. "Appendix E Probabilistic Approach to Address Exposure to Multiple Chemicals for Course-of-Action Analysis." Review of the Army's Technical Guides on Assessing and Managing Chemical Hazards to Deployed Personnel. Washington, DC: The National Academies Press, 2004.
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Review of the Army’s Technical Guides on Assessing and Managing Chemical Hazards to Deployed Personnel
4, Table 4-1); and σ is the estimate of the lognormal-model “shape” parameter, the inverse of which specifies the steepness of the corresponding fitted dose-response curve.
The subcommittee wishes to consider the general case in which deployed personnel are exposed to n subsets of chemicals, each ith subset of which contains ni chemicals (for i = 1, … n) that all induce a common (mechanism-specific) toxic end point Ti that is independent from any different Ti—specific mechanisms and from any different end points Tj (for j ≠ i) induced by other chemicals involved in the exposure scenario considered. Typically neither n nor ni will be large (i.e., exceed 2 or 3), but the case of multiple chemicals is treated here in general terms to explain the general approach clearly. The 1-hour respiratory concentration of the jth chemical in the ith subset shall be denoted Ci,j, where j = 1, …, ni and where again i = 1, …, n. Because this general treatment involves double-subscript notation, it will be convenient to adopt the alternative notation µ = C50 for the lognormal location-parameter estimate C50. Thus, for the jth chemical in the ith subset, Equation E-1 can be rewritten as
Different chemicals with similar values of σ as well as similar values of μ for a given end point can be treated as if they were all the same chemical. In the absence of information supporting an alternative assumption, it is reasonable to assume in the context of using the lognormal dose-response model that different chemicals with substantially different values of σ for a given end point act via independent mechanisms. Concentrations Ci,j of different chemicals affecting a common end point Ti, all of which have similar values of σi,j but have substantially different values of µi,j, can reasonably be assumed to represent corresponding weighted contributions to an aggregate effective concentration Ci that acts via a single underlying mechanism to elicit Ti. We now assume that, for all i, the ith set of median-response concentrations µi,j are sorted in order of ascending magnitude for j = 1, …, ni, such that µi,1 always denotes the smallest median-response concentration, which in turn corresponds to that chemical with the highest toxic potency among the ith subset of chemicals. It follows that the relative weight of the jth contribution to Ci is (µi,1/µi,j), and thus that