Simultaneous confidence bands for Abbott-adjusted quantal response models in benchmark analysis. (English) Zbl 1248.62207
Summary: We study the use of a Scheffé-style simultaneous confidence band as applied to low-dose risk estimation with quantal response data. We consider two formulations for the dose-response risk function, an Abbott-adjusted Weibull model and an Abbott-adjusted log-logistic model. Using the simultaneous construction, we derive methods for estimating upper confidence limits on the predicted extra risk and, by inverting the upper bands on the risk, lower bounds on the benchmark dose, or BMD, at a specific level of ‘benchmark risk’. Monte Carlo evaluations explore the operating characteristics of the simultaneous limits.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62N02 | Estimation in survival analysis and censored data |
| 92C50 | Medical applications (general) |
Keywords:
benchmark dose; carcinogenic risk assessment; Weibull dose-response model; log-logistic dose-response model; quantitative risk analysisReferences:
| [1] | Abbott, W. S., A method of computing the effectiveness of an insecticide, Journal of Economic Entomology, 18, 265-267 (1925) |
| [2] | Akaike, H., Information theory and an extension of the maximum likelihood principle, (Petrov, B. N.; Csaki, B., Proceedings of the Second International Symposium on Information Theory (1973), Akademiai Kiado: Akademiai Kiado Budapest), 267-281 · Zbl 0283.62006 |
| [3] | Al-Saidy, O. M.; Piegorsch, W. W.; West, R. W.; Nitcheva, D. K., Confidence bands for low-dose risk estimation with quantal response data, Biometrics, 59, 1056-1062 (2003) · Zbl 1225.62144 |
| [4] | Bailer, A. J.; Oris, J. T., Modeling reproductive toxicity in Ceriodaphnia tests, Environmental Toxicology and Chemistry, 12, 787-791 (1993) |
| [5] | Bailer, A. J.; See, K., Individual-based risk estimation for count responses, Environmental Toxicology and Chemistry, 17, 530-533 (1998) |
| [6] | Bently, K. S.; Kirkland, D.; Murphy, M.; Marshall, R., Evaluation of thresholds for benomyl- and carbendazim-induced aneuploidy in cultured human lymphocytes using fluorescence in situ hybridization, Mutation Research, 464, 41-51 (2000) |
| [7] | Casella, G.; Berger, R. L., Statistical Inference (2002), Duxbury: Duxbury Pacific Grove, CA |
| [8] | Chen, J. J.; Gaylor, D. W., Dose-response modeling of quantitative response for risk assessment, Communications in Statistics-Theory and Methods, 21, 2367-2381 (1992) |
| [9] | J.J. Coherssen, V.T. Covello, Risk Analysis: A Guide to Principles and Methods for Analyzing Health and Environmental Risks, Executive Office of the President, Washington, DC, 1989; J.J. Coherssen, V.T. Covello, Risk Analysis: A Guide to Principles and Methods for Analyzing Health and Environmental Risks, Executive Office of the President, Washington, DC, 1989 |
| [10] | Crump, K. S., A new method for determining allowable daily intake, Fundamental and Applied Toxicology, 4, 854-871 (1984) |
| [11] | Crump, K. S., Calculation of benchmark doses from continuous data, Risk Analysis, 15, 79-89 (1995) |
| [12] | Edler, L.; Kopp-Schneider, A., Statistical models for low dose exposure, Mutation Research, 405, 227-236 (1998) |
| [13] | Edler, L.; Kopp-Schneider, A.; Heinzl, H., Dose-response modeling, (Edler, L.; Kitsos, C. P., Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment (2005), John Wiley & Sons: John Wiley & Sons Chichester), 5-23 |
| [14] | Faustman, E. M.; Bartell, S. M., Review of noncancer risk assessment: Applications of benchmark dose methods, Human and Ecological Risk Assessment, 3, 893-920 (1997) |
| [15] | Foronda, N. M.; Fowles, J.; Smith, N.; Taylor, M.; Temple, W., A benchmark dose analysis for sodium monofluoroacetate (1080) using dichotomous toxicity data, Regulatory Toxicology and Pharmacology, 47, 84-89 (2007) |
| [16] | Gaylor, D. W.; Aylward, L. L., An evaluation of benchmark dose methodology for non-cancer continuous-data health effects in animals due to exposures to dioxin (TCDD), Regulatory Toxicology and Pharmacology, 40, 9-17 (2004) |
| [17] | Gaylor, D. W.; Kodell, R. L., Percentiles of the product of uncertainty factors for establishing probabilistic reference doses, Risk Analysis, 20, 245-250 (2000) |
| [18] | Gaylor, D. W.; Kodell, R. L., A procedure for developing risk-based reference doses, Regulatory Toxicology and Pharmacology, 35, 137-141 (2002) |
| [19] | Gaylor, D. W.; Slikker, W. L., Risk assessment for neurotoxic effects, NeuroToxicology, 11, 211-218 (1990) |
| [20] | Karita, K.; Yano, E.; Dakeishi, M.; Iwata, T.; Murata, K., Benchmark dose of lead inducing anemia at the workplace, Risk Analysis, 25, 957-962 (2005) |
| [21] | Kodell, R. L.; West, R. W., Upper confidence intervals on excess risk for quantitative responses, Risk Analysis, 13, 177-182 (1993) |
| [22] | Krewski, D.; van Ryzin, J., Dose response models for quantal response toxicity data, (Csörgö, M.; Dawson, D. A.; Rao, J. N.K.; Saleh, A. K.M. E., Statistics and Related Topics (1981), North-Holland: North-Holland Amsterdam), 201-231 · Zbl 0479.62085 |
| [23] | Markowski, V. P.; Zareba, G.; Stern, S.; Cox, C.; Weiss, B., Altered operant responding for motor reinforcement and the determination of benchmark doses following perinatal exposure to low-level 2, 3, 7, 8-tetrachlorodibenzo-p-dioxin, Environmental Health Perspectives, 109, 621-627 (2001) |
| [24] | Nitcheva, D. K.; Piegorsch, W. W.; West, R. W.; Kodell, R. L., Multiplicity-adjusted inferences in risk assessment: Benchmark analysis with quantal response data, Biometrics, 61, 277-286 (2005) |
| [25] | Pan, W.; Piegorsch, W. W.; West, R. W., Exact one-sided simultaneous confidence bands via Uusipaikka’s method, Annals of the Institute of Statistical Mathematics, 55, 243-250 (2003) · Zbl 1049.62082 |
| [26] | Portier, C. J., Biostatistical issues in the design and analysis of animal carcinogenicity experiments, Environmental Health Perspectives, 102, Suppl. 1, 5-8 (1994) |
| [27] | R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2005; R Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2005 |
| [28] | Scheffé, H., A method for judging all contrasts in the analysis of variance, Biometrika, 40, 87-104 (1953) · Zbl 0052.15202 |
| [29] | Schlosser, P. M.; Lilly, P. D.; Conolly, R. B.; Janszen, D. B.; Kimbell, J. S., 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, 473-487 (2003) |
| [30] | US EPA, Benchmark Dose Technical Guidance Document, US. Environmental Protection Agency, Washington, DC, 2000; US EPA, Benchmark Dose Technical Guidance Document, US. Environmental Protection Agency, Washington, DC, 2000 |
| [31] | US EPA, Help Manual for Benchmark Dose Software Version 1.3, National Center for Environmental Assessment, US Environmental Protection Agency, Research Triangle Park, NC, 2001; US EPA, Help Manual for Benchmark Dose Software Version 1.3, National Center for Environmental Assessment, US Environmental Protection Agency, Research Triangle Park, NC, 2001 |
| [32] | van Wijngaarden, E.; Beck, C.; Shamlaye, C. F.; Cernichiari, E.; Davidson, P. W.; Myers, G. J.; Clarkson, T. W., Benchmark concentrations for methyl mercury obtained from the 9-year follow-up of the Seychelles Child Development Study, NeuroToxicology, 27, 702-709 (2006) |
| [33] | West, R. W.; Piegorsch, W. W., Extra risk, (El-Shaarawi, A. H.; Piegorsch, W. W., Encyclopedia of Environmetrics, vol. 2 (2002), John Wiley & Sons: John Wiley & Sons Chichester), 731-732 |
| [34] | Wheeler, M. W., Benchmark dose estimation using \(SAS^®\), (Nelson, G. S., Proceedings of the Thirtieth Annual \(SAS^®\) Users Group International Conference (2005), SAS Institute Inc.: SAS Institute Inc. Cary, NC), 201-230 |
| [35] | Wogan, G. N.; Paglialunga, S.; Newberne, P. M., Carcinogenic effects of low dietary levels of Aflatoxin B1 in rats, Food and Cosmetics Toxicology, 12, 681-685 (1974) |
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.
