Advertisement

Benchmark dose calculation for ordered categorical responses with multiple endpoints

  • Chu-Chih ChenEmail author
  • Yin-Han Wang
Original Paper
  • 42 Downloads

Abstract

The benchmark dose (BMD) approach for the exposure limit in the risk assessment of cancer and non-cancer endpoints is well established; it is often based on dose–response modeling of the most critical or the most sensitive outcome. However, neither the most critical endpoint nor the most sensitive endpoint may necessarily be representative of the overall toxic effects. To have a whole picture, it is preferable to express responses for different endpoints with equivalent severity levels and integrate them into one analysis framework. In this paper, we derive BMD in the case of multivariate ordered categorical responses such as none, mild, adverse, and severe based on structural equation models (SEMs). First, for each of the ordered categorical responses, we obtain a latent continuous variable based on fictitious cutoffs of a standard normal distribution. Second, we use SEMs to integrate the multiple continuous variables into a single latent continuous variable and derive the corresponding BMD. We employed a Bayesian statistical approach using Markov chain Monte Carlo simulations to obtain the parameter estimates of the latent variables, SEMs, and the corresponding BMD. We illustrate the proposed procedure by simulation studies and analysis of an experimental study of acrylamide exposure in mice with multivariate endpoints of different severity levels.

Keywords

Categorical regression Latent variable Markov chain Monte Carlo simulation Multinomial distribution Structural equation models 

Notes

Acknowledgements

This research was funded by the Grants MOST 103-2118-M-400-002 from the Ministry of Science and Technology and PH-106-PP-09 from National Health Research Institutes. The authors declare they have no actual or potential competing financial interests.

Supplementary material

477_2018_1580_MOESM1_ESM.docx (24 kb)
Supplementary material 1 (DOCX 23 kb)

References

  1. Beck B, Conolly RB, Dourson ML et al (1993) Improvements in quantitative noncancer risk assessment. Fundam Appl Toxicol 20:1–14CrossRefGoogle Scholar
  2. Budtz-Jørgensen E (2007) Estimation of the benchmark dose by structural equation models. Biostatistics 8:675–688CrossRefGoogle Scholar
  3. Budtz-Jørgensen E, Keiding N, Grandjean P, Weihe P (2002) Estimation of health effects of prenatal methylmercury exposure using structural equation models. Environ Health 1:2CrossRefGoogle Scholar
  4. Chen CC, Chen JJ (2014) Benchmark dose calculation for ordered categorical responses. Risk Anal 34(8):1435–1447CrossRefGoogle Scholar
  5. Chiu W, Slob W (2015) A unified probabilistic framework for dose-response assessment of human health effects. Environ Health Perspect 123(12):1241–1254CrossRefGoogle Scholar
  6. Crump KS (1984) A new method for determining allowable daily intakes. Fundam Appl Toxicol 4:854–871CrossRefGoogle Scholar
  7. Crump KS, Kjellström T, Shipp AM, Silvers A, Stewart A (1998) Influence of a prenatal mercury exposure upon stochastic and psychological test performance: benchmark analysis of a New Zealand cohort. Risk Anal 18:701–713CrossRefGoogle Scholar
  8. Crump KS, Van Landingham C, Shamlaye C et al (2000) Benchmark concentrations for methylmercury obtained from the Seychelles child development study. Environ Health Perspect 108:257–263CrossRefGoogle Scholar
  9. Dourson ML, Teuschler LK, Durkin PR, Stiteler WM (1997) Category regression of toxicity data: a case study using aldicarb. Regul Toxicol Pharmacol 25:121–129CrossRefGoogle Scholar
  10. Gibson MC, deMonsabert SM, Orme-Zavalata J (1997) Comparison of noncancer risk assessment approaches for use in deriving drinking water criteria. Regul Toxicol Pharmacol 26:243–256CrossRefGoogle Scholar
  11. Gift JS, McGaughy R, Singh DV, Sonawane B (2008) Health assessment of phosgene: approaches for derivation of reference concentration. Regul Toxicol Pharmacol 51:98–107CrossRefGoogle Scholar
  12. Haber L, Strickland JA, Guth DJ (2001) Categorical regression analysis of toxicity data. Comments Toxicol 7:437–452Google Scholar
  13. Hertzberg RC (1989) Extrapolation and scaling of animal data to humans: fitting a model to categorical response data with application to species extrapolation of toxicology. Health Phys 57:405–409CrossRefGoogle Scholar
  14. Hertzberg RC, Dourson ML (1993) Using categorical regression instead of a NOAEL to characterize a toxicologist’s judgment in noncancer risk assessment. In: Ayyub BM (ed) Proceedings of the second international symposium on uncertainty modeling and analysis, College Park, MD. IEEE Computer Society Press, Los Alamitos, CA, pp 254–261Google Scholar
  15. Hertzberg RC, Miller M (1985) A statistical model for species extrapolating using categorical response data. Toxicol Ind Health 1(4):43–63CrossRefGoogle Scholar
  16. Hsiao IL, Wu C, Huang YJ, Chimeddulam D, Wu KY (2016) Probabilistic assessment of aggregate risk for bisphenol A by integrating the currently available environmental data. Stoch Environ Res Risk Assess 30:1851–1861CrossRefGoogle Scholar
  17. Johnson KA, Gorzinski SJ, Bodner KM et al (1986) Chronic toxicity and oncogenicity study on acrylamide incorporated in the drinking water of Fischer 344 rats. Toxicol Appl Pharmacol 85:154–168CrossRefGoogle Scholar
  18. Lee SY, Tang NH (2006) Bayesian analysis of structural equation models with mixed exponential family and ordered categorical data. Br J Math Stat Psychol 59:151–172CrossRefGoogle Scholar
  19. Lee HK, Yeh YY, Chen WM (2006) Cancer risk analysis and assessment of trihalomethanes in drinking water. Stoch Environ Res Risk Assess 21:1–13CrossRefGoogle Scholar
  20. Lu TY, Poon WY, Cheung SH (2015) Multiple comparisons with a control for a latent variable model with ordered categorical responses. Stat Methods Med Res 24(6):949–967CrossRefGoogle Scholar
  21. National Research Council (2009) Science and decisions. The National Academies Press, WashingtonGoogle Scholar
  22. Strickland JA, Foureman GL (2002) US EPA’s acute reference exposure methodology for acute inhalation exposures. Sci Total Environ 288:51–63CrossRefGoogle Scholar
  23. U.S. Environmental Protection Agency (2010) Integrated Risk Information System (IRIS) Chemical Assessment Summary: Acrylamide; CASRN 79-06-1. http://cfpub.epa.gov/ncea/iris/iris_documents/documents/subst/0286_summary.Pdf. Accessed 10 Apr 2017
  24. U.S. Environmental Protection Agency (2017a) categorical regression analysis CatReg 3.1. U.S. EPA National Center for Environmental Assessment, Washington, DC. http://www.epa.gov/bmds/catreg. Accessed 5 July 2017
  25. U.S. Environmental Protection Agency (2017b) Benchmark Dose Software (BMDS) Version 2.7. U.S. EPA National Center for Environmental Assessment, Washington, DC. http://www.epa.gov/bmds. Accessed 3 Dec 2017
  26. U.S. National Toxicology Program (2012) Technical report on the toxicology and carcinogenesis studies on acrylamide (CAS No. 79-06-1) in F344/N rats and B6C3F1 mice (feed and drinking water studies). NTP TR 575. NC: Research Triangle Park, U.S. NTP. http://ntp.niehs.nih.gov/ntp/htdocs/lt_rpts/tr575_508.pdf. Accessed 8 Oct 2016
  27. van Wijngaarden E, Beck C, Shamlaye CF et al (2006) Benchmark concentrations for methyl mercury obtained from the 9-year follow-up of the Seychelles child development study. NeuroToxicology 27:702–709CrossRefGoogle Scholar
  28. van Wijngaarden E, Myers GJ, Thurston SW, Shamlaye CF, Davidson PW (2009) Interpreting epidemiological evidence in the presence of multiple endpoints: an alternative analytic approach using the 9-year follow-up of the Seychelles child development study. Int Arch Occup Environ Health 82:1031–1041CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Division of Biostatistics and Bioinformatics, Institute of Population Health SciencesNational Health Research InstitutesMiaoliTaiwan

Personalised recommendations