Toxicity Curve Estimation: Fitting a Compartment Model to Median Survival Times

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Abstract
In an acute lethality toxicity test, organisms are continuously exposed to each of several concentrations of the toxicant and subsequent deaths are recorded. The results of the test are often summarized by the toxicity curve, which shows for each concentration the exposure time required to cause exactly 50% mortality. This paper presents a new statistical procedure for estimating the toxicity curve. It is based on a mathematical model derived from plausible assumptions about the biological mechanisms of acute toxicity. The statistical fit of the model is accomplished by nonlinear, weighted, least‐squares regression, estimated median survival times being responses and concentration being the independent variable. The usual methods for constructing a toxicity curve are encumbered by at least one of two weaknesses: Either the mathematical form of the curve has no apparent biological justification or the statistical fit of the curve treats concentration as the response and time as the independent variable, thereby reversing the cause‐effect relationship. The new method possesses neither of these deficiencies. Analyses of two toxicity tests indicate that the proposed mathematical model is not inconsistent with real data. Received February 4, 1984 Accepted February 28, 1985