Testing for Additivity at Select Mixture Groups of Interest Based on Statistical Equivalence Testing Methods

Several assumptions, defined and undefined, are used in the toxicity assessment of chemical mixtures. In scientific practice mixture components in the low-dose region, particularly subthreshold doses, are often assumed to behave additively (i.e., zero interaction) based on heuristic arguments. This assumption has important implications in the practice of risk assessment, but has not been experimentally tested. We have developed methodology to test for additivity in the sense of Berenbaum (Advances in Cancer Research, 1981), based on the statistical equivalence testing literature where the null hypothesis of interaction is rejected for the alternative hypothesis of additivity when data support the claim. The implication of this approach is that conclusions of additivity are made with a false positive rate controlled by the experimenter. The claim of additivity is based on prespecified additivity margins, which are chosen using expert biological judgment such that small deviations from additivity, which are not considered to be biologically important, are not statistically significant. This approach is in contrast to the usual hypothesis-testing framework that assumes additivity in the null hypothesis and rejects when there is significant evidence of interaction. In this scenario, failure to reject may be due to lack of statistical power making the claim of additivity problematic. The proposed method is illustrated in a mixture of five organophosphorus pesticides that were experimentally evaluated alone and at relevant mixing ratios. Motor activity was assessed in adult male rats following acute exposure. Four low-dose mixture groups were evaluated. Evidence of additivity is found in three of the four low-dose mixture groups. The proposed method tests for additivity of the whole mixture and does not take into account subset interactions (e.g., synergistic, antagonistic) that may have occurred and cancelled each other out.     

Estimation of the Joint Risk from Multiple-Compound Exposure Based on Single-Compound Experiments

In the absence of data from multiple-compound exposure experiments, the health risk from exposure to a mixture of chemical carcinogens is generally based on the results of the individual single-compound experiments. A procedure to obtain an upper confidence limit on the total risk is proposed under the assumption that total risk for the mixture is additive. It is shown that the current practice of simply summing the individual upper-confidence-limit risk estimates as the upper-confidence-limit estimate on the total excess risk of the mixture may overestimate the true upper bound. In general, if the individual upper-confidence-limit risk estimates are on the same order of magnitude, the proposed method gives a smaller upper-confidence-limit risk estimate than the estimate based on summing the individual upper-confidence-limit estimates; the difference increases as the number of carcinogenic components increases.     

Book reviews

L. Keeble and B.D. Loader (eds) Community Informatics. Shaping Computer-mediated Social Relations (London: Routledge, 2001), pp. 388, ISBN 0-415-23112-4 (pbk) £18.99.

H. Dreyfus, On the Internet: Thinking in Action (London: Routledge, 2001), pp. 136, ISBN 0-415228-077 (pbk).

D. Miller and D. Slater, The Internet: An Ethnographic Approach (Oxford and New York: Berg, 2000), pp. 217, ISBN 1-8S973-389-1 (pbk) £14.99.     

Transnational households and ritual: an overview

In this article we introduce five papers, all by social anthropologists, all concerned with transnational households and ritual. Despite wide–ranging research on transnational migration and diasporas, many aspects have been accorded less consideration than they deserve. The transnational practices of migrant families, other than remittances and other economic activity, remain under–investigated. Some thought has been given to the transnational dimension of religious belief systems, notably Islam, but the micro–politics of religion has been largely ignored, and there has been little discussion of transnational religious practices (rituals) at the level of households and families, especially those performed by migrants back in their countries of origin. Household–level analyses of the performances of and meanings attributed to life–crisis rituals and consideration of what Salih has called the ‘transnational division of ritual space’ offer a valuable route to understanding relations between place, culture, ethnicity and gender among migrants in a transnational world, and illuminate contemporary processes of globalization.