Any data that results from measurements on a sample (statistic) has a sampling dis- tribution. It is assumed that the data gen- erated by dose-response experimentation
will follow a Gaussian or normal distri- bution. When a normal distribution is present, the resulting frequency-response graph will appear bell-shaped, whereas the cumulative-response graph will appear sigmoidal. Although the lines on these two graphs appear to be different, in reality they are just different graphic presenta- tions of the same data.
Responses observed in actual test or- ganisms are assumed to be representative of the total or universal population of potential test organisms. The validity of this assumption is questionable when small numbers of test organisms are used. On the other hand, it is not cost-effective to perform dose-response experiments when large numbers of test organisms are used. Somewhere between too many and too few test organisms a decision must be made as to the minimum number of test organisms (N) needed to establish a sta- tistically valid dose-response conclusion. To make this decision requires informa- tion about the response variability within the population of potential test organisms, the desired statistical strength of any con- clusions that may result, and available resources (including cost of tests, time for testing, available personnel, and labora- tory space). By paying careful attention to research design, toxicologists can avoid the erroneous conclusions that may result from the use of too few test organisms during toxicity testing.
When the response measurements are normally distributed it is observed that the greatest number (frequency) of test organisms will exhibit the response at a dose somewhere between the lowest and highest doses tested. This is visually evi- dent in the apex of the bell-shaped line
Dose-Response Relationships 33
Figure 3–2. Dose-response graphs: (A) frequency-response graph and (B) cumulative- response graph showing subthreshold dose (STh), threshold dose (Th), and ceiling effect.
on a frequency dose-response graph or in the middle flat region of the line on a cumulative dose-response graph. A spe- cific point located in these regions repre- sents the mean (X–) or average response and is equal to the sum of all responses (!X) divided by the number of responses (N), or X–= !X/N
When the responses of test organisms follow a normal distribution there are al- ways a few organisms in which the pre- determined response will occur at a very low dose, as well as a few organisms that will not exhibit the response until a very high dose is given. These “supersensi- tive” or “hypersusceptible” and “hearty” or “resistant” test organisms are graphically represented on the sides of the bell and at the beginning and end of the sigmoidal line, respectively. The distance of these “outliers” from the mean (average) response is best stated by use of a statistic called the standard de- viation (SD). A large or small SD value is able to convey valuable information about the dose-response relationship in a test population.
For starters, ±1 SD accounts for 67% of test organism responses, ±2 SD ac- counts for 95%, and ±3 SD represents 99% of test organism responses. Assume that the mean response is constant for two toxicants. If the SD for toxicant A is very large and the SD for toxicant B is very small, it can be concluded that there is a wide range of doses over which the test organisms responded to toxicant A as compared with the small range of doses over which the test organisms re- sponded to toxicant B (Figure 3–3). Numbers such as the mean and standard deviation are useful; however, changes in
the shape of the bell-shaped line or in the sigmoidal line of the cumulative dose-re- sponse graph allow for rapid visual char- acterization and comparison of toxicants.
Three features characterize the sigmoi- dal line on a cumulative dose-response graph. First, there is a dose at which the first test organism will respond (Figure 3– 2B). This is referred to as the threshold dose, which can be seen on the graph as the left-side beginning of the sigmoidal line. Subthreshold doses are represented to the left of this point. At these doses no responses were observed. The following are often used to refer to this beginning region of the cumulative dose-response graphs: No Observable Effects Level (NOEL), No Observable Adverse Effect Level (NOAEL), Suggested No Adverse Response Level (SNARL), Lowest Observ- able Effect Limit (LOEL), and Threshold Limit Value (TLV).
At progressively higher doses, the ini- tially curved sigmoidal line begins to straighten out (Figure 3–2B). This second region of the graph represents the doses at which the majority of test organisms were observed to exhibit the response. Of interest is the cumulative 50% level, rep- resenting the dose at which the mean re- sponse occurred. Third, the right side of the line on a cumulative dose-response graph may be seen to once again curve and then become almost horizontal or flat (Figure 3–2B). This region represents the higher doses at which the remaining few test organisms finally exhibited the pre- determined end effect. This region is said to exhibit the ceiling effect, since an in- crease in dose produces little or no in- crease in response.
Dose-Response Relationships 35
Figure 3–3. (A) Frequency dose-response graph and (B) cumulative dose-response graph showing data from two toxicity studies that have the same mean doses (X–) but different distributions (i.e., standard deviations).
The cumulative 100% level is indicated on the right side, at the point where the graph line stops.