risk estimation for experimental studies of quantal responses. Risk Analysis25, 291-299.
[5] Bedrick, E. J., Christensen, R., and Johnson, W. O. (1996). A new perspective on priors for generalized linear models. Journal of the American Statistical Association91, 1450-1460. · Zbl 0882.62057
[6] Casella, G. and Berger, R. L. (2002). Statistical Inference, 2nd edn. Pacific Grove, California: Duxbury.
[7] Crump, K. S. (1984). A new method for determining allowable daily intake. Fundamental and Applied Toxicology4, 854-871.
[8] Crump, K. S. (1995). Calculation of benchmark doses from continuous data. Risk Analysis15, 79-89.
[9] Davis, J. A., Gift, J. S., and Zhao, Q. J. (2012). Introduction to benchmark dose methods and U.S. EPA’s Benchmark Dose Software (BMDS) version 2.1.1. Toxicology and Applied Pharmacology254, 181-191.
[10] Fang, Q. (2014). Hierarchical Bayesian Benchmark Risk Analysis. Ph.D thesis, Interdisciplinary Program in Statistics, University of Arizona, Tucson, Arizona.
[11] Faustman, E. M. and Bartell, S. M. (1997). Review of noncancer risk assessment: Applications of benchmark dose methods. Human and Ecological Risk Assessment3, 893-920.
[12] Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models. Bayesian Analysis1, 515-533. · Zbl 1331.62139
[13] Geweke, J. (1992). Evaluating the accuracy of sampling‐based approaches to the calculation of posterior moments. In Bayesian Statistics4, Bernardo, J. M., Berger, J. O., Dawid, A. P., and Smith, A. F. M., (eds.), 169-193. Oxford University Press, Oxford.
[14] Guha, N., Roy, A., Kopylev, L., Fox, J.Spassova, M., and White, P. (2013). Nonparametric Bayesian methods for benchmark dose estimation. Risk Analysis33, 1608-1619.
[15] Hoeting, J. A., Madigan, D., Raftery, A. E., and Volinsky, C. T. (1999). Bayesian model averaging: A tutorial. Statistical Science14, 382-401. (corr. 15, 193-195). · Zbl 1059.62525
[16] Kang, S. H., Kodell, R. L., and Chen, J. J. (2000). Incorporating model uncertainties along with data uncertainties in microbial risk assessment. Regulatory Toxicology and Pharmacology32, 68-72.
[17] Kodell, R. L. (2005). Managing uncertainty in health risk assessment. International Journal of Risk Assessment and Management14, 193-205.
[18] Lopes, H. F. and West, M. (2004). Bayesian model assessment in factor analysis. Statistica Sinica14, 41-67. · Zbl 1035.62060
[19] Meng, X. and WongW. H. (1996). Simulating ratios of normalizing constants via a simple identity: A theoretical exploration. Statistica Sinica6, 831-860. · Zbl 0857.62017
[20] Morales, K. H., Ibrahim, J. G., Chen, C.‐J., and Ryan, L. M. (2006). Bayesian model averaging with applications to benchmark dose estimation for arsenic in drinking water. Journal of the American Statistical Association101, 9-17. · Zbl 1118.62373
[21] Piegorsch, W. W. and Bailer, A. J. (2005). Analyzing Environmental Data. Chichester: John Wiley & Sons.
[22] Piegorsch, W. W., An, L., Wickens, A. A., West, R. W.Pe \(\widetilde{\operatorname{n}}\) a, E. A., and Wu, W. (2013). Information‐theoretic model‐averaged benchmark dose analysis in environmental risk assessment. Environmetrics24, 143-157. · Zbl 1525.62199
[23] Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., and Lin, L. (2012). Nonparametric estimation of benchmark doses in quantitative risk analysis. Environmetrics23, 717-728.
[24] Polson, N. G. and Scott, J. G. (2012). On the half‐Cauchy prior for a global scale parameter. Bayesian Analysis7, 887-902. · Zbl 1330.62148
[25] Portier, C. J. (1994). Biostatistical issues in the design and analysis of animal carcinogenicity experiments. Environmental Health Perspectives102, Suppl. 1, 5-8.
[26] R Development Core Team. (2012). R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3‐900051‐07‐0.
[27] Ringblom, J., Johanson, G., and Öberg, M. (2014). Current modeling practice may lead to falsely high benchmark dose estimates. Regulatory Toxicology and Pharmacology69, 171-177.
[28] Schlosser, P. M., Lilly, P. D., Conolly, R. B., Janszen, D. B., and Kimbell, J. S. (2003). 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 Analysis23, 473-487.
[29] Shao, K. (2012). A comparison of three methods for integrating historical information for Bayesian model averaged benchmark dose estimation. Environmental Toxicology and Pharmacology34, 288-296.
[30] Shao, K. and Gift, J. S. (2014). Model uncertainty and Bayesian model averaged benchmark dose estimation for continuous data. Risk Analysis34, 101-120.
[31] Shao, K. and Small, M. J. (2011). Potential uncertainty reduction in model‐averaged benchmark dose estimates informed by an additional dose study. Risk Analysis31, 1561-1575.
[32] Stern, A. H. (2008). Environmental health risk assessment. In Encyclopedia of Quantitative Risk Analysis and Assessment2, Melnick, E. L. and Everitt, B. S., (eds.), 580-589. Chichester: John Wiley & Sons.
[33] U.S. EPA (2012). Benchmark Dose Technical Guidance Document. Technical Report number EPA/100/R‐12/001. Washington, DC: U.S. Environmental Protection Agency.
[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. Technical Report number 542. Research Triangle Park, NC: U.S. Department of Health and Human Services, Public Health Service.
[35] West, R. W., Pigorsch, W. W., Pe \(\widetilde{\operatorname{n}}\) a, E. A., An, L., Wu, W., Wickens, A. A., Xiong, H., and Chen, W. (2012). The impact of model uncertainty on benchmark dose estimation. Environmetrics23, 706-716.
[36] Wheeler, M. W. and Bailer, A. J. (2009). Comparing model averaging with other model selection strategies for benchmark dose estimation. Environmental and Ecological Statistics16, 37-51.
[37] Wheeler, M. W. and Bailer, A. J. (2009). Benchmark dose estimation incorporating multiple data sources. Risk Analysis29, 249-256.
[38] Wheeler, M. W. and Bailer, A. J. (2012). Monotonic Bayesian semiparametric benchmark dose analysis. Risk Analysis32, 1207-1218.
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.