References

Abramowitz and Stegun (1972)

Abramowitz, M. and Stegun, I. A. Handbook of mathematical functions. National Bureau of Standards Applied Mathematics Series, 55:589–626, 1972.

Bopp et al. (2015)

Bopp, S., Berggren, E., Kienzler, A., van der Linden, S., and Worth, A. Scientific methodologies for the assessment of combined effects of chemicals - a survey and literature review. EUR - Scientific and Technical Research Reports, 2015. doi:10.2788/093511.

Box and Cox (1964)

Box, G. E. and Cox, D. R. An analysis of transformations. Journal of the Royal Statistical Society: Series B (Methodological), 26(2):211–243, 1964.

Butler Ellis et al. (2018)

Butler Ellis, M.C., Kennedy, M. C., Kuster, C.J., Alanis, R., and Tuck, C.R. Improvements in modelling bystander and resident exposure to pesticide spray drift: investigations into new approaches for characterizing the ‘collection efficiency’of the human body. Annals of work exposures and health, 62(5):622–632, 2018. doi:10.1093/annweh/wxy017.

Béchaux et al. (2013)

Béchaux, C., Zetlaoui, M., Tressou, J., Leblanc, J.-C., Héraud, F., and Crépet, A. Identification of pesticide mixtures and connection between combined exposure and diet. Food and chemical toxicology, 59:191–198, 2013. doi:10.1016/j.fct.2013.06.006.

Cramer et al. (1976)

Cramer, G.M., Ford, R.A., and Hall, R.L. Estimation of toxic hazard—a decision tree approach. Food and cosmetics toxicology, 16(3):255–276, 1976. doi:10.1016/S0015-6264(76)80522-6.

Dahlquist and Bjorck (1974)

Dahlquist, G. and Bjorck, A. Numerical methods (transl. by n. anderson). 1974.

de Boer and van der Voet (2011)

de Boer, W. J. and van der Voet. Mcra 7. a web-based program for monte carlo risk assessment. reference manual 2011-12-19, documenting mcra release 7.1. Technical Report, Biometris, Wageningen UR and National Institute for Public Health and the Environment (RIVM), Bilthoven, Wageningen., 2011. URL: https//mcra.rivm.nl.

de Boer et al. (2009)

de Boer, W. J., van der Voet, H., Bokkers, B. G., Bakker, M. I., and Boon, P. E. Comparison of two models for the estimation of usual intake addressing zero consumption and non-normality. Food Additives and Contaminants, 26(11):1433–1449, 2009.

Dodd (1996)

Dodd, K. A technical guide to c-side. Ames, Iowa: Department of Statistics and Center for Agricultural and Rural Development, Iowa State University, 1996.

EC (2018)

European Commission Standing Committee on Plants Animals Food and Feed. European commission working document sante-2015-10216 rev. 7. 2018.

Efron (1979)

Efron, B. Bootstrap methods: another look at the jackknife annals of statistics 7: 1–26. View Article PubMed/NCBI Google Scholar, 1979.

Efron and Tibshirani (1993)

Efron, B. and Tibshirani, R. J. An introduction to the bootstrap chapman & hall. New York, 1993.

EFSA (2011a)

European Food Safety Authority (EFSA). Report on the development of a food classification and description system for exposure assessment and guidance on its implementation and use. EFSA Journal, 9(12):84, 2011. doi:doi:10.2903/j.efsa.2011.2489.

EFSA (2011b)

European Food Safety Authority (EFSA). The food classification and description system foodex 2 (draft-revision 1). EFSA Journal, pages 438, 2011.

EFSA (2012)

European Food Safety Authority (EFSA). Guidance on the use of probabilistic methodology for modelling dietary exposure to pesticide residues. EFSA Journal, 10(10):2839, 2012. doi:10.2903/j.efsa.2012.2839.

EFSA (2014)

European Food Safety Authority (EFSA). Guidance on the assessment of exposure of operators, workers, residents and bystanders in risk assessment for plant protection products. EFSA Journal, 12(10):3874, 2014. doi:10.2903/j.efsa.2014.3874.

EFSA (2017a)

European Food Safety Authority (EFSA), Buist, H., Craig, P., Dewhurst, I., Hougaard Bennekou, S., Kneuer, C., Machera, K., Pieper, C., Court Marques, D., Guillot, G., Ruffo, F., and Chiusolo, A. Guidance on dermal absorption. EFSA Journal, 15(6):e04873, 2017. doi:10.2903/j.efsa.2017.4873.

EFSA (2017b)

EFSA Panel on Contaminants in the Food Chain (CONTAM), Knutsen, H. K., Alexander, J., Barregård, L., Bignami, M., Brüschweiler, B., Ceccatelli, S., Cottrill, B., Dinovi, M., Edler, L., Grasl‐Kraupp, B., Hogstrand, C., Hoogenboom, L. (Ron), Nebbia, C. S., Oswald, I. P., Petersen, A., Rose, M., Roudot, Alain‐Claude, Schwerdtle, T., Vleminckx, C., Vollmer, G., Wallace, H., Ruiz, J. A. G., and Binaglia, M. Risks for human health related to the presence of pyrrolizidine alkaloids in honey, tea, herbal infusions and food supplements. EFSA Journal, 7 2017. doi:10.2903/j.efsa.2017.4908.

EFSA (2018)

European Food Safety Authority (EFSA), Brancato, A., Brocca, D., Ferreira, L., Greco, L., Jarrah, S., Leuschner, R., Medina, P., Miron, I., Nougadere, A., Pedersen, R., Reich, H., Santos, M., Stanek, A., Tarazona, J., Theobald, A., and Villamar-Bouza, L. Use of efsa pesticide residue intake model (efsa primo revision 3). EFSA Journal, 16(1):e05147, 2018. URL: https://efsa.onlinelibrary.wiley.com/doi/abs/10.2903/j.efsa.2018.5147.

EFSA (2020a)

European Food Safety Authority (EFSA), Craig, P. S., Dujardin, B., Hart, A., Hernández-Jerez, A. F., Hougaard Bennekou, S., Kneuer, C., Ossendorp, B., Pedersen, R., Wolterink, G., and Mohimont, L. Cumulative dietary risk characterisation of pesticides that have acute effects on the nervous system. EFSA Journal, 18(4):e06087, 2020. URL: https://efsa.onlinelibrary.wiley.com/doi/abs/10.2903/j.efsa.2020.6087.

EFSA (2020b)

European Food Safety Authority (EFSA), Craig, P. S., Dujardin, B., Hart, A., Hernandez-Jerez, A. F., Hougaard Bennekou, S., Kneuer, C., Ossendorp, B., Pedersen, R., Wolterink, G., and Mohimont, L. Cumulative dietary risk characterisation of pesticides that have chronic effects on the thyroid. EFSA Journal, 18(4):e06088, 2020. URL: https://efsa.onlinelibrary.wiley.com/doi/abs/10.2903/j.efsa.2020.6088.

Gillis and Plemmons (2013)

Gillis, N. and Plemmons, R. J. Sparse nonnegative matrix underapproximation and its application to hyperspectral image analysis. Linear Algebra and its Applications, 438(10):3991–4007, 2013.

Goedhart et al. (2012)

Goedhart, P. W., van der Voet, H., Knüppel, S., Dekkers, A. L.M., Dodd, K. W., Boeing, H., and van Klaveren, J. D. A comparison by simulation of different methods to estimate the usual intake distribution for episodically consumed foods. Technical Report, Report: Supporting Publications 2012:EN-299, 2012. URL: http//www.efsa.europa.eu/publications.

Goodhardt et al. (1984)

Goodhardt, G. J., Ehrenberg, A. S., and Chatfield, C. The dirichlet: a comprehensive model of buying behaviour. Journal of the Royal Statistical Society. Series A (General), pages 621–655, 1984.

Hoyer (2004)

Hoyer, P. O. Non-negative matrix factorization with sparseness constraints. Journal of machine learning research, 5(Nov):1457–1469, 2004.

Husøy et al. (2019)

Husøy, T., Andreassen, M., Hjertholm, H., Carlsen, M.H., Norberg, N., Sprong, C., Papadopoulou, E., Sakhi, A.K., Sabaredzovic, A., and Dirven, H.A.A.M. The norwegian biomonitoring study from the eu project euromix: levels of phenols and phthalates in 24-hour urine samples and exposure sources from food and personal care products. Environment International, 132:105103, 2019. URL: https://www.sciencedirect.com/science/article/pii/S0160412019306944.

Jäckel (2005)

Jäckel, P. A note on multivariate gauss-hermite quadrature. London: ABN-Amro. Re, 2005.

Karrer et al. (2018)

Karrer, C., Roiss, T., von Goetz, N., Skledar, D. G., Mašič, L. P., and Hungerbühler, K. Physiologically based pharmacokinetic (pbpk) modeling of the bisphenols bpa, bps, bpf, and bpaf with new experimental metabolic parameters: comparing the pharmacokinetic behavior of bpa with its substitutes. Environmental Health Perspectives, 126(7):077002, 2018. URL: https://ehp.niehs.nih.gov/doi/abs/10.1289/EHP2739.

Karrer et al. (2019)

Karrer, Cecile, Boer, W. d., Delmaar, C., Cai, Y., Crépet, A., Hungerbühler, K., and Goetz, N. v. Linking probabilistic exposure and pharmacokinetic modeling to assess the cumulative risk from the bisphenols bpa, bps, bpf, and bpaf for europeans. Environmental science & technology, 53(15):9181–9191, 2019. doi:10.1021/acs.est.9b01749.

Karrer et al. (2020)

Karrer, C., Andreassen, M., von Goetz, N., Sonnet, F., Sakhi, A. K., Hungerbühler, K., Dirven, H., and Husøy, T. The euromix human biomonitoring study: source-to-dose modeling of cumulative and aggregate exposure for the bisphenols bpa, bps, and bpf and comparison with measured urinary levels. Environment International, 136:105397, 2020. URL: https://www.sciencedirect.com/science/article/pii/S0160412019324080.

Kennedy and Butler Ellis (2017)

Kennedy, M. C. and Butler Ellis, M.C. Probabilistic modelling for bystander and resident exposure to pesticides using the browse software. Biosystems engineering, 154:105–121, 2017. doi:10.1016/j.biosystemseng.2016.08.012.

Kennedy et al. (2012)

Kennedy, M. C., Butler Ellis, C. M.J., and Miller, P. C.H. Bream: a probabilistic bystander and resident exposure assessment model of spray drift from an agricultural boom sprayer. Computers and electronics in agriculture, 88:63–71, 2012. doi:10.1016/j.compag.2012.07.004.

Kennedy et al. (2015a)

Kennedy, M. C., Glass, C. R., Bokkers, B., Hart, A. D., Hamey, P. Y., Kruisselbrink, J. W., de Boer, W. J., van der Voet, H., Garthwaite, D. G., and van Klaveren, J. D. A european model and case studies for aggregate exposure assessment of pesticides. Food and Chemical Toxicology, 79:32–44, 2015.

Kennedy et al. (2015b)

Kennedy, M. C., van der Voet, H., Roelofs, V. J., Roelofs, W., Glass, C. R., de Boer, W. J., Kruisselbrink, J. W., and Hart, A. D.M. New approaches to uncertainty analysis for use in aggregate and cumulative risk assessment of pesticides. Food and Chemical Toxicology, 79:54–64, 2015.

Kennedy et al. (2020)

Kennedy, M. C., Hart, A. D.M., Kruisselbrink, J. W., van Lenthe, M., de Boer, W. J., van der Voet, H., Rorije, E., Sprong, C., and van Klaveren, J. A retain and refine approach to cumulative risk assessment. Food and Chemical Toxicology, April 2020. doi:10.1016/j.fct.2020.111223.

Kipnis et al. (2009)

Kipnis, V., Midthune, D., Buckman, D. W., Dodd, K. W., Guenther, P. M., Krebs-Smith, S. M., Subar, A. F., Tooze, J. A., Carroll, R. J., and Freedman, L. S. Modeling data with excess zeros and measurement error: application to evaluating relationships between episodically consumed foods and health outcomes. Biometrics, 65(4):1003–1010, 2009.

Lee and Seung (1999)

Lee, D. D. and Seung, H. S. Learning the parts of objects by non-negative matrix factorization. Nature, 401(6755):788, 1999.

Merz and Schrenk (2016)

Merz, K.-H. and Schrenk, D. Interim relative potency factors for the toxicological risk assessment of pyrrolizidine alkaloids in food and herbal medicines. Toxicology Letters, 263:44–57, 2016. doi:10.1016/j.toxlet.2016.05.002.

Mood et al. (1974)

Mood, A. M., Graybill, F. A., and Boes, D. C. Introduction to the Theory of Statistics 1974. McGraw-Hill Kogakusha, 1974.

Mulder et al. (2015)

Mulder, P. P.J., Sánchez, P. L., These, A., Preiss-Weigert, A., and Castellari, M. Occurrence of pyrrolizidine alkaloids in food. EFSA Supporting Publications, 12(8):859E, 2015. doi:10.2903/sp.efsa.2015.EN-859.

Munro et al. (1996)

Munro, I. C., Ford, R. A., Kennepohl, E., and Sprenger, J. G. Correlation of structural class with no-observed-effect levels: a proposal for establishing a threshold of concern. Food and Chemical Toxicology, 34(9):829–867, 1996. doi:10.1016/S0278-6915(96)00049-X.

Nusser et al. (1996)

Nusser, S. M., Carriquiry, A. L., Dodd, K. W., and Fuller, W. A. A semiparametric transformation approach to estimating usual daily intake distributions. Journal of the American Statistical Association, 91(436):1440–1449, 1996.

Nusser et al. (1997)

Nusser, S. M., Fuller, W. A., Guenther, P. M., and others. Estimating usual dietary intake distributions: adjusting for measurement error and nonnormality in 24-hour food intake data. Technical Report, Center for Agricultural and Rural Development (CARD) at Iowa State University, 1997.

Price and Han (2011)

Price, P. S. and Han, X. Maximum cumulative ratio (mcr) as a tool for assessing the value of performing a cumulative risk assessment. International journal of environmental research and public health, 8(6):2212–2225, 2011.

Saul and Lee (2002)

Saul, L. K. and Lee, D. D. Multiplicative updates for classification by mixture models. In Advances in Neural Information Processing Systems, 897–904. 2002.

Slob (2002)

Slob, W. Dose-Response Modeling of Continuous Endpoints. Toxicological Sciences, 66(2):298–312, 04 2002. URL: https://doi.org/10.1093/toxsci/66.2.298.

Slob (2006)

Slob, W. Probabilistic dietary exposure assessment taking into account variability in both amount and frequency of consumption. Food and Chemical Toxicology, 44(7):933–951, 2006.

Slob and Setzer (2013)

Slob, W. and Setzer, R. Shape and steepness of toxicological dose–response relationships of continuous endpoints. Critical reviews in toxicology, 44:, 11 2013. doi:10.3109/10408444.2013.853726.

Slob et al. (2010)

Slob, W., de Boer, W. J., and van der Voet, H. Can current dietary exposure models handle aggregated intake from different foods? a simulation study for the case of two foods. Food and chemical toxicology, 48(1):178–186, 2010.

Souverein et al. (2011)

Souverein, O. W., de Boer, W. J., Geelen, A., van der Voet, H., de Vries, J. H., Feinberg, M., and van't Veer, P. Uncertainty in intake due to portion size estimation in 24-hour recalls varies between food groups. The Journal of nutrition, 141(7):1396–1401, 2011. doi:10.3945/jn.111.139220.

Tebby et al. (2020)

Tebby, C., van der Voet, H., de Sousa, G., Rorije, E., Kumar, V., de Boer, W., Kruisselbrink, J. W., Bois, F. Y., Faniband, M., Moretto, A., and Brochot, C. A generic pbtk model implemented in the mcra platform: predictive performance and uses in risk assessment of chemicals. Food and Chemical Toxicology, 142:111440, 2020. URL: https://www.sciencedirect.com/science/article/pii/S0278691520303306.

Tooze et al. (2006)

Tooze, J. A., Midthune, D., Dodd, K. W., Freedman, L. S., Krebs-Smith, S. M., Subar, A. F., Guenther, P. M., Carroll, R. J., and Kipnis, V. A new statistical method for estimating the usual intake of episodically consumed foods with application to their distribution. Journal of the American Dietetic Association, 106(10):1575–1587, 2006.

van den Berg et al. (2016)

van den Berg, F., Jacobs, C.M.J., Butler Ellis, M.C., Spanoghe, P., Doan Ngoc, K., and Fragkoulis, G. Modelling exposure of workers, residents and bystanders to vapour of plant protection products after application to crops. Science of the Total Environment, 573:1010–1020, 2016. doi:10.1016/j.scitotenv.2016.08.180.

van der Voet and Slob (2007)

van der Voet, H. and Slob, W. Integration of probabilistic exposure assessment and probabilistic hazard characterization. Risk Analysis: An International Journal, 27(2):351–371, 2007. doi:10.1111/j.1539-6924.2007.00887.x.

van der Voet et al. (2009)

van der Voet, H., van der Heijden, G. W.A.M., Bos, P. M.J., Bosgra, S., Boon, P. E., Muri, S. D., and Brüschweiler, B. J. A model for probabilistic health impact assessment of exposure to food chemicals. Food and Chemical Toxicology, 47(12):2926–2940, 2009. doi:10.1016/j.fct.2008.12.027.

van der Voet et al. (2014)

van der Voet, H., Kruisselbrink, J.W., Boer, W.J., and Boon, P.E. Model-then-add: usual intake modelling of multimodal intake distributions. RIVM Letter report, 2014. URL: https://rivm.openrepository.com/handle/10029/314361.

van Klaveren et al. (2012)

van Klaveren, J. D., Goedhart, P. W., Wapperom, D., and van der Voet, H. A european tool for usual intake distribution estimation in relation to data collection by efsa. EFSA Supporting Publications, 9(6):300E, 2012. URL: https://efsa.onlinelibrary.wiley.com/doi/abs/10.2903/sp.efsa.2012.EN-300.

van Klaveren et al. (2019a)

van Klaveren, J.D., Kruisselbrink, J.W., de Boer, W.J., van Donkersgoed, G., Biesebeek, J.D. t., Sam, M., and van der Voet, H. Cumulative dietary exposure assessment of pesticides that have acute effects on the nervous system using mcra software. EFSA Supporting Publications, 16(9):1708E, 2019. URL: https://efsa.onlinelibrary.wiley.com/doi/abs/10.2903/sp.efsa.2019.EN-1708.

van Klaveren et al. (2019b)

van Klaveren, J.D., Kruisselbrink, J.W., de Boer, W.J., van Donkersgoed, G., Biesebeek, J.D. t., Sam, M., and van der Voet, H. Cumulative dietary exposure assessment of pesticides that have chronic effects on the thyroid using mcra software. EFSA Supporting Publications, 16(9):1707E, 2019. URL: https://efsa.onlinelibrary.wiley.com/doi/abs/10.2903/sp.efsa.2019.EN-1707.

Verkaik-Kloosterman et al. (2011)

Verkaik-Kloosterman, J., Dodd, K. W., Dekkers, A. L., van't Veer, P., and Ocké, M. C. A three-part, mixed-effects model to estimate the habitual total vitamin d intake distribution from food and dietary supplements in dutch young children. The Journal of nutrition, 141(11):2055–2063, 2011.

WHO (2018)

World Health Organization (WHO). Guidance document on evaluating and expressing uncertainty in hazard characterization. World Health Organization, 2018.

Zetlaoui et al. (2011)

Zetlaoui, M., Feinberg, M., Verger, P., and Clémençon, S. Extraction of food consumption systems by nonnegative matrix factorization (nmf) for the assessment of food choices. Biometrics, 67(4):1647–1658, 2011.