The Annals of Applied Statistics

Toxicity profiling of engineered nanomaterials via multivariate dose-response surface modeling

Trina Patel, Donatello Telesca, Saji George, and André E. Nel

Full-text: Access denied (no subscription detected)In 2007, access to the Annals of Applied Statistics was open. Beginning in 2008, you must hold a subscription or be a member of the IMS to view the full journal. For more information on subscribing, please visit: http://imstat.org/orders.If you are already an IMS member, you may need to update your Euclid profile following the instructions here: http://imstat.org/publications/eaccess.htm.

Abstract

New generation in vitro high-throughput screening (HTS) assays for the assessment of engineered nanomaterials provide an opportunity to learn how these particles interact at the cellular level, particularly in relation to injury pathways. These types of assays are often characterized by small sample sizes, high measurement error and high dimensionality, as multiple cytotoxicity outcomes are measured across an array of doses and durations of exposure. In this paper we propose a probability model for the toxicity profiling of engineered nanomaterials. A hierarchical structure is used to account for the multivariate nature of the data by modeling dependence between outcomes and thereby combining information across cytotoxicity pathways. In this framework we are able to provide a flexible surface-response model that provides inference and generalizations of various classical risk assessment parameters. We discuss applications of this model to data on eight nanoparticles evaluated in relation to four cytotoxicity parameters.

Article information

Source
Ann. Appl. Stat. Volume 6, Number 4 (2012), 1707-1729.

Dates
First available in Project Euclid: 27 December 2012

Permanent link to this document
http://projecteuclid.org/euclid.aoas/1356629057

Digital Object Identifier
doi:10.1214/12-AOAS563

Zentralblatt MATH identifier
06141545

Mathematical Reviews number (MathSciNet)
MR3058681

Citation

Patel, Trina; Telesca, Donatello; George, Saji; Nel, André E. Toxicity profiling of engineered nanomaterials via multivariate dose-response surface modeling. The Annals of Applied Statistics 6 (2012), no. 4, 1707--1729. doi:10.1214/12-AOAS563. http://projecteuclid.org/euclid.aoas/1356629057.


Export citation

References

  • Baladandayuthapani, V., Mallick, B. K. and Carroll, R. J. (2005). Spatially adaptive Bayesian penalized regression splines (P-splines). J. Comput. Graph. Statist. 14 378–394.
  • Besag, J. and Higdon, D. (1999). Bayesian analysis of agricultural field experiments. J. R. Stat. Soc. Ser. B Stat. Methodol. 61 691–746.
  • Calabrese, E. and Baldwin, L. (2003). Toxicology rethinks its central belief. Nature 421 691–692.
  • Emmens, C. (1940). The dose-response relation for certain principles of the pituitary gland, and of the serum and urine of pregnancy. Journal of Endocrinology 2 194–225.
  • Finney, D. J. (1979). Bioassay and the practice of statistical inference. Internat. Statist. Rev. 47 1–12.
  • Gelfand, A. E. and Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85 398–409.
  • Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models (comment on article by Browne and Draper). Bayesian Anal. 1 515–533 (electronic).
  • Geman, S. and Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 6 721–741.
  • George, S., Pokhrel, S., Xia, T., Gilbert, B., Ji, Z., Schowalter, M., Rosenauer, A., Damoiseaux, R., Bradley, K., Madler, L. and Nel, A. (2009). Use of a rapid cytotoxicity screening approach to engineer a safer zinc oxide nanoparticle through iron doping. ACS Nano 4 15–29.
  • George, S., Xia, T., Rallo, R., Zhao, Y., Ji, Z., Lin, S., Wang, X., Zhang, H., France, B., Schoenfeld, D., Damoiseaux, R., Liu, R., Lin, S., Bradley, K., Cohen, Y. and Nel, A. (2011). Use of a high-throughput screening approach coupled with in vivo zebrafish embryo screening to develop hazard ranking for engineered nanomaterials. ACS Nano 5 1805–1817.
  • Geys, H., Regan, M., Catalano, P. and Molenberghs, G. (2001). Two latent variable risk assessment approaches or mixed continuous and discrete outcomes from developmental toxicity data. J. Agric. Biol. Environ. Stat. 6 340–355.
  • Gneiting, T., Balabdaoui, F. and Raftery, A. E. (2007). Probabilistic forecasts, calibration and sharpness. J. R. Stat. Soc. Ser. B Stat. Methodol. 69 243–268.
  • Green, P. J. (1995). Reversible jump Markov chain Monte Carlo computation and Bayesian model determination. Biometrika 82 711–732.
  • Hastie, T. and Tibshirani, R. (1986). Generalized additive models. Statist. Sci. 1 297–318.
  • Hill, A. (1910). The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. The Journal of Physiology 40 iv–vii.
  • Hoheisel, J. (2006). Microarray technology: Beyond transcript profiling and genotype analysis. Nature Review Genetics 7 200–210.
  • Kahru, A. and Dubourguier, H. (2009). From ecotoxicology to nanoecotoxicolgy. Toxicology 269 105–119.
  • Kong, M. and Eubank, R. L. (2006). Monotone smoothing with application to dose-response curve. Comm. Statist. Simulation Comput. 35 991–1004.
  • Li, C.-S. and Hunt, D. (2004). Regression splines for threshold selection with application to a random-effects logistic dose-response model. Comput. Statist. Data Anal. 46 1–9.
  • Maynard, A., Aitken, R., Butz, T., Colvin, V., Donaldson, K., Oberdörster, G., Philbert, M., Ryan, J., Seaton, A., Stone, V., Tinkle, S., Tran, L., Walker, N. and Warheit, D. (2006). Safe handling of nanotechnology. Nature Biotechnology 444 267–268.
  • Meng, H., Liong, M., Xia, T., Li, Z., Ji, Z. Zink, J. and Nel, A. E. (2010). Engineered design of mesoporous silica nanoparticles to deliver doxorubicin and p-glycoprotein sirna to overcome drug resistance in a cancer cell line. ACS Nano 4 4539–4550.
  • Nel, A., Xia, T., Mädler, L. and Li, N. (2006). Toxic potential of materials at the nanolevel. Science 311 622–627.
  • Nel, A., Mädler, L., Velegol, D., Xia, T., Hoek, E., Somasundaran, P., Klaessig, F., Castranova, V. and Thompson, M. (2009). Understanding biophysicochemical interactions at the nano-bio interface. Nature Materials 8 543–557.
  • Patel, T., Telesca, D., George, S. and Nel, A. (2012). Supplement to “Toxicity profiling of engineered nanomaterials via multivariate dose-response surface modeling.” DOI:10.1214/12-AOAS563SUPP.
  • Plummerm, M., Best, N., Cowles, K. and Vines, K. (2006). CODA: Convergence diagnosis and output analysis for MCMC. R News 6 7–11.
  • Ramsay, J. (1988). Monotone regression splines in action. Statist. Sci. 3 425–461.
  • Regan, M. M. and Catalano, P. J. (1999). Bivariate dose-response modeling and risk estimation in developmental toxicology. J. Agric. Biol. Environ. Stat. 4 217–237.
  • Ritz, C. (2010). Toward a unified approach to dose-response modeling in ecotoxicology. Environ. Toxicol. Chem. 29 220–229.
  • Roberts, G. O. and Rosenthal, J. S. (2001). Optimal scaling for various Metropolis–Hastings algorithms. Statist. Sci. 16 351–367.
  • Scott, J. G. and Berger, J. O. (2006). An exploration of aspects of Bayesian multiple testing. J. Statist. Plann. Inference 136 2144–2162.
  • Severini, T. A. and Staniswalis, J. G. (1994). Quasi-likelihood estimation in semiparametric models. J. Amer. Statist. Assoc. 89 501–511.
  • Stanley, S., Westly, E., Pittet, M., Subramanian, A., Schreiber, S. and Weissleder, R. (2008). Pertubational profiling of nanomaterial biologic activity. Proc. Natl. Acad. Sci. USA 105 7387–7392.
  • Stern, S. and McNeil, S. (2008). Nanotechnology safely concerns revisited. Toxicological Sciences 101 4–21.
  • Tierney, L. (1994). Markov chains for exploring posterior distributions. Ann. Statist. 22 1701–1762.
  • West, M. (1984). Outlier models and prior distributions in Bayesian linear regression. J. Roy. Statist. Soc. Ser. B 46 431–439.
  • White, R. E. (2000). High-throughput screening in drug metabolism and pharmacokinetic support of drug discovery. Annu. Rev. Pharmacol. Toxicol. 40 133–157.
  • Xia, T., Kovochich, M., Brant, J., Hotze, M., Sempf, J., Oberley, T., Sioutas, C., Yeh, J., Wiesner, M. and AE, N. (2006). Comparison of the abilities of ambient and manufactured nanoparticles to induce cellular toxicity according to an oxidative stress paradigm. Nano Letters 6 1794–1807.
  • Yu, Z.-F. and Catalano, P. J. (2005). Quantitative risk assessment for multivariate continuous outcomes with application to neurotoxicology: The bivariate case. Biometrics 61 757–766.

Supplemental materials

  • Supplementary material: Supplementary Appendices. Full conditional distributions for the model described in Section 2 are provided in the supplemental article, Appendix A. Spline coefficients $\boldsymbol{\beta},\boldsymbol{\gamma}$ and $\boldsymbol{\delta}$ are directly sampled from their conditional posterior distributions via direct simulation (Gibbs step). To assess estimation of the model presented in Section 2, we present a simulation study in the supplemental article, Appendix B. The dose and time kinetics were simulated from various parametric functions. Both canonical and noncanonical profiles that are reasonably interpretable under a toxicity framework were generated. In addition, we assess sensitivity of the model results to our choice of prior parameters for population level interior knot parameters $\boldsymbol{\lambda}_{\boldsymbol{\phi}_{i}}$ and $\boldsymbol{\lambda}_{\boldsymbol{\phi}_{i}}$. In the supplemental article, Appendix C, we provide an additional sensitivity analysis assessing model results to our choice of prior model for the change-point parameters. Alternative prior models assessed include a truncated normal prior and a parameterization of the bivariate beta prior that results in a uniform prior on the simplex. The supplemental article, Appendix D, presents results associated with inference on the 6 remaining particles not presented in Section 4.3. Finally, Appendix E discusses model assessment and goodness-of-fit diagnostics associated with the model described in Section 2.