Paul I. Feder

Stagewise, adaptive dose allocation for quantal response dose-response studies

A principal design objective of many dose-response studies is to estimate extreme percentiles of a dose-response distribution, e.g., the ED95 dose for a particular drug therapy, as precisely as feasible using the smallest number of experimental subjects possible. Such a design requirement necessitates that allocation of subjects to drug doses be carried out in a stagewise fashion to maximize the information obtained from each subsequent experimental observation in light of what has previously been determined. This paper describes and illustrates specialized methods and associated computer programs to evaluate, on a stagewise basis, the anticipated relative sensitivities of alternative experimental plans in the case of dichotomous responses. Following each stage of experimentation, the current estimates of the dose-response distribution parameters, as well as the uncertainties in these estimates, are updated and are used to assign subjects to experimental dose levels for the next stage of testing. Competing dose allocations are compared with respect to anticipated improvement in estimation precision. The adoption of such a stagewise dose allocation strategy is illustrated by example.

Stagewise, group sequential experimental designs for quantal responses. one-sample and two-sample comparisons.

The use of stagewise, group sequential experimental designs with dichotomous responses in toxicity or drug screening programs is discussed. Such designs represent a compromise between the standard, fixed sample size designs and fully sequential designs. Stagewise group sequential designs place specified numbers of animals on test at each stage, up to a maximum number of stages. The greatest increases in sample size efficiency occur with small numbers of stages, particularly when going from one stage to two. Two-stage designs can result in a 15 to 20 percent reduction in average sample size. Five-stage designs can result in a 30 to 40 percent reduction in average sample size, with no appreciable decrease in Type 1 error or power. Examples of the efficiencies that arose in actual screening programs are given. This paper demonstrates that the routine use of stagewise, group sequential designs in standardized screening protocols can result in substantial savings in animal use with virtually no sacrifice of statistical sensitivity.

Statistical Analysis of Dose-Response Experiments by Maximum Likelihood Analysis and Iteratively Reweighted Nonlinear Least Squares Regression Techniques:

Dose-response studies often form integral parts of pharmacological investigations of drug activity and efficacy and of toxicological investigations of drug and chemical safety. Standardized dose-response study protocols, statistical models, model fitting techniques, and computer programs are widely available for such applications. Many studies however, require nonstandard models and model fitting procedures to adequately describe the resulting data. Maximum likelihood analysis can accommodate a wide variety of model structures in a unified manner. This presentation illustrates how general purpose nonlinear regression analysis routines, such as those that are available in SAS or in BMDP, can be used to obtain maximum likelihood model solutions and associated error analyses for nonstandard model fitting situations. This reduces the need for special purpose computer programs for individual modeling applications. Methodological considerations in the application of nonlinear regression modeling procedures to maximum likelihood estimation are discussed. The methodology is illustrated with several modeling situations.

Evaluating the similarity of complex drinking-water disinfection by-product mixtures: overview of the issues.

Humans are exposed daily to complex mixtures of environmental chemical contaminants, which arise as releases from sources such as engineering procedures, degradation processes, and emissions from mobile or stationary sources. When dose-response data are available for the actual environmental mixture to which individuals are exposed (i.e., the mixture of concern), these data provide the best information for dose-response assessment of the mixture. When suitable data on the mixture itself are not available, surrogate data might be used from a sufficiently similar mixture or a group of similar mixtures. Consequently, the determination of whether the mixture of concern is “sufficiently similar” to a tested mixture or a group of tested mixtures is central to the use of whole mixture methods. This article provides an overview for a series of companion articles whose purpose is to develop a set of biostatistical, chemical, and toxicological criteria and approaches for evaluating the similarity of drinking-water disinfection by-product (DBPs) complex mixtures. Together, the five articles in this series serve as a case study whose techniques will be relevant to assessing similarity for other classes of complex mixtures of environmental chemicals. Schenck et al. (2009) describe the chemistry and mutagenicity of a set of DBP mixtures concentrated from five different drinking-water treatment plants. Bull et al. (2009a, 2009b) describe how the variables that impact the formation of DBP affect the chemical composition and, subsequently, the expected toxicity of the mixture. Feder et al. (2009a, 2009b) evaluate the similarity of DBP mixture concentrates by applying two biostatistical approaches, principal components analysis, and a nonparametric “bootstrap” analysis. Important factors for determining sufficient similarity of DBP mixtures found in this research include disinfectant used; source water characteristics, including the concentrations of bromide and total organic carbon; concentrations and proportions of individual DBPs with known toxicity data on the same endpoint; magnitude of the unidentified fraction of total organic halides; similar toxicity outcomes for whole mixture testing (e.g., mutagenicity); and summary chemical measures such as total trihalomethanes, total haloacetic acids, total haloacetonitriles, and the levels of bromide incorporation in the DBP classes.

Chemical measures of similarity among disinfection by-product mixtures.

There are few measures that can be used to distinguish among mixtures of disinfection by-products (DBPs) produced in the chlorination or chloramination of drinking water. Objective measures of similarities among DBP mixtures would greatly simplify judgments about the risk that may be associated with exposure to DBPs in a given water supply. Major by-products of chlorination/chloramination include the trihalomethanes (THMs) and haloacetic acids (HAAs), which are routinely measured for compliance to regulations. A key question is whether measurement of similar amounts of these DBPs is indicative of the myriad other DBPs that are known to be produced. This article utilized data from a survey of 35 utilities in the United States that included several additional parameters, including members of the haloacetonitrile, trihaloacetaldehyde, and halopropanone classes. Based upon the distribution of bromine in the THM class, the concentrations of unmeasured brominated and bromochlorinated compounds could be determined. This allowed determination of whether measures of the THM and/or HAA classes reflected the amounts of these less abundant classes. Variations in relative yields among DBP classes were observed with water source type and with whether chlorine or chloramine was used as the disinfectant. However, most of the variability was attributable to geographic location. The relative abundance of brominated by-products also varied among water sources. Recent documentation that potent by-products, such as nitrosamines, are selectively produced in particular water systems and preferentially with chloramination indicates that more measures of individual DBP are needed to evaluate similarity among DBPs mixtures.

Evaluating sufficient similarity for disinfection by-product (DBP) mixtures: multivariate statistical procedures.

For evaluation of the adverse health effects associated with exposures to complex chemical mixtures in the environment, the U.S. Environmental Protection Agency (EPA) (2000) states, “if no data are available on the mixture of concern, but health effects data are available on a similar mixture … a decision must be made whether the mixture on which health effects are available is ‘sufficiently’ similar to the mixture of concern to permit a risk assessment.” This article provides a detailed discussion of statistical considerations for evaluation of the similarity of mixtures. Multivariate statistical procedures are suggested to determine whether individual samples of drinking-water disinfection by-products (DBPs) vary significantly from a group of samples that are considered to be similar. The application of principal components analysis to (1) reduce the dimensionality of the vectors of water samples and (2) permit visualization and statistical comparisons in lower dimensional space is suggested. Formal analysis of variance tests of homogeneity are illustrated. These multivariate statistical procedures are applied to a data set describing samples from multiple water treatment plants. Essential data required for carrying out sensitive analyses include (1) identification and measurement of toxicologically sensitive process input and output characteristics, and (2) estimates of variability within the data to construct statistically efficient estimates and tests.

Evaluating Sufficient Similarity for Drinking-Water Disinfection By-Product (DBP) Mixtures with Bootstrap Hypothesis Test Procedures

In chemical mixtures risk assessment, the use of dose-response data developed for one mixture to estimate risk posed by a second mixture depends on whether the two mixtures are sufficiently similar. While evaluations of similarity may be made using qualitative judgments, this article uses nonparametric statistical methods based on the “bootstrap” resampling technique to address the question of similarity among mixtures of chemical disinfectant by-products (DBP) in drinking water. The bootstrap resampling technique is a general-purpose, computer-intensive approach to statistical inference that substitutes empirical sampling for theoretically based parametric mathematical modeling. Nonparametric, bootstrap-based inference involves fewer assumptions than parametric normal theory based inference. The bootstrap procedure is appropriate, at least in an asymptotic sense, whether or not the parametric, distributional assumptions hold, even approximately. The statistical analysis procedures in this article are initially illustrated with data from 5 water treatment plants (Schenck et al., 2009), and then extended using data developed from a study of 35 drinking-water utilities (U.S. EPA/AMWA, 1989), which permits inclusion of a greater number of water constituents and increased structure in the statistical models.

Evaluation of compounds as barriers to dermal penetration of organophosphates using acetylcholinesterase inhibition.

An efficient, objective method for evaluating the efficacy of barrier compounds in preventing dermal penetration of organophosphates (OP) in rabbits was developed using time-dependent reduction in erythrocyte (RBC) acetylcholinesterase (AChE) activity as an endpoint. Anesthetized rabbits, with or without a dermal application of a mixture of high- and low-molecular-weight polyethylene glycols (mean molecular weight of 540 daltons; PEG 540), were exposed to different percutaneous doses of 3 highly toxic OP compounds. Dose-response curves were generated for RBC AChE inhibition as a function of percutaneous dose for each OP test material over time. From data generated, a single dose of each OP was selected to challenge PEG-540-protected and unprotected animals to validate the method as a means of differentiating effective from ineffective barriers to skin penetration. Data for a complete evaluation of a PEG 540 test barrier application were obtained within 4 h and anesthesia was maintained for the entire period.

Assessing Human Health Risks Using Information on Whole Mixtures

This chapter discusses whole mixture approaches to assessing the risks of potentially hazardous chemical mixtures in the environment within the context of the risk assessment paradigm. Here, “whole mixtures” represent the combination of chemicals in the exposure being assessed. For risk assessment purposes, the environmental mixtures considered as a whole mixture can range from complex mixtures, consisting of perhaps hundreds of component chemicals, to less complex whole mixtures, such as all of the members (i.e., components) of a defined class of compounds. Whole mixture approaches are preferred to component approaches in mixture risk assessments. Because of the variability of whole mixtures encountered in the environment and the paucity of health effect studies, including dose-response studies, conducted on whole mixtures, if toxicity data are not available for an environmental mixture, the risk assessment could be based on surrogate toxicity information obtained from testing a sufficiently similar mixture. Biostatistical approaches for evaluating whether mixtures are sufficiently similar are included here as potential approaches that may, with further evaluation, prove useful in regulatory risk assessment contexts. The chapter concludes with a discussion of future directions for whole mixture risk assessment research.

Mixture Experimental Design

There is a general consensus, based on a number of surveys and analytic efforts, that mixture study designs have historically been lacking. Although there has been considerable progress over the past decades, further improvement is necessary both in the development and application of experimental designs to yield data suitable for quantitative analytic methods and in the implementation of appropriate statistical analyses. This chapter reviews the state of the science with regard to the experimental and statistical quality of mixture studies. The importance of properly powering mixture experiments is emphasized; in particular when the focus is on the low-dose/low-effect region. Issues with powering defined mixture and complex mixture experiments are explored. Some designs that have proven useful in mixture experimentation are reviewed, including full and fractional factorial designs and statistical mixture designs such as the isobologram and the fixed ratio ray. General considerations are provided that will aid in the development of both experimental design and analysis strategies that address the question(s) being asked.