Wang Z, Walker GW, Muir DCG, Nagatani‑Yoshida K. Toward a global understanding of chemical pollution: A first comprehensive analysis of national and regional chemical inventories. Environ Sci Technol. 2020;54:2575–84.
Jiang C, Wang X, Li X, Inlore J, Wang T, Liu Q, et al. Dynamic human environmental exposome revealed by longitudinal personal monitoring. Cell. 2018;175:277–91.
Dwivedi AM, Johanson G, Lorentzen JC, Palmberg L, Sjögren B, Ernstgård L. Acute effects of acrolein in human volunteers during controlled exposure. Inhalation Toxicol. 2015;27:810–21.
Hamra GB, Guha N, Cohen A, Laden F, Raaschou-Nielsen O, Samet JM, et al. Outdoor particulate matter exposure and lung cancer: a systematic review and meta-analysis. Environ Health Perspect. 2014;122:906–11.
EPA. Human health risk assessment. 2025. https://www.epa.gov/risk/human-health-risk-assessment.
ECHA. Guidance on information requirements and chemical safety assessment. 2016. https://echa.europa.eu/documents/10162/2324909/ir_csa_part_d_caracal_en.pdf/.
EFSA. Safety assessment of titanium dioxide (E171) as a food additive. EFSA J. 2021;19:6585.
Tulve NS, Geller AM, Hagerthey S, Julius SH, Lavoie ET, Mazur SL, et al. Challenges and opportunities for research supporting cumulative impact assessments at the United States Environmental Protection Agency’s Office of Research and Development. Lancet Regional Health Americas. 2024;30:100666.
Wild CP. Complementing the genome with an “Exposome”: the outstanding challenge of environmental exposure measurement in molecular epidemiology. Cancer Epidemiol, Biomark Prev. 2005;14:1847–50.
RIVM. Aggregate exposure – exploring the use of an allocation factor in risk assessment. Letter report 2024-0127. 2024. https://rivm.openrepository.com/handle/10029/627870.
SCCS. Notes of guidance for the testing of cosmetic ingredients and their safety evaluation — 12th revision, SCCS/1647/22. 2023. https://health.ec.europa.eu/publications/sccs-notes-guidance-testing-cosmetic-ingredients-and-their-safety-evaluation-12th-revision_en.
Delmaar CJE, Schreurs R, Bakker MI, Minnema J, Bokkers BGH. PACEMweb: a tool for aggregate consumer exposure assessment. J Exposure Sci Environ Epidemiol. 2023;33:971–9.
EPA. Stochastic Human Exposure and Dose Simulation (SHEDS). 2025. https://www.sciensano.be/en/projects/national-food-consumption-surveyhttps://www.epa.gov/chemical-research/stochastic-human-exposure-and-dose-simulation-sheds.
RIVM. ConsExpo Web: Consumer exposure models – model documentation. Update for ConsExpo Web 1.0.2. Report 2017‑0197. 2017. https://www.rivm.nl/bibliotheek/rapporten/2017-0197.
EMA. Final feedback from European Medicine Agency (EMA) to the EU Commission request to evaluate the impact of the removal of titanium dioxide from the list of authorised food additives on medicinal products. 2021. https://www.ema.europa.eu/en/documents/report/final-feedback-european-medicine-agency-ema-eu-commission-request-evaluate-impact-removal-titanium-dioxide-list-authorised-food-additives-medicinal-products_en.pdf.
FDA. Titanium dioxide as a color additive in foods. 2025. https://www.fda.gov/industry/color-additives/titanium-dioxide-color-additive-foods.
Green MA, Watson AW, Brunstrom JM, Corfe BM, Johnstone AM, Williams EA, et al. Comparing supermarket loyalty card data with traditional diet survey data for understanding how protein is purchased and consumed in older adults for the UK, 2014–16. Nutr J. 2020;19:83.
Treitler JT, Tekle S, Ushe J, Zanin L, Capshaw T, Tardieu G, et al. Characterizing nutrient patterns of food items in adolescent diet using data from a novel citizen science project and the US National Health and Nutrition Examination Survey (NHANES). Front Nutr. 2023;10:1233141.
Dionisio KL, Phillips K, Price PS, Grulke CM, Williams A, Biryol D, et al. The Chemical and Products Database, a resource for exposure-relevant data on chemicals in consumer products. Sci Data. 2018;5:180125.
Open Food Facts contributors. Open Food Facts: A free, collaborative database of food products from around the world. 2025. https://world.openfoodfacts.org/.
EWG. Skin Deep Cosmetics Database. 2025. https://www.ewg.org/skindeep/.
Gelman A. Multilevel (hierarchical) modeling: what it can and cannot do. Technometrics. 2006;48:432–5.
Little RJ. Missing data assumptions. Annu Rev Stat Appl. 2021;8:89–107.
Richardson S, Gilks WR. A Bayesian approach to measurement error problems in epidemiology using conditional independence models. Am J Epidemiol. 1993;138:430–42.
Hoffman MD, Gelman A. The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo. J Mach Learn Res. 2014;15:1593–623.
Cerina R, Duch R. Polling India via regression and post-stratification of non-probability online samples. PLOS One. 2021;16:e0260092.
Downes M, Gurrin LC, English DR, Pirkis J, Currier D, Spittal MJ, et al. Multilevel regression and poststratification: a modeling approach to estimating population quantities from highly selected survey samples. Am J Epidemiol. 2018;187:1780–90.
Gelman A, Hill J. Data analysis using regression and multilevel/hierarchical models. Cambridge University Press; 2006.
Box GEP, Cox DR. An analysis of transformations. J R Stat Soc Ser B. 1964;26:211–43.
Paulo MJ, van der Voet H, Jansen MJ, ter Braak CJ, van Klaveren JD. Risk assessment of dietary exposure to pesticides using a Bayesian method. Pest Manag Sci. 2005;61:759–66.
Van Den Neucker S, Demaegdt H, Cerina R, Mast J, Grigoriev A, De Broe S, et al. Titanium dioxide levels in food and other ingested consumer products: a systematic review. Food Chem Adv. 2025;6:100918.
Cairat M, Huybrechts I, Fournier A. Exposure assessment of titanium dioxide via drugs available on the French market: a nationwide descriptive study. Therapies. 2024;79:718–29.
Petrović B, Kojić S, Milić L, Luzio A, Perić T, Marković E, et al. Toothpaste ingestion—evaluating the problem and ensuring safety: systematic review and meta-analysis. Front Public Health. 2023;11:1279915.
R Core Team. R: A language and environment for statistical computing, 4.2.0. Vienna, Austria: R Foundation for Statistical Computing; 2021.
Gabry J, Češnovar R, Johnson A. cmdstanr: R Interface to ‘CmdStan’. 2024. https://mc-stan.org/cmdstanr/reference/cmdstanr-package.
EFSA. Re-evaluation of titanium dioxide (E 171) as a food additive. EFSA J. 2016;14:e04545.
Weir A, Westerhoff P, Fabricius L, Hristovski K, von Goetz N. Titanium dioxide nanoparticles in food and personal care products. Environ Sci Technol. 2012;46:2242–50.
RIVM. Exposure assessment of the food additive titanium dioxide (E 171) based on use levels provided by the industry. Letter report 2015-0195. 2015. https://www.rivm.nl/bibliotheek/rapporten/2015-0195.
Rompelberg C, Heringa MB, Van Donkersgoed G, Drijvers J, Roos A, Westenbrink S, et al. Oral intake of added titanium dioxide and its nanofraction from food products, food supplements and toothpaste by the Dutch population. Nanotoxicology. 2016;10:1404–14.
Verleysen E, Brassinne F, Van Steen F, Waegeneers N, Cheyns K, Machiels R, et al. Towards a generic protocol for measuring the constituent particle size distribution of E171 in food by electron microscopy. Food Control. 2022;132:108492.
Blei DM, Kucukelbir A, McAuliffe JD. Variational inference: a review for statisticians. J Am Stat Assoc. 2017;112:859–77.
Tierney L, Kadane JB. Accurate approximations for posterior moments and marginal densities. J Am Stat Assoc. 1986;81:82–86.
Isaacs KK, Glen WG, Egeghy P, Goldsmith MR, Smith L, Vallero D, et al. SHEDS‑HT: an integrated probabilistic exposure model for prioritizing exposures to chemicals with near‑field and dietary sources. Environ Sci Technol. 2014;48:12750–9.
Wambaugh JF, Rager JE. Exposure forecasting – ExpoCast – for data‑poor chemicals in commerce and the environment. J Exposure Sci Environ Epidemiol. 2022;32:783–93.
Li L, Westgate JN, Hughes L, Zhang X, Givehchi B, Toose L, et al. A model for risk‑based screening and prioritization of human exposure to chemicals from near‑field sources. Environ Sci Technol. 2018;52:14235–44.
Rosenbaum RK, Bachmann TM, Gold LS, Huijbregts MAJ, Jolliet O, Juraske R, et al. USEtox ‒ The UNEP‑SETAC toxicity model: recommended characterisation factors for human toxicity and freshwater ecotoxicity in Life Cycle Impact Assessment. Int J Life Cycle Assess. 2008;13:532–46.
Ring CL, Arnot J, Bennett DH, Egeghy P, Fantke P, Huang L, et al. Consensus modeling of median chemical intake for the U.S. population based on predictions of Exposure Pathways. Environ Sci Technol. 2019;53:719–32.
Lamon L, Paini A, Siccardi M, Doyle J, McNamara C, Galea KS, et al. Physiologically based toxicokinetic models in aggregate exposure: a review. Toxicol Lett. 2025;413:111725.
Stanfield Z, Addington CK, Dionisio KL, Lyons D, Rager JE, Isaacs KK. Bayesian inference of chemical exposures from NHANES urine biomonitoring data. J Exposure Sci Environ Epidemiol. 2022;32:833–46.
Tornero‑Velez R, Egeghy PP, Cohen Hubal EA. Biogeographical analysis of chemical co‑occurrence data to identify priorities for mixtures research. Risk Anal. 2012;32:224–36.
Stanfield Z, Addington CK, Dionisio KL, Lyons D, Tornero-Velez R, Phillips KA, et al. Mining of consumer product ingredient and purchasing data to identify potential chemical coexposures. Environ Health Perspect. 2021;129:067006.
McNally K, Loizou GD. A probabilistic model of human variability in physiology for future application to dose reconstruction and QIVIVE. Front Pharmacol. 2015;6:213.
Bel S, Van den Abeele S, Lebacq T, Ost C, Brocatus L, Stiévenart C, et al. Protocol of the Belgian food consumption survey 2014: objectives design and methods. Archives of Public Health. 2016;74:20.
Demarest S, Berete F, Charafeddine R, Van der Heyden J. Gezondheidsenquête 2018: Methodologie. Report No. D/2019/14.440/34. 2019. https://www.gezondheidsenquete.be.
Ficheux AS, Wesolek NG, Chevillotte G, Roudot AC. Consumption of cosmetic products by the French population. First part: Frequency data. Food and Chemical Toxicology. 2015;78:159–169.
Ficheux AS, Chevillotte G, Wesolek N, Morisset T, Dornic, N. Bernard A, et al. Consumption of cosmetic products by the French population second part: Amount data. Food and Chemical Toxicology. 2016;90:130–141.