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

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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.

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

First available in Project Euclid: 27 December 2012

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Patel, Trina; Telesca, Donatello; George, Saji; Nel, André E. Toxicity profiling of engineered nanomaterials via multivariate dose-response surface modeling. Ann. Appl. Stat. 6 (2012), no. 4, 1707--1729. doi:10.1214/12-AOAS563.

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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.