The authors have developed an improved version of the up-and-down procedure (UDP) as one of the replacements for the traditional acute oral toxicity test formerly used by the Organisation for Economic Co-operation and Development member nations to characterize industrial chemicals, pesticides, and their mixtures. This method improves the performance of acute testing for applications that use the median lethal dose (classic LD50) test while achieving significant reductions in animal use. It uses sequential dosing, together with sophisticated computer-assisted computational methods during the execution and calculation phases of the test. Staircase design, a form of sequential test design, can be applied to acute toxicity testing with its binary experimental endpoints (yes/no outcomes). The improved UDP provides a point estimate of the LD50 and approximate confidence intervals in addition to observed toxic signs for the substance tested. It does not provide information about the dose-response curve. Computer simulation was used to test performance of the UDP without the need for additional laboratory validation.

The U.S. EPA must provide guidance as to health risk assessment of mixtures from a variety of sources such as wastewaters, hazardous waste sites and air particulates. One approach to risk assessment of mixtures is to add up risk assessments for individual components identified as part of the mixture, after considering the potential for interaction among those components. This provides an index of hazard potential but not a quantitative estimate. When data on mixture components are incomplete, but these components are isomers or congeners of a well-studied chemical, another technique--use of toxic equivalency factors--can be applied. This approach has been proposed for estimating risk associated with chlorinated dioxins and dibenzofurans. A third approach, that of relative or comparative potency, is based on the assumption that for similar but not necessarily definable complex mixtures, a measure of relative potency based on data from in vitro tests can be correlated in a constant fashion with relative potency from an in vivo bioassay. The degree of confidence in the appropriateness of a relative potency method rests upon the way potency is measured and the validity of underlying assumptions (the degree to which these assumptions can be tested). One class of assumptions involves choice of the model or procedure for deriving the quantitative risk estimates. A second set of assumptions deals with mechanism of action, and whether such considerations add bias or, in fact, refine the relative potency judgment. The choice of short-term tests appropriate for use in establishing the potency relationships is also a factor to be considered. This paper presents examples of proposed uses of relative potency in risk assessment and outlines some areas for further study.

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Methods for estimating a dichotomous response regression function are discussed. A smoothed nonparametric monotonic estimator is developed and a procedure for estimating its variance is given. In an institutional differences study, the probability of death from a burn injury is related to the severity of the burn injury for patients treated at several specialized burn care units.