Issues in Qualitative and Quantitative Risk Analysis for Developmental Toxicology1

The qualitative and quantitative evaluation of risk in developmental toxicology has been discussed in several recent publications.(^1–3) A number of issues still are to be resolved in this area. The qualitative evaluation and interpretation of end points in developmental toxicology depends on an understanding of the biological events leading to the end points observed, the relationships among end points, and their relationship to dose and to maternal toxicity. The interpretation of these end points is also affected by the statistical power of the experiments used for detecting the various end points observed. The quantitative risk assessment attempts to estimate human risk for developmental toxicity as a function of dose. The current approach is to apply safety (uncertainty) factors to die no observed effect level (NOEL). An alternative presented and discussed here is to model the experimental data and apply a safety factor to an estimated risk level to achieve an “acceptable” level of risk. In cases where the dose-response curves upward, this approach provides a conservative estimate of risk. This procedure does not preclude the existence of a threshold dose. More research is needed to develop appropriate dose-response models that can provide better estimates for low-dose extrapolation of developmental effects.     

A Comparison of Methods for Estimating the Benchmark Dose Based on Overdispersed Data from Developmental Toxicity Studies

Developmental anomalies resulting from prenatal toxicity can be manifested in terms of both malformations among surviving offspring and prenatal death. Although these two endpoints have traditionally been analyzed separately in the assessment of risk, multivariate methods of risk characterization have recently been proposed. We examined this and other issues in developmental toxicity risk assessment by evaluating the accuracy and precision of estimates of the effective dose ( ED ₀₅) and the benchmark dose ( BMD ₀₅) using computer simulation. Our results indicated that different variance structures (Dirichlet-trinomial and generalized linear model) used to characterize overdispersion yielded comparable results when fitting joint dose response models based on generalized estimating equations. (The choice of variance structure in separate modeling was also not critical.) However, using the Rao-Scott transformation to eliminate overdispersion tended to produce estimates of the ED ₀₅ with reduced bias and mean squared error. Because joint modeling ensures that the ED ₀₅ for overall toxicity (based on both malformations and prenatal death) is always less than the ED ₀₅ for either malformations or prenatal death, joint modeling is preferred to separate modeling for risk assessment purposes.     

Pharmacokinetic Principles for Dose-Rate Extrapolation of Carcinogenic Risk from Genetically Active Agents

Neither experimental animal exposures nor real-life human exposures are delivered at a constant level over a full lifetime. Although there are strong theoretical reasons why all pharmacokinetic processes must "go linear" at the limit of low dose rates, fluctuations in dose rate may produce nonlinearities that either increase or decrease actual risks relative to what would be expected for constant lifetime exposure. This paper discusses quantitative theory and specific examples for a number of processes that can be expected to give rise to pharmacokinetic nonlinearities at high dose rates–including transport processes (e.g., renal tubular secretion), activating and detoxifying metabolism, DNA repair, and enhancement of cell replication following gross toxicity in target tissues. At the extreme, full saturation of a detoxification or DNA repair process has the potential to create as much as a dose² dependence of risk on dose delivered in a single burst, and if more than one detoxification step becomes fully saturated, this can be compounded. Effects via changes in cell replication rates, which appear likely to be largely responsible for the steep upward turning curve of formaldehyde carcinogenesis in rats, can be even more profound over a relatively narrow range of dosage. General suggestions are made for experimental methods to detect nonlinearities arising from the various sources in premarket screening programs.     

An Evaluation of the Rai and Van Ryzin Dose-Response Model in Teratology

The underlying assumptions of the Rai and Van Ryzin dose-response model for reproductive toxicological data are evaluated on the basis of existing experimental data. The model under consideration is unusual in its use of litter size to completely account for extra-binomial variation in the data by associating litter size with reproductive outcome. The experimental data show that controlling litter size is not sufficient to account for the litter-to-litter variability in responses. It is also shown that the two linear components of the Rai and Van Ryzin model are inappropriate. For the component which applies to the dam, the data suggest a strong nonlinearity, supported by rejection of the linear model via statistical hypothesis tests. In the component involving litter size, a relationship with dose is not apparent. The litter size parameters offer considerable potential for bias in estimation; bias which is at least partly masked by the model having good prediction characteristics due to the increased number of parameters. A simulation study is presented to illustrate how the Rai and Van Ryzin model can exaggerate litter size effects on the probability of response when the simulated data arise from a model involving a nonlinear dam component, common to this type of data, and no effect of litter size.     

Comparison of the Dependence of the TD50 on Maximum Tolerated Dose for Mutagens and Nonmutagens

The relationship between the minimum TD50 (i.e., the TD50 measured at the most sensitive site) and the maximum dose administered (maxD) in rodent carcinogenicity bioassays was investigated separately for mice and rats. The relationship between log(1/TD50) and log(1/maxD) was analyzed as a function of (1) mutagenicity and (2) the statistical significance cutoff for selecting the minimum TD50 values. For rat bioassays, the variance of log(1/TD50) is larger and the correlation of log(1/TD50) with log(1/maxD) is weaker for mutagens than for nonmutagens, suggesting that the relationship between minimum TD50 and MTD is, in general, stronger for nonmutagens than for mutagens. The difference in correlation does not depend on the TD50 statistical significance cutoff, but the difference in variance is not significant for the most stringently selected dataset. For mouse bioassays, no significant mutagen/nonmutagen differences in log(1/TD50) variance are found. A significantly weaker correlation of log(1/TD50) with log(1/maxD) for mutagens in comparison to nonmutagens occurs only for the dataset with minimum TD50 chosen at the least stringent level, suggesting that this difference may be due to chance variation. We also looked for changes in correlation and regression parameters as a function of mutagenic potency in Salmonella; the variance of log(1/TD50) and its correlation with log(1/maxD) are not found to vary in a consistent manner. Taken as a whole, our results indicate that (1) mutagenicity is a determinant of the TD50/maxD relationship in rats and (2) any effect that mutagenicity may exert on the TD50/maxD relationship in mice is unimportant.(ABSTRACT TRUNCATED AT 250 WORDS)     

The Use of Generalized Estimating Equations for Risk Assessment in Developmental Toxicity

This paper reviews and compares several approaches to fitting dose-response models to developmental toxicity data. The main issue of interest is how to appropriately account for litter effects. Among the approaches reviewed are Beta Binomial models, models that attempt to characterize the litter effect through the use of covariates, and models that avoid the complication of correlated offspring by modeling "affected litter" rather than fetus-specific outcomes. Finally, we discuss our recommended approach, which is to use Generalized Estimating Equations, or quasi-likelihood. We give a number of reasons for preferring the latter and illustrate its application with an example.     

Nonparametric estimators for shift in quantal bioassay

Let F(x) and F(x+θ) be log dose-response curves for a standard preparation and a test preparation, respectively, in a parallel quantal bioassay designed to test the relative potency of a drug, toxicant, or some other substance, and suppose the form of F is unknown. Several estimators of the shift parameter θ or relative potency, are compared, including some generalized and trimmed Spearman-Kärber estimators and a non parametric maximum likelihood estimator. Both point and interval estimation are discussed. Some recommendations concerning the choices of estimators are offered.     

Quantal resp0nse assays by inverse regression

A general inverse regression procedure for estimating dose-response curves in quanta1 response assays is presented. Asymptotic distributional properties are developed. The special case is given, where after suitable transformation, the -dose response curve is linear. The inverse method has a decided advantage over the more classical methods in this case, both inflexibility and in ease of application. The procedure will be shown to be fully efficient, in the asymptotic context*     

Comparison of Six Dose-Response Models for Use with Food-Borne Pathogens

Food-related illness in the United States is estimated to affect over six million people per year and cost the economy several billion dollars. These illnesses and costs could be reduced if minimum infectious doses were established and used as the basis of regulations and monitoring. However, standard methodologies for dose-response assessment are not yet formulated for microbial risk assessment. The objective of this study was to compare dose-response models for food-borne pathogens and determine which models were most appropriate for a range of pathogens. The statistical models proposed in the literature and chosen for comparison purposes were log-normal, log-logistic, exponential, -Poisson and Weibull-Gamma. These were fit to four data sets also taken from published literature, Shigella flexneri, Shigella dysenteriae,Campylobacter jejuni, and Salmonella typhosa, using the method of maximum likelihood. The Weibull-gamma, the only model with three parameters, was also the only model capable of fitting all the data sets examined using the maximum likelihood estimation for comparisons. Infectious doses were also calculated using each model. Within any given data set, the infectious dose estimated to affect one percent of the population ranged from one order of magnitude to as much as nine orders of magnitude, illustrating the differences in extrapolation of the dose response models. More data are needed to compare models and examine extrapolation from high to low doses for food-borne pathogens.     

Cancer Dose-Response Modeling of Epidemiological Data on Worker Exposures to Aldrin and Dieldrin

The paper applies classical statistical principles to yield new tools for risk assessment and makes new use of epidemiological data for human risk assessment. An extensive clinical and epidemiological study of workers engaged in the manufacturing and formulation of aldrin and dieldrin provides occupational hygiene and biological monitoring data on individual exposures over the years of employment and provides unusually accurate measures of individual lifetime average daily doses. In the cancer dose-response modeling, each worker is treated as a separate experimental unit with his own unique dose. Maximum likelihood estimates of added cancer risk are calculated for multistage, multistage-Weibull, and proportional hazards models. Distributional characterizations of added cancer risk are based on bootstrap and relative likelihood techniques. The cancer mortality data on these male workers suggest that low-dose exposures to aldrin and dieldrin do not significantly increase human cancer risk and may even decrease the human hazard rate for all types of cancer combined at low doses (e.g., 1 g/kg/day). The apparent hormetic effect in the best fitting dose-response models for this data set is statistically significant. The decrease in cancer risk at low doses of aldrin and dieldrin is in sharp contrast to the U.S. Environmental Protection Agency's upper bound on cancer potency based on mouse liver tumors. The EPA's upper bound implies that lifetime average daily doses of 0.0000625 and 0.00625 g/kg body weight/day would correspond to increased cancer risks of 0.000001 and 0.0001, respectively. However, the best estimate from the Pernis epidemiological data is that there is no increase in cancer risk in these workers at these doses or even at doses as large as 2 g/kg/day.