Commonly Used Methods for the Calculation of Endpoints

As reviewed by C. E. Stephan (1977) and Bartell et al. (1992), there are several methods available for the estimation of toxic endpoints. The next few paragraphs discuss some of the advantages and disadvantages of the popular methods. 

Graphical interpolation essentially is the plotting of the dose-response curve and reading the concentration that corresponds to the LC50 or the LC10. 

Curve fitting using a variety of regression models is an alternative method to graphing. Each model has its own set of data specifications in order to be successful. 

The probit method is perhaps the most widely used method for calculating toxicity vs. concentration or dose. As its name implies, the method used a probit transformation of the data. A probit is a unit of divergence from the mean of a normal distribution equal to one standard deviation. The central value of a probit would be 5.0, representing the median effect of the toxicity test. A disadvantage of the method is that it requires two sets of partial kills. However, a confidence interval is easily calculated and can then be used to compare toxicity results. There are several programs available for the calculation, and as discussed below, they provide comparable results. 

If only one or no partial kills are observed in the data, the Litchfield and Wilcoxin method can be employed. This method can provide confidence intervals but is partially graphical in nature and employs judgment by the investigator. The probit method is generally preferred, but the Litchfield and Wilcoxin method can be used when the partial kill criteria for the probit are not met. 

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