Walter W. Piegorsch

The University of Arizona, Tucson, Arizona, United States

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Publications (130)210.65 Total impact

  • Source
    Lizhen Lin, Walter W Piegorsch, Rabi Bhattacharya
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    ABSTRACT: We propose a new method for risk-analytic benchmark dose (BMD) estimation in a dose-response setting when the responses are measured on a continuous scale. For each dose level d, the observation X(d) is assumed to follow a normal distribution: N µ(d), σ 2 . No specific parametric form is imposed upon the mean µ(d), however. Instead, nonparametric maximum likelihood estimates of µ(d) and σ are obtained under a monotonicity constraint on µ(d). For purposes of quantitative risk assessment, a 'hybrid' form of risk function is defined for any dose d as R(d) = P [X(d) < c], where c > 0 is a constant independent of d. The BMD is then determined by inverting the additional risk function R A (d) = R(d) − R(0) at some specified value of benchmark response (BMR). Asymptotic theory for the point estimators is derived and a finite-sample study is conducted, using both real and simulated data. When a large number of doses is available, we propose an adaptive grouping method for estimating the BMD, which is shown to have optimal MISE (mean integrated squared error) under appropriate designs.
    Scandinavian Journal of Statistics 12/2014; · 1.06 Impact Factor
  • Walter W. Piegorsch, Peter Guttorp
    Environmetrics 12/2014; 25(8). · 1.49 Impact Factor
  • Source
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    ABSTRACT: This paper describes several approaches for estimating the benchmark dose (BMD) in a risk assessment study with quantal dose-response data and when there are competing model classes for the dose-response function. Strategies involving a two-step approach, a model-averaging approach, a focused-inference approach, and a nonparametric approach based on a PAVA-based estimator of the dose-response function are described and compared. Attention is raised to the perils involved in data "double-dipping" and the need to adjust for the model-selection stage in the estimation procedure. Simulation results are presented comparing the performance of five model selectors and eight BMD estimators. An illustration using a real quantal-response data set from a carcinogenecity study is provided.
    11/2014;
  • Source
    Qijun Fang, Walter W. Piegorsch, Katherine Y. Barnes
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    ABSTRACT: An important objective in environmental risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs) that induce a pre-specified Benchmark Response (BMR) in a target population. Established inferential approaches for BMD analysis typically involve one-sided, frequentist confidence limits, leading in practice to what are called Benchmark Dose Lower Limits (BMDLs). Appeal to Bayesian modeling and credible limits for building BMDLs is far less developed, however. Indeed, for the few existing forms of Bayesian BMDs, informative prior information is seldom incorporated. We develop reparameterized quantal-response models that explicitly describe the BMD as a target parameter. Our goal is to obtain an improved estimation and calculation archetype for the BMD and for the BMDL, by employing quantifiable prior belief to represent parameter uncertainty in the statistical model. Implementation is facilitated via a Monte Carlo-based adaptive Metropolis (AM) algorithm to approximate the posterior distribution. An example from environmental carcinogenicity testing illustrates the calculations.
    06/2014;
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    ABSTRACT: Benchmark dose estimation is widely used in various regulatory and industrial settings to estimate acceptable exposure levels to hazardous or toxic agents by predefining a level of excess risk (US EPA in Benchmark dose technical guidance document. Technical Report #EPA/100/R-12/001. U.S. Environmental Protection Agency, Washington, DC, 2012). Although benchmark dose estimation is a popular method for identifying exposure levels of agents, there are some limitations and cautions on use of this methodology. One such concern is choice of the underlying risk model. Recently, advances have been made using Bayesian model averaging to improve benchmark dose estimation in the face of model uncertainty. Herein we employ the strategies of Bayesian model averaging to build model averaged estimates for the benchmark dose. The methodology is demonstrated via a simulation study and with real data.
    Environmental and Ecological Statistics 04/2014; 22(1). · 0.97 Impact Factor
  • Source
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    ABSTRACT: An important objective in biomedical risk assessment is estimation of minimum exposure levels that induce a pre-specified adverse response in a target population. The exposure/dose points in such settings are known as Benchmark Doses (BMDs). Recently, parametric Bayesian estimation for finding BMDs has become popular. A large variety of candidate dose-response models is available for applying these methods, however, leading to questions of model adequacy and uncertainty. Here we enhance the Bayesian estimation technique for BMD analysis by applying Bayesian model averaging to produce point estimates and (lower) credible bounds. We include reparameterizations of traditional dose-response models that allow for more-focused use of elicited prior information when building the Bayesian hierarchy. Performance of the method is evaluated via a short simulation study. An example from carcinogenicity testing illustrates the calculations.
    02/2014;
  • Edited by Susan Cutter, 12/2013; Cambridge University Press.
  • Linda J. Young, Walter W. Piegorsch, Peter Guttorp
    Environmetrics 08/2013; 24(5). · 1.49 Impact Factor
  • Source
    Roland C Deutsch, Walter W Piegorsch
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    ABSTRACT: Benchmark analysis is a widely used tool in biomedical and environmental risk analysis. Therein, estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a pre-specified Benchmark Response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This paper demonstrates how the benchmark modeling paradigm can be expanded from the single-agent setting to joint-action, two-agent studies. Focus is on continuous response outcomes. Extending the single-exposure setting, representations of risk are based on a joint-action dose-response model involving both agents. Based on such a model, the concept of a benchmark profile (BMP) – a two-dimensional analog of the single-dose BMD at which both agents achieve the specified BMR – is defined for use in quantitative risk characterization and assessment.
    Biometrical Journal 07/2013; 55(5):741. · 1.15 Impact Factor
  • Walter W Piegorsch, Hui Xiong, Rabi N Bhattacharya, Lizhen Lin
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    ABSTRACT: Estimation of benchmark doses (BMDs) in quantitative risk assessment traditionally is based upon parametric dose-response modeling. It is a well-known concern, however, that if the chosen parametric model is uncertain and/or misspecified, inaccurate and possibly unsafe low-dose inferences can result. We describe a nonparametric approach for estimating BMDs with quantal-response data based on an isotonic regression method, and also study use of corresponding, nonparametric, bootstrap-based confidence limits for the BMD. We explore the confidence limits' small-sample properties via a simulation study, and illustrate the calculations with an example from cancer risk assessment. It is seen that this nonparametric approach can provide a useful alternative for BMD estimation when faced with the problem of parametric model uncertainty.
    Risk Analysis 05/2013; · 2.28 Impact Factor
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    ABSTRACT: An important objective in environmental risk assessment is estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a pre-specified Benchmark Response (BMR) in a dose-response experiment. In such settings, representations of the risk are traditionally based on a specified parametric model. It is a well-known concern, however, that existing parametric estimation techniques are sensitive to the form employed for modeling the dose response. If the chosen parametric model is in fact misspecified, this can lead to inaccurate low-dose inferences. Indeed, avoiding the impact of model selection was one early motivating issue behind development of the BMD technology. Here, we apply a frequentist model averaging approach for estimating benchmark doses, based on information-theoretic weights. We explore how the strategy can be used to build one-sided lower confidence limits on the BMD, and we study the confidence limits' small-sample properties via a simulation study. An example from environmental carcinogenicity testing illustrates the calculations. It is seen that application of this information-theoretic, model averaging methodology to benchmark analysis can improve environmental health planning and risk regulation when dealing with low-level exposures to hazardous agents.
    Environmetrics 05/2013; 24(3):143-157. · 1.49 Impact Factor
  • Roland C. Deutsch, Brian Habing, Walter W. Piegorsch
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    ABSTRACT: Binary response models are often applied in dose–response settings where the number of dose levels is limited. Commonly, one can find cases where the maximum likelihood estimation process for these models produces infinite values for at least one of the parameters, often corresponding to the ‘separated data’ issue. Algorithms for detecting such data have been proposed, but are usually incorporated directly into in the parameter estimation. Additionally, they do not consider the use of asymptotes in the model formulation. In order to study this phenomenon in greater detail, we define the class of specifiably degenerate functions where this can occur (including the popular logistic and Weibull models) that allows for asymptotes in the dose–response specification. We demonstrate for this class that the well-known pool-adjacent-violators algorithm can efficiently pre-screen for non-estimable data. A simulation study demonstrates the frequency with which this problem can occur for various response models and conditions.
    Journal of Statistical Computation and Simulation 04/2013; · 0.71 Impact Factor
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    ABSTRACT: We study the popular benchmark dose (BMD) approach for estimation of low exposure levels in toxicological risk assessment, focusing on dose-response experiments with quantal data. In such settings, representations of the risk are traditionally based on a specified, parametric, dose-response model. It is a well-known concern, however, that uncertainty can exist in specification and selection of the model. If the chosen parametric form is in fact misspecified, this can lead to inaccurate, and possibly unsafe, lowdose inferences. We study the effects of model selection and possible misspecification on the BMD, on its corresponding lower confidence limit (BMDL), and on the associated extra risks achieved at these values, via large-scale Monte Carlo simulation. It is seen that an uncomfortably high percentage of instances can occur where the true extra risk at the BMDL under a misspecified or incorrectly selected model can surpass the target BMR, exposing potential dangers of traditional strategies for model selection when calculating BMDs and BMDLs.
    Environmetrics 12/2012; 23(8):706-716. · 1.49 Impact Factor
  • Walter W Piegorsch, Hui Xiong, Rabi N Bhattacharya, Lizhen Lin
    [Show abstract] [Hide abstract]
    ABSTRACT: An important statistical objective in environmental risk analysis is estimation of minimum exposure levels, called benchmark doses (BMDs), that induce a pre-specified benchmark response in a dose-response experiment. In such settings, representations of the risk are traditionally based on a parametric dose-response model. It is a well-known concern, however, that if the chosen parametric form is misspecified, inaccurate and possibly unsafe low-dose inferences can result. We apply a nonparametric approach for calculating benchmark doses, based on an isotonic regression method for dose-response estimation with quantal-response data (Bhattacharya and Kong, 2007). We determine the large-sample properties of the estimator, develop bootstrap-based confidence limits on the BMDs, and explore the confidence limits' small-sample properties via a short simulation study. An example from cancer risk assessment illustrates the calculations.
    Environmetrics 12/2012; 23(8):717-728. · 1.49 Impact Factor
  • Roland C Deutsch, Walter W Piegorsch
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    ABSTRACT: Summary Benchmark analysis is a widely used tool in public health risk analysis. Therein, estimation of minimum exposure levels, called Benchmark Doses (BMDs), that induce a prespecified Benchmark Response (BMR) is well understood for the case of an adverse response to a single stimulus. For cases where two agents are studied in tandem, however, the benchmark approach is far less developed. This article demonstrates how the benchmark modeling paradigm can be expanded from the single-dose setting to joint-action, two-agent studies. Focus is on response outcomes expressed as proportions. Extending the single-exposure setting, representations of risk are based on a joint-action dose-response model involving both agents. Based on such a model, the concept of a benchmark profile (BMP) - a two-dimensional analog of the single-dose BMD at which both agents achieve the specified BMR - is defined for use in quantitative risk characterization and assessment. The resulting, joint, low-dose guidelines can improve public health planning and risk regulation when dealing with low-level exposures to combinations of hazardous agents.
    Biometrics 12/2012; 68(4):1313-22. · 1.52 Impact Factor
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    ABSTRACT: Propiconazole (PPZ) is a conazole fungicide that is not mutagenic, clastogenic, or DNA damaging in standard in vitro and in vivo genetic toxicity tests for gene mutations, chromosome aberrations, DNA damage, and cell transformation. However, it was demonstrated to be a male mouse liver carcinogen when administered in food for 24 months only at a concentration of 2,500 ppm that exceeded the maximum tolerated dose based on increased mortality, decreased body weight gain, and the presence of liver necrosis. PPZ was subsequently tested for mutagenicity in the Big Blue® transgenic mouse assay at the 2,500 ppm dose, and the result was reported as positive by Ross et al. ([2009]: Mutagenesis 24:149-152). Subsets of the mutants from the control and PPZ-exposed groups were sequenced to determine the mutation spectra and a multivariate clustering analysis method purportedly substantiated the increase in mutant frequency with PPZ (Ross and Leavitt. [2010]: Mutagenesis 25:231-234). However, as reported here, the results of the analysis of the mutation spectra using a conventional method indicated no treatment-related differences in the spectra. In this article, we re-examine the Big Blue® mouse findings with PPZ and conclude that the compound does not act as a mutagen in vivo.
    Environmental and Molecular Mutagenesis 01/2012; 53(1):1-9. · 2.55 Impact Factor
  • Source
    Walter W Piegorsch
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    ABSTRACT: Translational development - in the sense of translating a mature methodology from one area of application to another, evolving area - is discussed for the use of benchmark doses in quantitative risk assessment. Illustrations are presented with traditional applications of the benchmark paradigm in biology and toxicology, and also with risk endpoints that differ from traditional toxicological archetypes. It is seen that the benchmark approach can apply to a diverse spectrum of risk management settings. This suggests a promising future for this important risk-analytic tool. Extensions of the method to a wider variety of applications represent a significant opportunity for enhancing environmental, biomedical, industrial, and socio-economic risk assessments.
    Journal of Risk Research 07/2010; 13(5):653-667. · 1.27 Impact Factor
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    ABSTRACT: Many inferential procedures for generalized linear models rely on the asymptotic normality of the maximum likelihood estimator (MLE). Fahrmeir & Kaufmann (1985, Ann. Stat., 13, 1) present mild conditions under which the MLEs in GLiMs are asymptotically normal. Unfortunately, limited study has appeared for the special case of binomial response models beyond the familiar logit and probit links, and for more general links such as the complementary log-log link, and the less well-known complementary log link. We verify the asymptotic normality conditions of the MLEs for these models under the assumption of a fixed number of experimental groups and present a simple set of conditions for any twice differentiable monotone link function. We also study the quality of the approximation for constructing asymptotic Wald confidence regions. Our results show that for small sample sizes with certain link functions the approximation can be problematic, especially for cases where the parameters are close to the boundary of the parameter space.
    Advances and applications in statistics. 02/2010; 14(2):101-116.
  • Source
    Walter W Piegorsch, A John Bailer
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    ABSTRACT: The combination of information from diverse sources is a common task encountered in computational statistics. A popular label for analyses involving the combination of results from independent studies is meta-analysis. The goal of the methodology is to bring together results of different studies, re-analyze the disparate results within the context of their common endpoints, synthesize where possible into a single summary endpoint, increase the sensitivity of the analysis to detect the presence of adverse effects, and provide a quantitative analysis of the phenomenon of interest based on the combined data. This entry discusses some basic methods in meta-analytic calculations, and includes commentary on how to combine or average results from multiple models applied to the same set of data.
    Wiley interdisciplinary reviews. Computational statistics. 11/2009; 1(3):354-360.
  • Article: Response.
    Walter W Piegorsch, Susan L Cutter
    Risk Analysis 08/2009; · 2.28 Impact Factor

Publication Stats

1k Citations
210.65 Total Impact Points

Institutions

  • 2007–2014
    • The University of Arizona
      • • Department of Mathematics
      • • BIO5 Institute
      Tucson, Arizona, United States
  • 2012
    • University of North Carolina at Greensboro
      • Department of Mathematics & Statistics
      Greensboro, NC, United States
  • 2009
    • Texas A&M University
      • Department of Statistics
      College Station, TX, United States
  • 2008
    • Northern Kentucky University
      • Department of Mathematics & Statistics
      Highland Heights, Kentucky, United States
  • 1993–2008
    • University of South Carolina
      • Department of Statistics
      Columbia, South Carolina, United States
  • 1991–2008
    • Miami University
      • Department of Mathematics
      Oxford, OH, United States
  • 2000
    • The Ohio State University
      Columbus, Ohio, United States
  • 1986–1994
    • National Institute of Environmental Health Sciences
      Durham, North Carolina, United States