Walter W. Piegorsch

The University of Arizona, Tucson, Arizona, United States

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Publications (156)243.66 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.
    Full-text · Article · Sep 2015 · Scandinavian Journal of Statistics
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    ABSTRACT: Motivation: The conventional approach to personalized medicine relies on molecular data analytics across multiple patients. The path to precision medicine lies with molecular data analytics that can discover interpretable single-subject signals (N-of-1). We developed a global framework, N-of-1-pathways, for a mechanistic-anchored approach to single-subject gene expression data analysis. We previously employed a metric that could prioritize the statistical significance of a deregulated pathway in single subjects, however, it lacked in quantitative interpretability (e.g. the equivalent to a gene expression fold-change). Results: In this study, we extend our previous approach with the application of statistical Mahalanobis distance (MD) to quantify personal pathway-level deregulation. We demonstrate that this approach, N-of-1-pathways Paired Samples MD (N-OF-1-PATHWAYS-MD), detects deregulated pathways (empirical simulations), while not inflating false-positive rate using a study with biological replicates. Finally, we establish that N-OF-1-PATHWAYS-MD scores are, biologically significant, clinically relevant and are predictive of breast cancer survival (P < 0.05, n = 80 invasive carcinoma; TCGA RNA-sequences). Conclusion: N-of-1-pathways MD provides a practical approach towards precision medicine. The method generates the magnitude and the biological significance of personal deregulated pathways results derived solely from the patient's transcriptome. These pathways offer the opportunities for deriving clinically actionable decisions that have the potential to complement the clinical interpretability of personal polymorphisms obtained from DNA acquired or inherited polymorphisms and mutations. In addition, it offers an opportunity for applicability to diseases in which DNA changes may not be relevant, and thus expand the 'interpretable 'omics' of single subjects (e.g. personalome).
    Full-text · Article · Jun 2015 · Bioinformatics
  • Source
    Walter W. Piegorsch
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    ABSTRACT: This article discusses estimation of low-dose “benchmark” points in environmental risk analysis. Focus is on the increasing recognition that model uncertainty and misspecification can drastically affect point estimators and confidence limits built from limited dose–response data, which in turn can lead to imprecise risk assessments with uncertain, even dangerous, policy implications. Some possible remedies are mentioned, including use of parametric model averaging and nonparametric dose–response analysis.
    Preview · Article · Dec 2014
  • Walter W. Piegorsch · Peter Guttorp

    No preview · Article · Dec 2014 · Environmetrics
  • Source
    Edsel A. Pena · Wensong Wu · Walter Piegorsch · Ronald W. West · Lingling An
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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.
    Full-text · Article · Nov 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.
    Preview · Article · Jun 2014 · Environmetrics
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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.
    No preview · Article · Apr 2014 · Environmental and Ecological Statistics
  • Source
    Qijun Fang · Walter W. Piegorsch · Susan J. Simmons · Xiaosong Li · Cuixian Chen · Yishi Wang
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    ABSTRACT: An important objective in biomedical and environmental risk assessment is estimation of minimum exposure levels that induce a pre-specified adverse response in a target population. The exposure points in such settings are typically referred to as benchmark doses (BMDs). Parametric Bayesian estimation for finding BMDs has grown in popularity, and a large variety of candidate dose-response models is available for applying these methods. Each model can possess potentially different parametric interpretation(s), however. We present reparameterized dose-response models that allow for explicit use of prior information on the target parameter of interest, the BMD. We also enhance our Bayesian estimation technique for BMD analysis by applying Bayesian model averaging to produce point estimates and (lower) credible bounds, overcoming associated questions of model adequacy when multimodel uncertainty is present. An example from carcinogenicity testing illustrates the calculations. © 2015, The International Biometric Society.
    Full-text · Article · Feb 2014 · Biometrics

  • No preview · Book · Dec 2013
  • 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.
    Full-text · Article · Sep 2013 · Biometrical Journal
  • Linda J. Young · Walter W. Piegorsch · Peter Guttorp

    No preview · Article · Aug 2013 · Environmetrics
  • 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.
    No preview · Article · May 2013 · Risk Analysis
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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.
    No preview · Article · May 2013 · Environmetrics
  • 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.
    No preview · Article · Apr 2013 · Journal of Statistical Computation and Simulation
  • Walter W. Piegorsch

    No preview · Chapter · Jan 2013
  • 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.
    No preview · Article · Dec 2012 · Environmetrics
  • 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.
    No preview · Article · Dec 2012 · Biometrics
  • [Show abstract] [Hide abstract]
    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.
    No preview · Article · Dec 2012 · Environmetrics
  • S.L. Cutter · C.T. Emrich · J.T. Mitchell · W.W. Piegorsch · M.M. Smith · L. Weber
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    ABSTRACT: Hurricane Katrina slammed into the Gulf Coast in August 2005 with devastating consequences. Almost all analyses of the disaster have been dedicated to the way the hurricane affected New Orleans. This volume examines the impact of Katrina on southern Mississippi. While communities along Mississippi's Gulf Coast shared the impact, their socioeconomic and demographic compositions varied widely, leading to different types and rates of recovery. This volume furthers our understanding of the pace of recovery and its geographic extent, and explores the role of inequalities in the recovery process and those antecedent conditions that could give rise to a “recovery divide. ” It will be especially appealing to researchers and advanced students of natural disasters and policy makers dealing with disaster consequences and recovery. © Susan L. Cutter, Christopher T. Emrich, Jerry T. Mitchell, Walter W. Piegorsch, Mark M. Smith, and Lynn Weber 2014.
    No preview · Article · Jan 2012
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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.
    No preview · Article · Jan 2012 · Environmental and Molecular Mutagenesis

Publication Stats

2k Citations
243.66 Total Impact Points

Institutions

  • 2007-2015
    • The University of Arizona
      • Department of Mathematics
      Tucson, Arizona, United States
  • 1991-2008
    • Miami University
      • Department of Mathematics
      Oxford, OH, United States
  • 1993-2007
    • University of South Carolina
      • • Department of Geography
      • • Department of Statistics
      Columbia, South Carolina, United States
  • 2002
    • John Wiley And Sons
      New York City, New York, United States
  • 1998
    • University of North Carolina at Chapel Hill
      North Carolina, United States
  • 1985-1994
    • National Institute of Environmental Health Sciences
      • • Laboratory of Molecular Genetics (LMG)
      • • Cellular & Molecular Pathology Branch
      Durham, North Carolina, United States
  • 1992
    • Oak Ridge National Laboratory
      • Physics Division
      Oak Ridge, Florida, United States
  • 1990
    • Princeton University
      Princeton, New Jersey, United States
  • 1989
    • Cornell University
      Итак, New York, United States