Analysis of Incremental Toxicity

While the breadth of the histogram provides a general indication of the variability of the biological response of the test population to a test chemical, the numbers on the x-axis indicate the actual doses of a chemical that produce the toxic effect of concern. One of these numbers, the midpoint, is commonly used to characterize the test population as a whole. The midpoint of any frequency distribution is a statistic called the median. Because this is a dose-effect histogram, the median is referred to as the median dose. 

The definition of the median dose is that half of the animals in the test population manifest the specific toxic endpoint (e.g., cancer, blindness, anemia, birth defect, death) at doses below the median, and the other half manifests the specific toxic effect at doses above the median. In other words, the median is the midpoint of the frequency distribution of the toxic effect of concern. It is important to note that the median dose is not the same as the mean, or average, dose. The average is calculated as the sum of all the doses of the test chemical divided by the number of dosage groups. It turns out that the mean dose coincides with the median dose only if the dose-effect histogram is a perfect bell-shaped curve. In practice, the frequency distribution is seldom perfectly bell-shaped, and the mean is rarely equal to the median. 

Essentials of Toxic Chemical Risk Science and Society 

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