Bayesian model-averaged benchmark dose analysis via reparameterized quantal-response models.

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.

Comparison of Hyperbolic and Constant Width Simultaneous Confidence Bands in Multiple Linear Regression under MVCS Criterion.

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.

The male rat carcinogens limonene and sodium saccharin are not mutagenic to male Big Blue rats.

Limonene and sodium saccharin are male rat specific carcinogens giving rise to renal and bladder tumours, respectively. Both compounds give negative results in genetic toxicity assays suggesting a non-genotoxic mode of action for their carcinogenicity. The alpha 2U-globulin accumulation theory has been invoked to explain the renal carcinogenicity of limonene: the accumulation of micro masses of calcium phosphate in the bladder, coupled with a high pH environment in the male rat bladder, has been suggested to be responsible for the bladder carcinogenicity of sodium saccharin. The implication of these proposed mechanisms is that limonene and sodium saccharin will not be mutagenic to the rat kidney and bladder, respectively. This proposal has been evaluated by assessing the mutagenic potential of the two chemicals to male lacI transgenic (Big Blue) rats. Male Big Blue rats were exposed for 10 consecutive days to either limonene in diet, at a dose level in excess of that used in the original National Toxicology Program gavage carcinogenicity bioassay, or to sodium saccharin in diet at the dose known to induce bladder tumours. The multi-site rat carcinogen 4-aminobiphenyl was used as a positive control for the experiment. Limonene failed to increase the mutant frequency in the liver or kidney of the rats, and sodium saccharin failed to increase the mutant frequency in the liver or bladder of the rats. 4-Aminobiphenyl was mutagenic to all three of these tissues. These results add further support to a non-genotoxic mechanism of carcinogenic action for both limonene and sodium saccharin.

On a likelihood-based goodness-of-fit test of the beta-binomial model.

When faced with proportion data that exhibit extra-binomial variation, data analysts often consider the beta-binomial distribution as an alternative model to the more common binomial distribution. A typical example occurs in toxicological experiments with laboratory animals, where binary observations on fetuses within a litter are often correlated with each other. In such instances, it may be of interest to test for the goodness of fit of the beta-binomial model; this effort is complicated, however, when there is large variability among the litter sizes. We investigate a recent goodness-of-fit test proposed by Brooks et al. (1997, Biometrics 53, 1097-1115) but find that it lacks the ability to distinguish between the beta-binomial model and some severely non-beta-binomial models. Other tests and models developed in their article are quite useful and interesting but are not examined herein.

From quantal counts to mechanisms and systems: the past, present, and future of biometrics in environmental toxicology.

As appreciation for human impact on the environment has developed, so have the experimental systems and associated statistical tools that quantify this impact. Toxicological study in particular has grown in its complexity and its need for advanced statistical support. Within this perspective, we describe statistical practice in environmental toxicology and risk assessment. We present two case studies, one from mammalian toxicology and one from aquatic toxicology, that highlight the evolution of statistical practice in environmental toxicology.

Estimation and testing with overdispersed proportions using the beta-logistic regression model of Heckman and Willis.

Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where similarity among conceptuses within a litter leads to intralitter correlations and to overdispersion in the observed proportions. Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The specification was introduced previously for econometric applications by Heckman and Willis; it induces a form of logistic regression for the mean response, together with a reciprocal biexponential model for the intralitter correlation. Large-sample, likelihood-based methods for estimating and testing the joint proportion-correlation response are studied. A developmental toxicity data set illustrates the methods.

Statistical modeling and analyses of a base-specific Salmonella mutagenicity assay.

Statistical features of a base-specific Salmonella mutagenicity assay are considered in detail, following up on a previous report comparing responses of base-specific Salmonella (Ames II) strains with those of traditional tester strains. In addition to using different Salmonella strains, the new procedure also differs in that it is performed as a microwell fluctuation test, as opposed to the standard plate or preincubation test. This report describes the statistical modeling of data obtained from the use of these new strains in the microwell test procedure. We emphasize how to assess any significant interactions between replicate cultures and exposure doses, and how to identify a significant increase in the mutagenic response to a series of concentrations of a test substance.

Sources of variability in data from a positive selection lacZ transgenic mouse mutation assay: an interlaboratory study.

Experimental features of a positive selection transgenic mouse mutation assay based on a lambda lacZ transgene are considered in detail, with emphasis on results using germ cells as the target tissue. 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 frequencies. The sources include plate-to-plate (within packages), package-to-package (within animals), and animal-to-animal variability. Data from five laboratories are evaluated in detail. Results suggest only scattered patterns of excess variability below the animal-to-animal level, but, generally, significant excess variability at the animal-to-animal level. Using source of variability analyses to guide the choice of statistical methods, control-vs-treatment comparisons are performed for assessing the male germ cell mutagenicity of ethylnitrosourea (ENU), isopropyl methanesulfonate (iPMS), and methyl methanesulfonate (MMS). Results on male germ cell mutagenesis of ethyl methanesulfonate (EMS) and methylnitrosourea (MNU) are also reported.

Optimal statistical design for toxicokinetic studies.

Optimal statistical design strategies are applied to toxicokinetic experiments, for determining proper allocations of subjects and/or spacings of sampling times under a variety of nonlinear concentration-time models. The strategies include: (i) optimal allocations of subjects assuming the placement of time points is fixed, (ii) optimal spacing of design time points while assuming an equal allocation of subjects per time points and (iii) allocations/time-point spacings optimized jointly. Emphasis is placed on the first case, where a variance-minimization method is illustrated for optimizing the allocations when estimating specific toxicokinetic parameters. Appeals to forms of D-optimality are also considered, for cases when no specific toxicokinetic parameter is of specialized interest.

The Ames test: the two-fold rule revisited.

Mutagenicity in the Ames assay is evaluated by comparing the number of revertants observed in treated cultures to those in untreated cultures. Often, some form of the '2-fold rule' is employed, whereby a compound is judged mutagenic if a 2-fold or greater increase is seen in a treated culture. In order to understand the underpinnings of this approach, we study some of its statistical properties. We assume that the number of revertants on any plate from a given two-group experiment follows a Poisson distribution and we address the following questions: (1) what is the false-positive error probability of observing at least a doubling of the number of colonies from the control to the treatment group?; (2) if a given mean number of colonies is postulated for a control group, what number of colonies above the observed control mean provides a false-positive rate of 5%? We also present results for question 1 in the case where the number of revertants follows a negative binomial distribution.

Study design and sample sizes for a lacI transgenic mouse mutation assay.

Design features that adjust and account for excess variation in a transgenic mouse mutation assay based on a lacI target transgene from E. coli are considered. These features include proper identification of plate, packaging reaction, and animal identifier codes throughout the experimental and analysis phases of the study, "blocking" of exposed and unexposed animals when preparing and plating multiple packaging reactions from the same genomic DNA sample, separating sectored mutant plaques and complete mutant plaques before performing any quantitative analyses, and testing for sources of excess variation attributable to features of the experimental protocol--such as plate-to-plate (within packaging reactions), packaging reaction-to-packaging reaction (within animals), and animal-to-animal (within study). Control and ethylnitrosourea-treated animal data are presented from a fully designed study in the lacI assay. The study design incorporates many of these experimental principles. Statistical methods to identify excess variability are noted, and the designed study data are used to illustrate the types of variability encountered in practice. A standard statistical test for two-sample testing is highlighted, from which recommendations are made for sample size selection in future studies.

Computer program for the analysis of mutational spectra: application to p53 mutations.

Mutations in the p53 oncogene are extremely common in human cancers, and environmental exposure to mutagenic agents may play a role in the frequency and nature of the mutations. Differences in the patterns of p53 mutations have been observed for different tumor types. It is not trivial to determine if the differences observed in two mutational spectra are statistically significant. To this end, we present a computer program for comparison of two mutational spectra. The program runs on IBM-compatible personal computers and is freely available. The input for the program is a text file containing the number and nature of mutations observed in the two spectra. The output of the program is a P value, which indicates the probability that the two spectra are drawn from the same population. To demonstrate the program, the mutational spectra of single base substitutions in the p53 gene are compared in (i) bladder cancers from smokers and non-smokers, (ii) small-cell lung cancers, non-small-cell lung cancers and colon cancers and (iii) hepatocellular carcinomas from high- and low-aflatoxin exposure groups. p53 mutations differ in several important aspects from a typical mutational spectra experiment, where a homogeneous population of cells is treated with a specific mutagen and mutations at a specific locus are recovered by phenotypic selection. The means by which p53 mutations are recognized is by the appearance of a cancer, and this phenotype is very complex and varied.

Combining environmental information.

Workshop proceedings and summary reports will appear in scientific periodicals and will also be available in various forms as technical reports from the NISS in Research Triangle Park, North Carolina. In particular, study papers from the workshop will be prepared that will serve as indicators of further research directions, as well as current summaries of the complex issue of combining environmental data. Potential applications and improvements in associated areas of scientific/statistical research include census sampling, geostatistics, and biological effect modeling. This workshop was an experiment in how to stimulate and foster research and collaborations across disciplinary lines. Its motivation derives, however, from ever-growing social, political, economic, and scientific needs; with such strong background, it is hoped that the workshop stimulus will be strong, compelling, and fruitful.

Non-hierarchical logistic models and case-only designs for assessing susceptibility in population-based case-control studies.

This article describes how genetic components of disease susceptibility can be evaluated in case-control studies, where cases and controls are sampled independently from the population at large. Subjects are assumed unrelated, in contrast to studies of familial aggregation and linkage. The logistic model can be used to test collapsibility over phenotypes or genotypes, and to estimate interactions between environmental and genetic factors. Such interactions provide an example of a context where non-hierarchical models make sense biologically. Also, if the exposure and genetic categories occur independently and the disease is rare, then analyses based only on cases are valid, and offer better precision for estimating gene-environment interactions than those based on the full data.

Statistical approaches for analyzing mutational spectra: some recommendations for categorical data.

In studies examining the patterns or spectra of mutational damage, the primary variables of interest are expressed typically as discrete counts within defined categories of damage. Various statistical methods can be applied to test for heterogeneity among the observed spectra of different classes, treatment groups and/or doses of a mutagen. These are described and compared via computer simulations to determine which are most appropriate for practical use in the evaluation of spectral data. Our results suggest that selected, simple modifications of the usual Pearson X2 statistic for contingency tables provide stable false positive error rates near the usual alpha = 0.05 level and also acceptable sensitivity to detect differences among spectra. Extensions to the problem of identifying individual differences within and among mutant spectra are noted.

Sources of variability in data from a lacI transgenic mouse mutation assay.

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.

Statistical models for genetic susceptibility in toxicological and epidemiological investigations.

Models are presented for use in assessing genetic susceptibility to cancer (or other diseases) with animal or human data. Observations are assumed to be in the form of proportions, hence a binomial sampling distribution is considered. Generalized linear models are employed to model the response as a function of the genetic component; these include logistic and complementary log forms. Susceptibility is measured via odds ratios of response, relative to a background genetic group. Significance tests and confidence intervals for these odds ratios are based on maximum likelihood estimates of the regression parameters. Additional consideration is given to the problem of gene-environment interactions and to testing whether certain genetic identifiers/categories may be collapsed into a smaller set of categories. The collapsibility hypothesis provides an example of a mechanistic context wherein nonhierarchical models for the linear predictor can sometimes make sense.

Some comments on potency measures in mutagenicity research.

In this article, the measurement of the potency of a chemical or mixture from its dose response in a particular assay is addressed. Attention is focused on data from the Ames Salmonella assay. Three measures of potency are explored and shown to be highly correlated. The presentation then discusses specific areas of research that might benefit from a study of potency.

Relative probability of mutagenic translesion synthesis on the leading and lagging strands during replication of UV-irradiated DNA in a human cell extract.

We have previously demonstrated mutagenic bypass of pyrimidine dimers during SV40 origin-dependent replication of UV-irradiated DNA in human cell extracts [Thomas, D. C., & Kunkel, T. A. (1993) Proc. Natl. Acad. Sci. U.S.A. 90, 7744-7748]. Here we use two vectors having the origin of replication on opposite sides of a lacZ alpha reporter gene to examine the relative probability of mutagenic translesion synthesis on the leading and lagging strands. Although replication of both vectors is inhibited by UVB irradiation in a dose-dependent manner, the covalently closed DNA products of replication contain T4 endonuclease sensitive sites, indicating that bypass of cyclobutane pyrimidine dimers occurred. At fluences of 70 and 100 J/m2, the mutant frequencies obtained with both vectors are substantially higher than with control DNAs. Sequence analysis of mutants obtained with both vectors reveal three types of mutations at frequencies significantly above those obtained from replication of undamaged DNA. These are C-->T transitions, accounting for about two-thirds of the mutants, a small number of CC-->TT substitutions, and complex mutations. Comparing the distribution of C-->T substitutions in the two spectra permits an estimation of the probability of mutagenic translesion replication of the same sequence when replicated as the leading or lagging strand. The data suggest that the overall average UV-independent C-->T substitution probability per phenotypically detectable dipyrimidine site is the same during leading and lagging strand replication. However, statistically significant differences are observed when the distribution of C-->T substitutions is considered.(ABSTRACT TRUNCATED AT 250 WORDS)

Assessing overdispersion and dose-response in the male dominant lethal assay.

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.