Walter W Piegorsch

Interests

Research

Environmental Statistics/Environmetrics, Quantitative Risk Assessment, Informatics for Precision Medicine

Teaching

Statistical Computing, Supervised Learning, Statistical Learning, Environmental Statistics

Courses

Scholarly Contributions

Books

• Piegorsch, W. W., Levine, R. A., Zhang, H., & Lee, T. C. (2022). Computational Statistics in Data Science. Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2015). Statistical Data Analytics.
• Balakrishnan, N., Brandimarte, P., Everitt, B., Molenberghs, G., Piegorsch, W. W., & Ruggeri, F. (2014). Wiley StatsRef: Statistics Reference Online. Chichester: John Wiley & Sons.
• Cutter, S. L., Emrich, C. T., Mitchell, J. T., Piegorsch, W. W., Smith, M. M., & Weber, L. (2014). Hurricane Katrina and the Forgotten Coast of Mississippi. Cambridge: Cambridge University Press.
• Piegorsch, W. W. (2012). Hurricane Katrina and the forgotten coast of Mississippi.
• Piegorsch, W. W. (2009). Gene-nutrient interactions in nutritional epidemiology.
• Piegorsch, W. W. (2005). Analyzing Environmental Data.
• Piegorsch, W. W. (2000). 14 Quantitative potency estimation to measure risk with bio-environmental hazards.
• Piegorsch, W. W. (1994). 15 Environmental biometry: Assessing impacts of environmental stimuli via animal and microbial laboratory studies.

Chapters

• Piegorsch, W. W. (2015). Joint action models. In Wiley StatsRef: Statistics Reference Online. Chichester: John Wiley & Sons. doi:10.1002/9781118445112.stat07719.pub2
• Piegorsch, W. W. (2014). Binary data and quantal response. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat07340). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Dispersion parameter. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat07375). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Distribution function. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat07524). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Environmental mutagenesis, Statistics in. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat03788). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Joint action models. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat07719). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Low-dose extrapolation. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat03804). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Mutagenicity study. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat05476). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Potency estimation. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat03811). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Proportional hazards model: Introduction. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat07448). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Quantal response data. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat07556). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Random effects. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat07558). Chichester: John Wiley & Sons.
• Piegorsch, W. W. (2014). Z-Statistic. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat07427). Chichester: John Wiley & Sons.
• Piegorsch, W. W., & Bailer, A. J. (2014). Combining information. In Wiley StatsRef: Statistics Reference Online(pp doi:10.1002/9781118445112.stat03704). Chichester: John Wiley & Sons.

Journals/Publications

• Aberasturi, D. T., Piegorsch, W. W., Bedrick, E. J., & Lussier, Y. A. (2022). Accounting for extra-binomial variability with differentially expressed genetic pathway data: a collaborative bioinformatic study. Stat, 12, Article No. e518. doi:10.1002/sta4.518
• Liu, J., Piegorsch, W. W., Cutter, S. L., McCaster, R. R., & Schissler, A. G. (2022). Adjusting statistical benchmark risk analysis to account for non-spatial autocorrelation, with application to natural hazard risk assessment. Journal of Applied Statistics, 49, 2349-2369. doi:10.1080/02664763.2021.1904385
• Aberasturi, D., Pouladi, N., Zaim, S. R., Kenost, C., Berghout, J., Piegorsch, W. W., & Lussier, Y. A. (2021). 'Single-subject studies'-derived analyses unveil altered biomechanisms between very small cohorts: implications for rare diseases. Bioinformatics (Oxford, England), 37(Suppl_1), i67-i75.
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  Identifying altered transcripts between very small human cohorts is particularly challenging and is compounded by the low accrual rate of human subjects in rare diseases or sub-stratified common disorders. Yet, single-subject studies (S3) can compare paired transcriptome samples drawn from the same patient under two conditions (e.g. treated versus pre-treatment) and suggest patient-specific responsive biomechanisms based on the overrepresentation of functionally defined gene sets. These improve statistical power by: (i) reducing the total features tested and (ii) relaxing the requirement of within-cohort uniformity at the transcript level. We propose Inter-N-of-1, a novel method, to identify meaningful differences between very small cohorts by using the effect size of 'single-subject-study'-derived responsive biological mechanisms.
• Piegorsch, W. W., McCaster, R. R., & Cutter, S. L. (2021). From terrorism to flooding: how vulnerable is your city?. Significance, 18(1), 22-27. doi:10.1111/1740-9713.01487
• Sans-Fuentes, M. A., & Piegorsch, W. W. (2021). Benchmark dose risk analysis with mixed-factor quantal data in environmental risk assessment. Environmetrics, 32(5), Article No. e2677.
• Wheeler, M. W., Piegorsch, W. W., & Bailer, A. J. (2019). Quantal Risk Assessment Database: A Database for Exploring Patterns in Quantal Dose-Response Data in Risk Assessment and its Application to Develop Priors for Bayesian Dose-Response Analysis. Risk analysis : an official publication of the Society for Risk Analysis, 39(3), 616-629.
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  Quantitative risk assessments for physical, chemical, biological, occupational, or environmental agents rely on scientific studies to support their conclusions. These studies often include relatively few observations, and, as a result, models used to characterize the risk may include large amounts of uncertainty. The motivation, development, and assessment of new methods for risk assessment is facilitated by the availability of a set of experimental studies that span a range of dose-response patterns that are observed in practice. We describe construction of such a historical database focusing on quantal data in chemical risk assessment, and we employ this database to develop priors in Bayesian analyses. The database is assembled from a variety of existing toxicological data sources and contains 733 separate quantal dose-response data sets. As an illustration of the database's use, prior distributions for individual model parameters in Bayesian dose-response analysis are constructed. Results indicate that including prior information based on curated historical data in quantitative risk assessments may help stabilize eventual point estimates, producing dose-response functions that are more stable and precisely estimated. These in turn produce potency estimates that share the same benefit. We are confident that quantitative risk analysts will find many other applications and issues to explore using this database.
• Piegorsch, W. W. (2018). Autologistic models for benchmark risk or vulnerability assessment of urban terrorism outcomes. Journal of the Royal Statistical Society. Series A: Statistics in Society.
• Peña, E. A., Wu, W., Piegorsch, W. W., West, R. W., & An, L. (2017). Model Selection and Estimation with Quantal-Response Data in Benchmark Risk Assessment. Risk analysis : an official publication of the Society for Risk Analysis, 37(4), 716-732. doi:10.1111_risa.12644
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  This article 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.
• Piegorsch, W. W. (2017). Are p-values under attack? Contribution to the discussion of 'A critical evaluation of the current "p-value controversy" '. Biometrical journal. Biometrische Zeitschrift, 59(5), 889-891.
• Schissler, A. G., Li, Q., Chen, J. L., Kenost, C., Achour, I., Billheimer, D. D., Li, H., Piegorsch, W. W., & Lussier, Y. A. (2016). Analysis of aggregated cell-cell statistical distances within pathways unveils therapeutic-resistance mechanisms in circulating tumor cells. Bioinformatics (Oxford, England), 32(12), i80-i89.
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  As 'omics' biotechnologies accelerate the capability to contrast a myriad of molecular measurements from a single cell, they also exacerbate current analytical limitations for detecting meaningful single-cell dysregulations. Moreover, mRNA expression alone lacks functional interpretation, limiting opportunities for translation of single-cell transcriptomic insights to precision medicine. Lastly, most single-cell RNA-sequencing analytic approaches are not designed to investigate small populations of cells such as circulating tumor cells shed from solid tumors and isolated from patient blood samples.
• Fang, Q., Piegorsch, W. W., Simmons, S. J., Li, X., Chen, C., & Wang, Y. (2015). Bayesian model-averaged benchmark dose analysis via reparameterized quantal-response models. Biometrics, 71(4), 1168-75.
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  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.
• Piegorsch, W. W. (2015). Bayesian benchmark dose analysis. Environmetrics.
• Piegorsch, W. W. (2015). Bayesian model averaging for benchmark dose estimation. Environmental and Ecological Statistics.
• Piegorsch, W. W. (2015). Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data. Scandinavian Journal of Statistics.
• Schissler, A. G., Gardeux, V., Li, Q., Achour, I., Li, H., Piegorsch, W. W., & Lussier, Y. A. (2015). Dynamic changes of RNA-sequencing expression for precision medicine: N-of-1-pathways Mahalanobis distance within pathways of single subjects predicts breast cancer survival. Bioinformatics (Oxford, England), 31(12), i293-302.
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  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).
• Piegorsch, W. W. (2014). A pool-adjacent-violators-algorithm approach to detect infinite parameter estimates in one-regressor dose-response models with asymptotes. Journal of Statistical Computation and Simulation.
• Piegorsch, W. W. (2014). Benchmark dose analysis via nonparametric regression modeling. Risk Analysis.
• Piegorsch, W. W. (2014). Environmetrics silver anniversary special issue. Environmetrics.
• Piegorsch, W. W. (2014). Model uncertainty in environmental dose-response risk analysis. Statistics and Public Policy, 1(1), 79-85.
• Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. (2014). Benchmark Dose Analysis via Nonparametric Regression Modeling. Risk analysis : an official publication of the Society for Risk Analysis, 34(1), 135-51.
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  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.
• Deutsch, R. C., & Piegorsch, W. W. (2013). Benchmark dose profiles for joint-action continuous data in quantitative risk assessment. Biometrical journal. Biometrische Zeitschrift, 55(5), 741-54.
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  Benchmark analysis is a widely used tool in biomedical and environmental risk assessment. 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 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-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.
• Piegorsch, W. W. (2013). In memory of George Casella. Environmetrics.
• Piegorsch, W. W., An, L., Wickens, A. A., West, R. W., Peña, E. A., & Wu, W. (2013). Information-theoretic model-averaged benchmark dose analysis in environmental risk assessment. Environmetrics, 24(3), 143-157.
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  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.
• Deutsch, R. C., & Piegorsch, W. W. (2012). Benchmark dose profiles for joint-action quantal data in quantitative risk assessment. Biometrics, 68(4), 1313-22.
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  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.
• Piegorsch, W. W., Xiong, H., Bhattacharya, R. N., & Lin, L. (2012). Nonparametric estimation of benchmark doses in environmental risk assessment. Environmetrics, 23(8), 717-728.
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  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.
• Shane, B. S., Zeiger, E., Piegorsch, W. W., Booth, E. D., Goodman, J. I., & Peffer, R. C. (2012). Re-evaluation of the Big Blue® mouse assay of propiconazole suggests lack of mutagenicity. Environmental and molecular mutagenesis, 53(1), 1-9.
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  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.
• West, R. W., Piegorsch, W. W., Peña, E. A., An, L., Wu, W., Wickens, A. A., Xiong, H., & Chen, W. (2012). The Impact of Model Uncertainty on Benchmark Dose Estimation. Environmetrics, 23(8), 706-716.
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  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.
• Deutsch, R. C., Grego, J. M., Habing, B., & Piegorsch, W. W. (2010). Maximum likelihood estimation with binary-data regression models: small-sample and large-sample features. Advances and applications in statistics, 14(2), 101-116.
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  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.
• Guttorp, P., & Piegorsch, W. W. (2010). Editorial. Environmetrics, 21(1), 1-2.
• Piegorsch, W., & Piegorsch, W. W. (2010). Translational benchmark risk analysis. Journal of risk research, 13(5).
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  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.
• Buckley, B. E., Piegorsch, W. W., & West, R. W. (2009). Confidence limits on one-stage model parameters in benchmark risk assessment. Environmental and ecological statistics, 16(1), 53-62.
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  In modern environmental risk analysis, inferences are often desired on those low dose levels at which a fixed benchmark risk is achieved. In this paper, we study the use of confidence limits on parameters from a simple one-stage model of risk historically popular in benchmark analysis with quantal data. Based on these confidence bounds, we present methods for deriving upper confidence limits on extra risk and lower bounds on the benchmark dose. The methods are seen to extend automatically to the case where simultaneous inferences are desired at multiple doses. Monte Carlo evaluations explore characteristics of the parameter estimates and the confidence limits under this setting.
• Liu, W., Hayter, A. J., & Piegorsch, W. W. (2009). Comparison of Hyperbolic and Constant Width Simultaneous Confidence Bands in Multiple Linear Regression under MVCS Criterion. Journal of multivariate analysis, 100(7), 1432-1439.
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  A simultaneous confidence band provides useful information on the plausible range of the unknown regression model, and different confidence bands can often be constructed for the same regression model. For a simple regression line, it is proposed in Liu and Hayter (2007) to use the area of the confidence set that corresponds to a confidence band as an optimality criterion in comparison of confidence bands; the smaller is the area of the confidence set, the better is the corresponding confidence band. This minimum area confidence set (MACS) criterion can clearly be generalized to the minimum volume confidence set (MVCS) criterion in study of confidence bands for a multiple linear regression model. In this paper the hyperbolic and constant width confidence bands for a multiple linear regression model over a particular ellipsoidal region of the predictor variables are compared under the MVCS criterion. It is observed that whether one band is better than the other depends on the magnitude of one particular angle that determines the size of the predictor variable region. When the angle and so the size of the predictor variable region is small, the constant width band is better than the hyperbolic band but only marginally. When the angle and so the size of the predictor variable region is large the hyperbolic band can be substantially better than the constant width band.
• Piegorsch, W. W. (2009). Introduction: Modern benchmark analysis for environmental risk assessment. Environmental and Ecological Statistics.
• Piegorsch, W. W., & Bailer, A. J. (2009). Combining information. Wiley interdisciplinary reviews. Computational statistics, 1(3), 354-360.
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  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.
• West, R. W., Nitcheva, D. K., & Piegorsch, W. W. (2009). Bootstrap methods for simultaneous benchmark analysis with quantal response data. Environmental and ecological statistics, 16(1), 63-73.
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  A primary objective in quantitative risk assessment is the characterization of risk which is defined to be the likelihood of an adverse effect caused by an environmental toxin or chemcial agent. In modern risk-benchmark analysis, attention centers on the "benchmark dose" at which a fixed benchmark level of risk is achieved, with a lower confidence limits on this dose being of primary interest. In practice, a range of benchmark risks may be under study, so that the individual lower confidence limits on benchmark dose must be corrected for simultaneity in order to maintain a specified overall level of confidence. For the case of quantal data, simultaneous methods have been constructed that appeal to the large sample normality of parameter estimates. The suitability of these methods for use with small sample sizes will be considered. A new bootstrap technique is proposed as an alternative to the large sample methodology. This technique is evaluated via a simulation study and examples from environmental toxicology.
• Buckley, B. E., & Piegorsch, W. W. (2008). Simultaneous Confidence Bands for Abbott-Adjusted Quantal Response Models. Statistical methodology, 5(3), 209-219.
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  We study use of a Scheffé-style simultaneous confidence band as applied to low-dose risk estimation with quantal response data. We consider two formulations for the dose-response risk function, an Abbott-adjusted Weibull model and an Abbott-adjusted log-logistic model. Using the simultaneous construction, we derive methods for estimating upper confidence limits on predicted extra risk and, by inverting the upper bands on risk, lower bounds on the benchmark dose, or BMD, at which a specific level of 'benchmark risk' is attained. Monte Carlo evaluations explore the operating characteristics of the simultaneous limits.
• Piegorsch, W. W. (2008). Construction of exact simultaneous confidence bands for a simple linear regression model. International Statistical Review.
• Piegorsch, W. W., & Schuler, E. (2008). Communicating the risks, and the benefits, of nanotechnology. International journal of risk assessment and management, 10(1-2), 57-69.
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  Issues surrounding the wide spectrum of (perceived) risks and possible benefits associated with the rapid advance of modern nanotechnology are deliberated. These include the current realities of nanotechnological hazards, their impact vis-à-vis perceived nanotech-risks and perceived nanotech-benefits, and the consequent repercussions on the public and society. It is argued that both the risks and the benefits of nanoscientific advances must be properly communicated if the public is to support this emerging technology.
• Schmidtlein, M. C., Deutsch, R. C., Piegorsch, W. W., & Cutter, S. L. (2008). A sensitivity analysis of the social vulnerability index. Risk analysis : an official publication of the Society for Risk Analysis, 28(4), 1099-114.
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  The Social Vulnerability Index (SoVI), created by Cutter et al. (2003), examined the spatial patterns of social vulnerability to natural hazards at the county level in the United States in order to describe and understand the social burdens of risk. The purpose of this article is to examine the sensitivity of quantitative features underlying the SoVI approach to changes in its construction, the scale at which it is applied, the set of variables used, and to various geographic contexts. First, the SoVI was calculated for multiple aggregation levels in the State of South Carolina and with a subset of the original variables to determine the impact of scalar and variable changes on index construction. Second, to test the sensitivity of the algorithm to changes in construction, and to determine if that sensitivity was constant in various geographic contexts, census data were collected at a submetropolitan level for three study sites: Charleston, SC; Los Angeles, CA; and New Orleans, LA. Fifty-four unique variations of the SoVI were calculated for each study area and evaluated using factorial analysis. These results were then compared across study areas to evaluate the impact of changing geographic context. While decreases in the scale of aggregation were found to result in decreases in the variance explained by principal components analysis (PCA), and in increases in the variance of the resulting index values, the subjective interpretations yielded from the SoVI remained fairly stable. The algorithm's sensitivity to certain changes in index construction differed somewhat among the study areas. Understanding the impacts of changes in index construction and scale are crucial in increasing user confidence in metrics designed to represent the extremely complex phenomenon of social vulnerability.
• Nitcheva, D. K., Piegorsch, W. W., & West, R. W. (2007). On use of the multistage dose-response model for assessing laboratory animal carcinogenicity. Regulatory toxicology and pharmacology : RTP, 48(2), 135-47.
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  We explore how well a statistical multistage model describes dose-response patterns in laboratory animal carcinogenicity experiments from a large database of quantal response data. The data are collected from the US EPA's publicly available IRIS data warehouse and examined statistically to determine how often higher-order values in the multistage predictor yield significant improvements in explanatory power over lower-order values. Our results suggest that the addition of a second-order parameter to the model only improves the fit about 20% of the time, while adding even higher-order terms apparently does not contribute to the fit at all, at least with the study designs we captured in the IRIS database. Also included is an examination of statistical tests for assessing significance of higher-order terms in a multistage dose-response model. It is noted that bootstrap testing methodology appears to offer greater stability for performing the hypothesis tests than a more-common, but possibly unstable, "Wald" test.
• Piegorsch, W. W. (2007). Vulnerability of U.S. cities to environmental hazards. Journal of Homeland Security and Emergency Management.
• Piegorsch, W. W., Cutter, S. L., & Hardisty, F. (2007). Benchmark analysis for quantifying urban vulnerability to terrorist incidents. Risk analysis : an official publication of the Society for Risk Analysis, 27(6), 1411-25.
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  We describe a quantitative methodology to characterize the vulnerability of U.S. urban centers to terrorist attack, using a place-based vulnerability index and a database of terrorist incidents and related human casualties. Via generalized linear statistical models, we study the relationships between vulnerability and terrorist events, and find that our place-based vulnerability metric significantly describes both terrorist incidence and occurrence of human casualties from terrorist events in these urban centers. We also introduce benchmark analytic technologies from applications in toxicological risk assessment to this social risk/vulnerability paradigm, and use these to distinguish levels of high and low urban vulnerability to terrorism. It is seen that the benchmark approach translates quite flexibly from its biological roots to this social scientific archetype.
• Piegorsch, K. M., Watkins, K. W., Piegorsch, W. W., Reininger, B., Corwin, S. J., & Valois, R. F. (2006). Ergonomic decision-making: a conceptual framework for experienced practitioners from backgrounds in industrial engineering and physical therapy. Applied Ergonomics, 37(5), 587-98.
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  Ergonomists play an important role in preventing and controlling work-related injuries and illnesses, yet little is known about the decision-making processes that lead to their recommendations. This study (1) generated a data-grounded conceptual framework, based on schema theory, for ergonomic decision-making by experienced practitioners in the USA and (2) assessed the adequacy of that framework for describing the decision-making of ergonomics practitioners from backgrounds in industrial engineering (IE) and physical therapy (PT). A combination of qualitative and quantitative analyses, within and across 54 decision-making situations derived from in-depth interviews with 21 practitioners, indicated that a single framework adequately describes the decision-making of experienced practitioners from these backgrounds. Results indicate that demands of the practitioner environment and practitioner factors such as personality more strongly influence the decision-making of experienced ergonomics practitioners than does practitioner background in IE or PT.
• Piegorsch, W. W. (2006). Excess risk estimation under multistage model misspecification. Journal of Statistical Computation and Simulation.
• Piegorsch, W. W. (2006). Multiplicity-adjusted inferences in risk assessment: Benchmark analysis with continuous response data. Environmental and Ecological Statistics.
• Piegorsch, W. W. (2005). Benchmark analysis: Shopping with proper confidence. Risk Analysis.
• Piegorsch, W. W. (2005). Low dose risk estimation via simultaneous statistical inferences. Journal of the Royal Statistical Society. Series C: Applied Statistics.
• Piegorsch, W. W. (2005). Multiplicity-adjusted inferences in risk assessment: Benchmark analysis with quantal response data. Biometrics.
• Piegorsch, W. W. (2005). Simultaneous confidence bounds for low-dose risk assessment with nonquantal data. Journal of Biopharmaceutical Statistics.
• Piegorsch, W. W. (2004). Sample sizes for improved binomial confidence intervals. Computational Statistics and Data Analysis, 46(2), 309-316.
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  Abstract: Sample size equations are reviewed for different types of confidence intervals on a binomial success probability. Based on recommendations for improved binomial confidence limits given by Brown et al. (Statist. Sci. 16 (2001) 101), the intervals expand upon or enhance the traditional Wald-type interval. Some useful sample size relations appear. © 2003 Elsevier B.V. All rights reserved.
• Piegorsch, W. W. (2004). Sample sizes for improved binomial confidence intervals. Computational Statistics and Data Analysis.
• Piegorsch, W. W. (2003). Combining environmental information via hierarchical modeling: An example using mutagenic potencies. Environmetrics.
• Piegorsch, W. W. (2003). Confidence Bands for Low-Dose Risk Estimation with Quantal Response Data. Biometrics.
• Piegorsch, W. W. (2003). Detection of oxidative DNA damage in isolated marine bivalve hemocytes using the comet assay and formamidopyrimidine glycosylase (Fpg). Mutation Research - Genetic Toxicology and Environmental Mutagenesis.
• Piegorsch, W. W. (2003). Empirical Bayes analysis for a hierarchical poisson generalized linear model. Journal of Statistical Planning and Inference.
• Piegorsch, W. W. (2003). Environmetrics: Preface. Environmetrics.
• Piegorsch, W. W. (2003). Exact one-sided simultaneous confidence bands via Uusipaikka's method. Annals of the Institute of Statistical Mathematics.
• Piegorsch, W. W. (2003). Introduction to the special section on statistics and the environment. Statistical Science.
• Piegorsch, W. W. (2002). What shall we teach in environmental statistics?. Environmental and Ecological Statistics.
• Piegorsch, W. W. (2001). Large-sample pairwise comparisons among multinomial proportions with an application to analysis of mutant spectra. Journal of Agricultural, Biological, and Environmental Statistics.
• Piegorsch, W. W. (2001). The male rat carcinogens limonene and sodium saccharin are not mutagenic to male Big Blue™ rats. Mutagenesis.
• Piegorsch, W. W. (2000). Asymmetric confidence bands for simple linear regression over bounded intervals. Computational Statistics and Data Analysis.
• Piegorsch, W. W. (2000). Estimation and testing with overdispersed proportions using the beta- logistic regression model of Heckman and Willis. Biometrics.
• Piegorsch, W. W. (2000). From quantal counts to mechanisms and systems: The past, present, and future of biometrics in environmental toxicology. Biometrics.
• Piegorsch, W. W. (2000). On a likelihood-based goodness-of-fit test of the beta-binomial model. Biometrics.
• Piegorsch, W. W. (2000). Parametric empirical Bayes estimation for a class of extended log-linear regression models. Environmetrics.
• Piegorsch, W. W. (2000). Statistical modeling and analyses of a base-specific Salmonella mutagenicity assay. Mutation Research - Genetic Toxicology and Environmental Mutagenesis.
• Piegorsch, W. W. (1999). Experimental evidence of subsurface feeding by the burrowing ophiuroid Amphipholis gracillima (Echinodermata). Marine Ecology Progress Series.
• Piegorsch, W. W. (1998). Introduction to binary response regression and associated trend analyses. Journal of Quality Technology.
• Piegorsch, W. W. (1998). Statistical Advances in Environmental Science. Statistical Science.
• Piegorsch, W. W. (1998). Statistical aspects for combining information and meta-analysis in environmental toxicology. Journal of Environmental Science and Health - Part C Environmental Carcinogenesis and Ecotoxicology Reviews.
• Piegorsch, W. W. (1997). Optimal statistical design for toxicokinetic studies. Statistical Methods in Medical Research.
• Piegorsch, W. W. (1997). Sources of variability in data from a positive selection lacZ transgenic mouse mutation assay: An interlaboratory study. Mutation Research - Genetic Toxicology and Environmental Mutagenesis.
• Piegorsch, W. W. (1996). Combining environmental information. I: Environmental monitoring, measurement and assessment. Environmetrics.
• Piegorsch, W. W. (1996). Empirical Bayes estimation for logistic regression and extended parametric regression models. Journal of Agricultural, Biological, and Environmental Statistics.
• Piegorsch, W. W. (1996). Life-stage-specific toxicity of sediment-associated chlorpyrifos to a marine, infaunal copepod. Environmental Toxicology and Chemistry.
• Piegorsch, W. W. (1996). The Ames test: The two-fold rule revisited. Mutation Research - Genetic Toxicology.
• Piegorsch, W. W., & Cox, L. H. (1996). Combining environmental information. II: Environmental epidemiology and toxicology. Environmetrics, 7(3), 309-324.
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  Abstract: An increasingly important concern in epidemiological and toxicological studies of environmental exposures is the need to combine information from diverse sources that relate to a common endpoint. This is clearly a statistical activity, but statistical techniques for data combination are still only developmental. Herein, we illustrate some current applications of combining information in environmental epidemiology and toxicology, with emphasis on the burgeoning use of meta-analyses for environmental settings. Our goal is to inform readers about modern statistical techniques useful for combining environmental information, with emphasis on more recently developed approaches.
• Piegorsch, W. W. (1995). Discussion. Environmental and Ecological Statistics.
• Piegorsch, W. W. (1995). Study design and sample sizes for a lacI transgenic mouse mutation assay. Environmental and Molecular Mutagenesis.
• Piegorsch, W. W. (1994). Combining environmental information.. Environmental Health Perspectives.
• Piegorsch, W. W. (1994). Computer program for the analysis of mutational spectra: Application to p53 mutations. Carcinogenesis.
• Piegorsch, W. W. (1994). Non-hierarchical logistic models and case-only designs for assessing susceptibility in population-based case-control studies. Statistics in Medicine.
• Piegorsch, W. W. (1994). Some comments on potency measures in mutagenicity research. Environmental Health Perspectives.
• Piegorsch, W. W. (1994). Statistical approaches for analyzing mutational spectra: Some recommendations for categorical data. Genetics.
• Piegorsch, W. W. (1994). Statistical models for genetic susceptibility in toxicological and epidemiological investigations. Environmental Health Perspectives.
• Piegorsch, W. W., Lockhart, A. -., Margolin, B. H., Tindall, K. R., Gorelick, N. J., Short, J. M., Carr, G. J., Thompson, E. D., & Shelby, M. D. (1994). Sources of variability in data from a lacI transgenic mouse mutation assay. Environmental and Molecular Mutagenesis, 23(1), 17-31.
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  PMID: 8125080;Abstract: Experimental features of a transgenic mouse mutation assay based on a lacI target transgene from Escherichia coli are considered in detail. Sources of variability in the experimental protocol that can affect the statistical nature of the observations are examined with the goal of identifying sources of excess variation in the observed mutant fractions. The sources include plate-to-plate (within packages), package-to-package (within animals), and animal-to-animal (within study) variability. Data from two laboratories are evaluated, using various statistical methods to identify excess variability. Results suggest only scattered patterns of excess variability, except possibly in those cases where genomic DNA from test animals is stored for extended periods (e.g., > 90 days) after isolation from tissues. Further study is encouraged to examine the validity and implications of this time/storage-related effect.
• Piegorsch, W. W. (1993). Biometrical methods for testing dose effects of environmental stimuli in laboratory studies. Environmetrics.
• Gutierrez-Espeleta, G. A., Hughes, L. A., Piegorsch, W. W., Shelby, M. D., & Generoso, W. M. (1992). Acrylamide: dermal exposure produces genetic damage in male mouse germ cells. Fundamental and applied toxicology : official journal of the Society of Toxicology, 18(2), 189-92.
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  Acrylamide is used extensively in sewage and wastewater treatment plants, in the paper and pulp industry, in treatment of potable water, and in research laboratories for chromatography, electrophoresis, and electron microscopy. Dermal contact is a major route of human exposure. It has been shown that acrylamide is highly effective in breaking chromosomes of germ cells of male mice and rats when administered intraperitoneally or orally, resulting both in the early death of conceptuses and in the transmission of reciprocal translocations to live-born progeny. It is now reported that acrylamide is absorbed through the skin of male mice, reaches the germ cells, and induces chromosomal damage. The magnitude of genetic damage appears to be proportional to the dose administered topically.
• Lockhart, A. M., Piegorsch, W. W., & Bishop, J. B. (1992). Assessing overdispersion and dose-response in the male dominant lethal assay. Mutation research, 272(1), 35-58.
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  In dominant lethal studies the primary variables of interest are typically expressed as discrete counts or proportions (e.g., live implants, resorptions, percent pregnant). Simple statistical sampling models for discrete data such as binomial or Poisson generally do not fit this type of data because of extra-binomial or extra-Poisson departures from variability predicted under these simple models. Extra-variability in the fetal response may originate from parental contributions. These can lead to over- or under-dispersion seen as, e.g., extra-binomial variability in the proportion response. Utilizing a large control database, we investigated the relative impact of extra-variability from male or female contributions on the endpoints of interest. Male-related effects did not seem to contribute to overdispersion in our database; female-related effects were, however, evidenced. Various statistical methods were considered to test for significant treatment differences under these forms of sampling variability. Computer simulations were used to evaluate these methods and to determine which are most appropriate for practical use in the evaluation of dominant lethal data. Our results suggest that distribution-free statistical methods such as a nonparametric permutation test or rank-based tests for trend can be recommended for use.
• Piegorsch, W. W. (1992). Concordance of carcinogenic response between rodent species: Potency dependence and potential underestimation. Risk Analysis.
• Piegorsch, W. W. (1992). Statistical methods for assessing environmental effects on human genetic disorders. Environmetrics.
• Generoso, W. M., Shourbaji, A. G., Piegorsch, W. W., & Bishop, J. B. (1991). Developmental response of zygotes exposed to similar mutagens. Mutation research, 250(1-2), 439-446. doi:10.1016/0027-5107(91)90200-8
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  Exposure of mouse zygotes to ethylene oxide (EtO) or ethyl methanesulfonate (EMS) led to high incidences of fetal death and of certain classes of fetal malformations (Generoso et al., 1987, 1988; Rutledge and Generoso, 1989). These effects were not associated with induced chromosomal aberrations (Katoh et al., 1989) nor are they likely to be caused by gene mutations (Generoso et al., 1990). Nevertheless, the anomalies observed in these studies resemble the large class of stillbirths and sporadic defects in humans that are of unknown etiology, such as cleft palate, omphalocoel, clubfoot, hydrops and stillbirths (Czeizel, 1985; Oakley, 1986). Therefore, we continue to study the possible mechanisms relating to induction of these types of zygote-derived anomalies in mice. Effects of zygote exposure to the compounds methyl methanesulfonate (MMS), dimethyl sulfate (DMS), and diethyl sulfate (DES), which have similar DNA-binding properties as EtO and EMS, were studied. DMS and DES, but not MMS, induced effects that are similar to those induced by EtO and EMS. Thus, no site-specific alkylation product was identifiable as the critical target for these zygote-derived anomalies. We speculate that the developmental anomalies arose as a result of altered programming of gene expression during embryogenesis.
• Piegorsch, W. W. (1991). Multiple comparisons for analyzing dichotomous response. Biometrics.
• Piegorsch, W. W., & Haseman, J. K. (1991). Statistical methods for analyzing developmental toxicity data. Teratogenesis, carcinogenesis, and mutagenesis, 11(3), 115-33.
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  A description and review of methods for performing per-litter analyses involving extrabinomial proportion response is provided. It is stressed that the litter should be regarded as the appropriate experimental unit for quantitative analysis in studies for teratogenic or heritable mutagenic effects. Attention is directed at statistical identification of possible treatment effects, such as a positive dose response to a chemical stimulus. The methods range from distribution-free, nonparametric analyses to models involving parametric distributions such as the beta-binomial density. It is seen that most current methods require computer implementation. When concern is raised over misspecification of assumptions critical to the statistical analysis, it is argued that relatively parameter-free methods are appropriate for use. These include statistical bootstrapping and rank-based analyses.
• Bailer, A. J., & Piegorsch, W. W. (1990). Estimating integrals using quadrature methods with an application in pharmacokinetics. Biometrics, 46(4), 1201-11.
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  The estimation of integrals using numerical quadrature is common in many biological studies. For instance, in biopharmaceutical research the area under curves is a useful quantity in deriving pharmacokinetic parameters and in providing a surrogate measure of the total dose of a compound at a particular site. In this paper, statistical issues as separate from numerical issues are considered in choosing a quadrature rule. The class of Newton-Côtes numerical quadrature procedures is examined from the perspective of minimizing mean squared error (MSE). The MSE are examined for a variety of functions commonly encountered in pharmacokinetics. It is seen that the simplest Newton-Côtes procedure, the trapezoidal rule, frequently provides minimum MSE for a variety of concentration-time shapes and under a variety of response variance conditions. A biopharmaceutical example is presented to illustrate these considerations.
• Piegorsch, W. W. (1990). Fisher's contributions to genetics and heredity, with special emphasis on the Gregor Mendel controversy. Biometrics, 46(4), 915-24.
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  R. A. Fisher is widely respected for his contributions to both statistics and genetics. For instance, his 1930 text on The Genetical Theory of Natural Selection remains a watershed contribution in that area. Fisher's subsequent research led him to study the work of (Johann) Gregor Mendel, the 19th century monk who first developed the basic principles of heredity with experiments on garden peas. In examining Mendel's original 1865 article, Fisher noted that the conformity between Mendel's reported and proposed (theoretical) ratios of segregating individuals was unusually good, "too good" perhaps. The resulting controversy as to whether Mendel "cooked" his data for presentation has continued to the current day. This review highlights Fisher's most salient points as regards Mendel's "too good" fit, within the context of Fisher's extensive contributions to the development of genetical and evolutionary theory.
• Piegorsch, W. W. (1990). Maximum likelihood estimation for the negative binomial dispersion parameter. Biometrics, 46(3), 863-7.
• Piegorsch, W. W. (1990). One-sided significance tests for generalized linear models under dichotomous response. Biometrics, 46(2), 309-16.
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  Dichotomous response models are common in many experimental settings. Often, concomitant explanatory variables are recorded, and a generalized linear model, such as a logit model, is fit. In some cases, interest in specific model parameters is directed only at one-sided departures from some null effect. In these cases, procedures can be developed for testing the null effect against a one-sided alternative. These include Bonferroni-type adjustments of univariate Wald tests, and likelihood ratio tests that employ inequality-constrained multivariate theory. This paper examines such tests of significance. Monte Carlo evaluations are undertaken to examine the small-sample properties of the various procedures. The procedures are seen to perform fairly well, generally achieving their nominal sizes at total sample sizes near 100 experimental units. Extensions to the problem of one-sided tests against a control or standard are also considered.
• Whittaker, S. G., Moser, S. F., Maloney, D. H., Piegorsch, W. W., Resnick, M. A., & Fogel, S. (1990). The detection of mitotic and meiotic chromosome gain in the yeast Saccharomyces cerevisiae: effects of methyl benzimidazol-2-yl carbamate, methyl methanesulfonate, ethyl methanesulfonate, dimethyl sulfoxide, propionitrile and cyclophosphamide monohydrate. Mutation research, 242(3), 231-58.
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  The diploid yeast strain BR1669 was used to study induction of mitotic and meiotic chromosome gain by selected chemical agents. The test relies on a gene dosage selection system in which hyperploidy is detected by the simultaneous increase in copy number of two alleles residing on the right arm of chromosome VIII: arg4-8 and cup1S (Rockmill and Fogel. 1988; Whittaker et al., 1988). Methyl methanesulfonate (MMS) induced mitotic, but not meiotic, chromosome gain. Methyl benzimidazol-2-yl carbamate (MBC) and ethyl methanesulfonate (EMS) induced both mitotic and meiotic chromosome gain. Propionitrile, a polar aprotic solvent, induced only mitotic chromosome gain; a reliable response was only achieved by overnight incubation of treated cultures at 0 degrees C. MBC is postulated to act by binding directly to tubulin. The requirement for low-temperature incubation suggests that propionitrile also induces aneuploidy by perturbation of microtubular dynamics. The alkylating agents MMS and EMS probably induce recombination which might in turn perturb chromosome segregation. Cyclophosphamide monohydrate and dimethyl sulfoxide (DMSO) failed to induce mitotic or meiotic chromosome gain.
• Whittaker, S. G., Zimmermann, F. K., Dicus, B., Piegorsch, W. W., Resnick, M. A., & Fogel, S. (1990). Detection of induced mitotic chromosome loss in Saccharomyces cerevisiae--an interlaboratory assessment of 12 chemicals. Mutation research, 241(3), 225-42.
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  Induced mitotic chromosome loss was assayed using diploid yeast strain S. cerevisiae D61.M. The test relies upon the uncovering and expression of multiple recessive markers reflecting the presumptive loss of the chromosome VII homologue carrying the corresponding wild-type alleles. An interlaboratory study was performed in which 12 chemicals were tested under code in 2 laboratories. The results generated by the Berkeley and the Darmstadt laboratories were in close agreement. The solvents benzonitrile and methyl ethyl ketone induced significantly elevated chromosome loss levels. However, a treatment regime that included overnight storage at 0 degree C was required to optimize chromosome loss induction. Hence, these agents are postulated to induce chromosome loss via perturbation of microtubular assembly. Fumaronitrile yielded inconsistent results: induction of chromosome loss and respiratory deficiency was observed in both laboratories, but the response was much more pronounced in the Darmstadt trial than that observed in Berkeley. The mammalian carcinogens, benzene, acrylonitrile, trichloroethylene, 1,1,1-trichloroethane and 1,1,1,2-tetrachloroethane failed to induce chromosome loss but elicited high levels of respiratory deficiency, reflecting anti-mitochondrial activity. Trifluralin, cyclophosphamide monohydrate, diazepam and diethylstilbestrol dipropionate failed to induce any detectable genetic effects. These data suggest that the D61.M system is a reproducible method for detecting induced chromosome loss in yeast.
• Piegorsch, W. W. (1989). Durand's rules for approximate integration. Historia Mathematica.
• Piegorsch, W. W. (1989). Early use of matrix diagonal increments in statistical problems. SIAM Review.
• Piegorsch, W. W. (1989). Optimal design allocations for estimating area under curves for studies employing destructive sampling. Journal of Pharmacokinetics and Biopharmaceutics.
• Piegorsch, W. W. (1989). Quantification of toxic response and the development of the median effective dose (ED50) - A historical perspective. Toxicology and Industrial Health.
• Piegorsch, W. W. (1989). Quantitative approaches for assessing chromosome loss in Saccharomyces cerevisiae: general methods for analyzing downturns in dose response. Mutation Research/Genetic Toxicology.
• Piegorsch, W. W., & Margolin, B. H. (1989). Quantitative methods for assessing a synergistic or potentiated genotoxic response. Mutation research, 216(1), 1-8.
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  The problem of assessing chemical interactions in studies of genotoxicity is discussed. Attention is focused on assessing possible synergism or potentiation when the observed genotoxic response is binary (yes-no). Different forms of enhancement are distinguished based upon different assumptions on the genotoxic activity of the experimental treatments. A generalized linear statistical model is considered that links the probability of the binary response to the doses, and data-analytic strategies are described for detecting synergy and potentiation in factorially designed experiments. This approach is illustrated with a series of analyses of various genotoxicity data-sets.
• Piegorsch, W. W., Zimmermann, F. K., Fogel, S., Whittaker, S. G., & Resnick, M. A. (1989). Quantitative approaches for assessing chromosome loss in Saccharomyces cerevisiae: general methods for analyzing downturns in dose response. Mutation research, 224(1), 11-29.
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  Statistical methods are considered for analysis of data arising from a mitotic chromosome loss assay in Saccharomyces cerevisiae strain D61.M. The methods make use of reproducibility trial data from the assay (presented herein) and previous data, which suggest a unimodal, 'umbrella-patterned' dose response. Computer simulations are employed to illustrate the operating characteristics of the umbrella response methods. These methods are generally applicable to any toxicity assay that exhibits a downturn in dose response. Experimental design considerations are also discussed. These include applications of 2-stage sampling rules to first gauge the dose window of peak response, then test if the response deviates significantly from untreated levels.
• Rao, G. N., Piegorsch, W. W., Crawford, D. D., Edmondson, J., & Haseman, J. K. (1989). Influence of viral infections on body weight, survival, and tumor prevalence of B6C3F1 (C57BL/6N x C3H/HeN) mice in carcinogenicity studies. Fundamental and applied toxicology : official journal of the Society of Toxicology, 13(1), 156-64.
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  Sendai virus (SV), mouse hepatitis virus (MHV), and pneumonia virus of mice (PVM) are common viral infections of mice. Influence of these viral infections on the prevalence of liver tumors, lung tumors, and lymphoma is of concern in chemical carcinogenicity studies. Body weight, survival, and tumor prevalence of B6C3F1 mice with and without viral infections in 33 male and 34 female untreated control groups and 32 male and 32 female low- and high-dose groups of 2-year chemical carcinogenicity studies were evaluated. In male mice, the SV infection was associated with significantly (p less than 0.05) higher survival of control, low-dose, and high-dose groups, and higher prevalence of liver tumors and lymphoma. The increases in tumor prevalence are possibly due to an increase in the survival of male mice that had SV infection. However, when interlaboratory variability and time-related effects were taken into account, the number of significant effects was consistent with the expected false-positive rate inherent to the statistical procedures. The MHV and PVM infections did not cause consistent changes in body weight, survival, and tumor prevalences in the control and chemical treatment groups of male mice. Viral infections did not cause consistent increases or decreases in body weight, survival, or tumor prevalence in the control and chemical treatment groups of female B6C3F1 mice.
• Whittaker, S. G., Zimmermann, F. K., Dicus, B., Piegorsch, W. W., Fogel, S., & Resnick, M. A. (1989). Detection of induced mitotic chromosome loss in Saccharomyces cerevisiae--an interlaboratory study. Mutation research, 224(1), 31-78.
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  The diploid yeast strain D61.M was used to study induction of mitotic chromosome loss. The test relies upon the uncovering and expression of multiple recessive markers reflecting the presumptive loss of the chromosome VII homologue carrying the corresponding wild-type alleles. The underlying 'loss event' is probably complex since the predicted centromere-linked lethal tetrad segregations for chromosome VII are not recovered. Instead, the homologue bearing the multiple recessive markers is patently homozygous. An interlaboratory study was performed in which 16 chemicals were tested under code in 2 laboratories. The results generated by the Berkeley and Darmstadt laboratories were in close agreement. Acetonitrile, ethyl acetate, 4-acetylpyridine, propionitrile and nocodazole were identified as potent inducers of mitotic chromosome loss. Acetone, dimethyl sulfoxide and 2-methoxyethyl acetate either elicited weak responses or yielded ambiguous results. Water, carbon tetrachloride, 4-fluoro-D,L-phenylalanine, amphotericin B, griseofulvin, cadmium chloride, ethyl methanesulfonate and methylmercury(II) chloride failed to induce chromosome loss. These data suggest that the system described herein represents a reliable assay for chemically induced chromosome loss in yeast.
• Piegorsch, W. W. (1988). Confidence bands for logistic regression with restricted predictor variables. Biometrics.
• Piegorsch, W. W. (1988). Exploring relationships between mutagenic and carcinogenic potencies. Mutation Research/Reviews in Genetic Toxicology.
• Piegorsch, W. W. (1988). Exploring simple independent action in multifactor tables of proportions. Biometrics.
• Piegorsch, W. W. (1988). Respiratory tract lesions in F344/N rats and B6C3F1 mice after inhalation exposure to 1,2-epoxybutane. Toxicology.
• Piegorsch, W. W., & Hoel, D. G. (1988). Exploring relationships between mutagenic and carcinogenic potencies. Mutation research, 196(2), 161-75.
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  Salmonella mutagenic and rodent carcinogenic potencies are calculated for 112 compounds recently studied by the U.S. National Toxicology Program. 28 of the 112 compounds are seen to exhibit simultaneous non-zero mutagenic and carcinogenic potencies. These are combined with an earlier list of mutagenic and carcinogenic compounds (McCann et al., 1988) in order to study possible trends in the data. A significant positive correlation is exhibited between mutagenic and carcinogenic potencies in the combined data, although the observed scatter is too great for the overall result to be predictive. Classification by chemical class further indicates positive correlations near one for chemicals classified as nitroaromatic and related compounds. Patterns in mutagenic and carcinogenic potency over time are also examined. Mean potencies of recently-studied compounds are seen to trend lower than those of compounds studied 10 or more years ago.
• Kitamura, H., Inayama, Y., Ito, T., Yabana, M., Piegorsch, W. W., & Kanisawa, M. (1987). Morphologic alteration of mouse Clara cells induced by glycerol: ultrastructural and morphometric studies. Experimental lung research, 12(4), 281-302.
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  In our studies on activation of the Clara cell by biological substances and its relationship to pulmonary carcinogenesis, we found that large doses of glycerol induced drastic morphologic changes selectively in the Clara cell among distal airway epithelial cells in ddY mice. Subcutaneous injection of glycerol (7.2 g/Kg body weight) caused cytoplasmic edema with disruption of endoplasmic reticulum membranes at 1 and 3 hours, followed by hyperplasia of smooth endoplasmic reticulum (SER) at 12 and 24 hours. Concentric lamination of SER was observed at 48 and 96 hours. Oral administration of 5% glycerol in drinking water for 2 to 8 weeks induced more conspicuous hyperplasia and hypertrophy of SER in the Clara cells. Electron microscopic morphometry revealed a 3-fold increase in the profile area of SER in the Clara cells of the animals at 2 and 8 weeks. Both the profile area and the number of secretory granules increased significantly at 2 and 8 weeks, and those of mitochondria tended to increase with time of glycerol treatment. In both experiments, the mitochondria of the Clara cells exhibited marked elongation and distortion of the contour associated with appearance of prominent cristae. These results suggest that large doses of glycerol induce marked alteration in the functional activity of the mouse Clara cell.
• Piegorsch, W. W. (1987). Influence of body weight on the incidence of spontaneous tumors in rats and mice of long-term studies.. American Journal of Clinical Nutrition.
• Piegorsch, W. W. (1987). Performance of likelihood-based interval estimates for two-parameter exponential samples subject to type I censoring.. Technometrics.
• Piegorsch, W. W. (1986). Confidence bands for polynomial regression with fixed intercepts.. Technometrics.
• Piegorsch, W. W. (1986). Testing for simple independent action between two factors for dichotomous response data.. Biometrics.
• Piegorsch, W. W. (1986). The Gregor Mendel controversy: early issues of goodness-of-fit and recent issues of genetic linkage.. History of science; an annual review of literature, research and teaching.
• Piegorsch, W. W., & Gladen, B. C. (1986). Note on the use of prior interval information in constructing interval estimates for a gamma mean.. Technometrics, 28(3), 269-273.
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  Abstract: Methods are presented for construction of interval estimates on the mean of a gamma distribution when there is some prior interval information as to the location of this parameter. The methods produce posterior intervals by constructing prior distributions for the mean parameter from the prior interval information. Both Bayesian and pseudo-Bayesian approaches for the construction of the priors are considered. These concepts are illustrated by an experiment assessing the operating characteristics of a laboratory chemical analyzer.

Presentations

• Piegorsch, W. W. (2021, April). "Collaboration is the best part of statistics". Stats+Stories™ Podcast Episode #183.
• Piegorsch, W. W. (2021, April). "The probability of the next terrorist attack". Stats+Stories™ Podcast Episode #182.
• Piegorsch, W. W. (2021, August). "Predicting drug toxicity and flood risk with data science". Arizona BIO5 Institute Science Talks, Podcast Episode #16.
• Piegorsch, W. W. (2019, May). Model uncertainty in environmental risk assessment. University of Nevada Department of Mathematics & Statistics Colloquium Series. University of Nevada, Reno, NV: University of Nevada Department of Mathematics & Statistics.
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  Statistical estimation of low-dose ‘benchmark’ points in environmental risk analysis is discussed. 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 (frequentist) model averaging over a suite of potential dose-response models, and nonparametric dose-response analysis via isotonic regression. An example on formaldehyde toxicity illustrates the calculations.
• Pena, E., Wu, W., Piegorsch, W. W., West, W., & An, L. -. (2013, March). Model Selection and BMD Estimation with Quantal-Response Data. The International Biometric Society (IBS) - ENAR Spring meeting. Orlando, FL: IBS Eastern North American Region.