BENCHMARK DOSES

A benchmark dose is a characterization of the dose corresponding to a specified increase in the probability of a specified response.  For example, an ED₁₀ is the estimated dose corresponding to an increase of 0.10 in the probability of the specified response relative to the probability of that same response at dose zero.  Similarly, an ED₀₅ is the estimated dose corresponding to an increase of 0.05 in the probability of the specified response relative to the probability of that same response at dose zero.  A graphical illustration of the definitions of ED₁₀ and ED₀₅ is given in Figure 13.

If

P(d) = probability of the specified response at dose d

then

P(ED₁₀) - P(0) = 0.10

and

P(ED₀₅) - P(0) = 0.05.

The ED₁₀ or ED₀₅ depend upon the specified response of concern.  For example, the specified response might be malignant lung carcinomas.  The ED₁₀ also depends on the population in which the probability of the specified response is being observed.  For example, if an animal bioassay has been conducted using male B6C3F1 mice, then the ED₁₀ for this population is the dose that causes the probability of a malignant lung carcinoma in male B6C3F1 mice to increase from its background value to its background value plus 0.10.  For a different example, if human workers were being observed for malignant lung carcinomas in a human epidemiology study, then the ED₁₀ for this population is the dose that causes the probability of a malignant lung carcinoma in human workers to increase from its background value to its background value plus 0.10. 

Both ED₁₀ and ED₀₅ are estimated doses calculated, for example, using the maximum likelihood estimates of the probability of a specified response in a dose-response model (like the multistage dose-response model).  The benchmark dose could be defined to be either ED₁₀ or ED₀₅.  Although both ED₁₀ and ED₀₅ have been proposed as candidates for the benchmark dose, the ED₁₀ is usually a dose level closer to the dose levels actually observed in the experimental data and hence is probably the leading candidate to be defined as the benchmark dose.

It has sometimes been proposed that the benchmark dose be defined in terms of a lower bound (rather than a maximum likelihood estimate) for the dose corresponding to a specified increase in the probability of a specified response.  For example, an LED₁₀ is the lower bound on the dose corresponding to an increase of 0.10 in the probability of the specified response relative to the probability of that same response at dose zero.  The definition of the LED₁₀ and its relation to the ED₁₀ is illustrated in Figure 14.  The LED₁₀ in Figure 14 is a lower bound on the dose corresponding to an increase of 0.10 in the probability of a specified response and is calculated using the upper bounds on risk in the linearized multistage model.  The ED₁₀ in Figure 14 is a maximum likelihood estimate of the dose corresponding to an increase of 0.10 in the probability of a specified response and is calculated using the maximum likelihood estimates of risk in the multistage model. 

Because the ED₁₀ is more directly related to the observed dose-response relationship than the LED₁₀ and the ED₁₀ does not require any complex statistical confidence limit procedures to calculate, the recommendation is frequently made to use the ED₁₀ instead of the LED₁₀ as the benchmark dose.

>> Figure 14