Links to Publishers' Listings for more recent publications are available here.
Walter W. Piegorsch, Susan J. Simmons, and Errol Zeiger
Key Words and Phrases: Ames test, bioinformatics, feature extraction, knowledge discovery in databases, mutagenic potency, Salmonella assay.
University of South Carolina, Columbia, SC 29208
Walter W. Piegorsch
Abstract
Environmental biometry is the study and application of statistical methods in environmental studies on biological systems. In the areas of toxicology and environmental health, the damaging effects of environmental chemicals or other stimuli are often studied in animal and microbial systems. Data from such experiments are analyzed via various statistical approaches, each depending on the nature of the endpoint and aspects of the particular assay under study. Among major endpoints of interest, those of carcinogenicity, mutagenicity, and teratogenicity often garner greatest attention, and analyses for these three endpoints are discussed in this chapter. Statistical issues of interest include dose-response estimation and testing, including settings where variance heterogeneity and overdispersion are present. Similarities among the various endpoints and their biometric analyses are illustrated with data on toxicological response to 1,3-butadiene, a gaseous toxin found in cigarette smoke and automobile exhaust. [Handbook of Statistics Vol. 12: Environmental Statistics, G.P. Patil and C.R. Rao, eds., New York: North-Holland/Elsevier, pp. 535-559 (1994).]
Key Words: Biometry; Discrete data; Dose response; Overdispersion; Significance test; Trend test.
ABSTRACT
In the areas of toxicology and environmental biology, the damaging effects of environmental chemicals or other stimuli on biological systems are often studied in controlled laboratory experiments. These usually involve animal and microbial systems. Data from such experiments are analyzed via various statistical approaches, depending on the nature of the endpoint and aspects of the particular assay under study. Major endpoints of interest include carcinogenicity, mutagenicity, and teratogenicity. When the environmental stimulus is administered over a range of doses, it is of interest to estimate and/or test features of the dose-response. In some instances, variance heterogeneity and overdispersion are present, and adjustments to the statistical methods are required. Herein, such methods for assessing dose response for the major endpoints noted above are discussed, with emphasis directed at testing for an increasing dose-response. [Environmetrics 4, 483-505 (1993).]
KEY WORDS: Discrete data; Dose response; Overdispersion; Quantal response; Significance test; Trend test.
Laboratory of Molecular Genetics and Statistics and Biomathematics Branch,
National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina 27709
^{*} To whom correspondences should be sent.
^{1} Laboratory of Molecular Genetics.
^{2} Statistics and Biomathematics Branch.
Minimum mean squared error linear estimators of the area under a curve are considered for cases when the observations are observed with error. The underlying functional form giving rise to the observations is left unspecified, leading to use of quadrature estimators for the true area. The optimal estimator is calculated as a shrinkage of some preliminary estimator (based on, e.g., the trapezoidal rule). Applications to selected exponential functions demonstrate that savings in mean squared error varies with the levels of underlying variance. For cases where variance at each time point is large, the proposed rule can bring about savings in mean squared error of as much as 30%. For experiments with small underlying variance at each time point, squared bias is of greater importance than variance in contributing to mean squared error, and the value of higher-order quadrature routines that focus on minimizing approximation error is noted. [Journal of Statistical Computation and Simulation 46, 217-234 (1993).]
ABSTRACT
Key Words: Case-control study, ecogenetics, epidemiology, gene-environment interaction, genetic susceptibility, logistic regression, maximum likelihood, multinomial sampling, multiplicative null model, odds ratio, synergy.
^{1,2}Division of Biometry and Risk Assessment, U.S. National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709 U.S.A.
Walter W. Piegorsch
Statistics and Biomathematics Branch
U.S. National Institute of Environmental Health Sciences
Research Triangle Park, NC 27709, USA
ABSTRACT
Rank-based statistical methods are described for analysis of data arising from various bioassays for genotoxic damage in micro-organisms. The alternative hypothesis is a specific form of unimodal departure known as an "umbrella pattern," where the dose-response first increases, then decreases. Motivation for this alternative structure is taken from a genotoxicity assay that assesses chromosome loss (a form of "aneuploidy") in yeast. Monte Carlo evaluations are employed to illustrate the small-sample operating characteristics of the umbrella response methods. These methods are generally applicable to any toxicity assay that exhibits a downturn in dose response. Examples are presented, illustrating applications to data from the aneuploidy assay, and from a mutagenicity assay in bacteria. [Order Statistics and Nonparametrics: Theory and Applications, P.K. Sen and I.A. Salama, eds. Amsterdam: North-Holland, 419-430 (1992).]
AMS Subject Classification: Primary 62G10, Secondary 62E99
Key Words and Phrases: Mutagenesis; recursive estimation and testing; test for trend; umbrella alternatives.
Keywords: Statistical methods; Germ cell mutagenesis; Heritable disease; Litter effect; Mouse; Extra-binomial variability; Underdispersion; Dose-response analysis
Summary
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. [Mutation Research 272, 35-58 (1992).]
Use and implementation of the complementary log regression model are discussed, integrating various applications of the model under the form of a generalized linear model. Some motivation is drawn from cases where an underlying random variable is reduced to a dichotomous form. Estimation and testing are facilitated by recognizing the complementary log as a specific link function within a generalized linear framework. Testing for goodness-of-link via efficient scores is also discussed. [American Statistician 46, 94-99 (1992).]
KEY WORDS: Binomial model; Extended link family; Data Truncation; Goodness-of-link testing; Logistic regression; Non-linear regression.
* Walter W. Piegorsch was a Mathematical Statistician in the Statistics and Biomathematics Branch, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709 at the time of preparation of this article. He thanks Norman Kaplan, Barry H. Margolin, Clarice R. Weinberg and two anonymous reviewers for their helpful suggestions during the preparation of this manuscript, and Arnold R. Brody and Lilla H. Hill for providing selected data.
Acrylamide: Dermal exposure produces genetic damage in male mouse germ cells. (1992) Fundamental and Applied Toxicology 18, 189-192.
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 chromotography, 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 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.
Keywords: Foetal anomalies; Zygotes; Methyl methanesulfonate; Dimethyl sulphate; Diethyl sulphate
Summary
Exposures 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 withinduced 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 effects 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. [Mutation Research 250, 439-446 (1991).]
ABSTRACT
KEY WORDS: Ames assay; concordance; genotoxicology; Kappa coefficient; measures of agreement; measures of association; mutagenicity.
SUMMARY
Dichotomous response models are common in many experimental settings. Statistical parameters of interest are typically the probabilities, p_{i}, that an experimental unit will respond at various treatment levels indexed by i. Herein, simultaneous procedures are considered for multiple comparisons among these probabilities, with attention directed at construction of simultaneous confidence intervals for various functions of the p_{i}. The inferences are based on the asymptotic normality of the maximum likelihood estimator of p_{i}. Specific applications include all pairwise comparisons and comparisons with a fixed (control) treatment. Monte Carlo evaluations are undertaken to examine the small-sample properties of the various procedures. It is seen that use of the usual estimates of variance leads to less-than-nominal empirical coverage for most sample sizes examined. For very large samples, nominal coverage is achieved. A reformulation of the pairwise comparisons using a form of inverted score test is shown to exhibit generally nominal empirical coverage, and is recommended for use with small-to-moderate sample sizes [Biometrics 47, 45-52 (1991).]
Key Words: Binomial distribution; Comparisons with a control; Confidence intervals; Monte Carlo evaluations; Pairwise comparisons; Quantal response; Simultaneous inference.
^{1}Department of Mathematics and Statistics, Miami University,
Oxford, Ohio 45056, U.S.A.
and
^{2}Statistics and Biomathematics Branch,
National Institute of Environmental Health Sciences,
Research Triangle Park, NC 27709, U.S.A.
SUMMARY
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-Cotes numerical quadrature procedures is examined from the perspective of minimizing mean-squared error (MSE). The MSEs are examined for a variety of functions commonly encountered in pharmacokinetics. It is seen that the simplest Newton-Cotes 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. [Biometrics 46, 1201-1211 (1990).]
Key words: Area under curve; Exponential disposition models; Mean-squared error, Newton-Cotes quadrature, Numerical integration.
SUMMARY
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. [Biometrics 46, 915-924 (1990).]
Key words: Chi-Square Test, Evolution, Goodness of fit, History of science, Natural selection, P-values.
SUMMARY
A follow-up investigation to that given by Clark and Perry (1989 Biometrics 45, 309-316) is presented, giving details for maximum likelihood estimation for the dispersion parameter from a negative binomial distribution. [Biometrics 46, 863-867 (1990).]
Key words: Generalized linear model; Monte Carlo evaluation; Negative binomial distribution.
SUMMARY
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 article 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. [Biometrics 46, 309-316 (1990).]
Key words: Bonferroni adjustments; Chi-bar-squared statistic; Complementary-log regression; Dunnett's test; Linear inequality constraints; Logistic regression; Probit regression; Simultaneous inference.
National Institute of Environmental Health Sciences,
Research Triangle Park, North Carolina 27709
AMS subject classifications: Primary, 01A55, 65-03, 65D30; Secondary, 65C60.
KEY WORDS: numerical integration, quadrature, trapezoidal rule, Simpson's rule.
Optimal allocations of experimental resources for the estimation of integrals is considered for experiments that use destructive sampling. Given a set of sampling times, a minimum mean square error rule is given for the allotment of fixed experimental resources to the independent variable. The results are seen to be functionally dependent upon the pattern f underlying variability assumed in the model and upon the quadrature rule used to estimate the integral. Extensions to other optimality criteria, including a minimum mean absolute deviation criterion, and to cases involving multiple treatment groups, are also noted. [Journal of Pharmacokinetics and Biopharmaceutics 17, 493-507 (1989).]
KEY WORDS: mean squared error; mean absolute deviation; nonlinear experimental design; numerical quadrature; trapezoidal rule.
^{1}Statistics and Biomathematics Branch, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709.
^{2}Department of Mathematics and Statistics, Miami University, Oxford, Ohio 45056.
Abstract. The early motivation for and development of diagonal increments to ease matrix inversion in least squares (LS) problems is discussed. It is noted that this diagonal incrementation evolved from three major directions: modification of existing methodology in nonlinear LS, utilization of additional information in linear regression, and improvement of the numerical condition of a matrix. The interplay among these factors and the advent of ridge regression are considered in an historical and comparative framework. [SIAM Review 31, 428-434 (1989).] Erratum: Inverting a sum of matrices. SIAM Review 32, 470 (1990).
Key words. matrix inversion, matrix ill-conditioning, nonlinear least squares
AMS(MOS) subject classifications. 65F10, 65C60
^{1} Biometrics Unit, Cornell University, Ithaca, NY 14853.
^{2} Dept. of Statistics, Univ. of So. Carolina, Columbia, SC 29208.
Keywords: Aneuploidy; Chromosome loss; Control reproducibility trials; Umbrella alternatives; Nonparametric statistical tests
Summary
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 two-stage sampling rules to first gauge the dose window of peak response, then test if the response deviates significantly from untreated levels. [Mutation Research 224, 11-29 (1989).]
Keywords: Interaction; Binary data; Fluctuation assay; Chromosome aberrations; Factorial experiments; Simple independent action; Simple similar action
Summary
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. [Mutation Research 216, 1-8 (1989).]
and
George Casella
Biometrics Unit
Cornell University
Ithaca, NY 14853, U.S.A.
SUMMARY
Confidence bands are constructed for the logistic response function when there is an interval restriction on each of the predictor variables. The construction involves application of a general fitting procedure using Scheffé's S-method. Specific details are given for the case of one predictor variable, along with details for a fixed-width alternative to the S-method bands. For the one-predictor case, Monte Carlo results suggest that both bands are conservative if sample sizes are as low as N= 25. By N= 200, the S-method's coverage probabilities attain their nominal levels, while the fixed-width bands remain conservative. The procedures are illustrated with data from a genetic toxicology experiment. [Biometrics 44, 739-750 (1988).]
Key words: Binomial distribution; Monte Carlo evaluations; Quantal response; Restricted predictor variables, Simultaneous inference.
Keywords: Bioassays, Chemical class analysis, Correlation, Predictivity, TD_{50}
Summary
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. [Mutation Research 196, 161-175 (1988).]
SUMMARY
The problem of assessing synergistic or antagonistic departure from simple independent action in multifactor tables of proportions is discussed. A generalized linear model is employed in which additivity corresponds to simple independent action. Data-analytic strategies are proposed for exploring departures from simple independent action in various extensions of the 2x2 table of proportions. This methodology is illustrated with a series of models fitted to cellular differentiation and murine toxicity data. [Biometrics 44, 595-603 (1988).]
Key Words: Dichotomous response; Exploratory data analysis; GLIM; Interaction; Maximum likelihood; Synergy.
KEY WORDS: Coverage probability; Mean axis coverage; Quadratic regression; Simple linear regression.
^{*} Walter W. Piegorsch was a Mathematical Statistician in the Biometry and Risk Assessment Program, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709 at the time of preparation of this article. The author thanks Barry Margolin for helping to develop the problem and giving continuing encouragement and Kenneth Risko and a referee for their many helpful comments.
KEY WORDS: Confidence region; Maximum likelihood estimation; Monte Carlo evaluation; Simultaneous confidence bounds.
This paper compares small sample performances of test statistics for assessing the degree of interaction between two exposure with respect to the occurrence of a time-stratified dichotomous outcome. Particular attention is focused towards cancer bioassays. A null model of simple, independent, joint action is adopted. Sizes and powers are examined via Monte Carlo simulations for the various test statistics proposed under a variety of parameter configurations. [Journal of Statistical Computation and Simulation 26, 1-19 (1986).]
KEY WORDS: Interaction, simple independent action, simulation.
Biometry and Risk Assessment Program,
National Institute of Environmental Health Sciences,
Research Triangle Park, North Carolina 27709, U.S.A.
SUMMARY
This paper compares three test statistics for testing simple independent action between two dichotomous factors with respect to the occurrence of a dichotomous outcome. Sizes and powers are examined for the statistics proposed, under a variety of model parameterizations. The results suggest that a test based on the ratio of the nonresponse probability estimates [considered originally by Wahrendorf, Zentgraf, and Brown (1981, Biometrics 37, 45-54)] has proper size and acceptable power, and is recommended for use in this setting. [Biometrics 42, 413-419 (1986).]
Key words: Interaction; Maximum likelihood; Size of test, Synergy.
KEY WORDS: Simultaneous inference; Regression through the origin; Quadratic regression; Weighted least squares.
KEY WORDS: Simultaneous confidence intervals; Prior weight functions; Constrained minimization.
^{*} Walter W. Piegorsch was a Mathematical Statistician in the Biometry and Risk Assessment Program, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709 at the time of appearance of this article. This research was initiated while the author was a graduate fellow in the Biometrics Unit, Cornell University, and was supported in part by grants from Sigma Xi, the Scientific Research Society. Thanks are due George Casella, for his aid and assistance during the preparation of the manuscript, L.D. Brown, the associate editor, and the referees for their many helpful comments.
Cornell University
^{1} Research supported, in part, by grants from Sigma Xi, the Scientific Research Society. Additional computing support provided by the National Institute of Environmental Health Sciences, Research Triangle Park, NC. This is paper no. BU-835-M in the Biometrics Unit Series, Cornell University, Ithaca, New York.
AMS subject classifications. Primary 62C15, secondary 62F25.
Key words and phrases. Simultaneous inference, complete classes.
The question of the existence of negative moments of a continuous probability density function is explored. A sufficient condition for the existence of the first negative moment is given. The condition is easy to verify, as it involves limits rather than integrals. An example is given, however, that shows that this simple condition is not necessary for the existence of the first negative moment. The delicacy of the characterization of existence is explored further with some results concerning the existence of moments surrounding the first negative moment. [American Statistician 39, 60-62 (1985).]
KEY WORDS: Inverse moment; Sufficient conditions; Limit conditions.
* Walter W. Piegorsch was a Mathematical Statistician in the Biometry and Risk Assessment Program, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709 and George Casella was Associate Professor, Biometrics Unit, Cornell University, Ithaca, New York 14853 at the time of appearance of this article. The work was performed while both authors were at Cornell University. The second author's research was supported by National Science Foundation Grant MCS81-02541. The authors wish to thank the associate editor and referees for their helpful comments.