Pharmaceutical Statistics Using SAS

7.4. Regression Models with Unknown Parameters in the Variance Function

In various pharmaceutical applications it is often assumed that the variance of the error term, σ², depends not only on the control variable x, but also on the unknown parameter θ, i.e., σ_i² = S(x_i,θ).

Consider, for instance, the four-parameter logistic model introduced in Section 7.2. The variance of the response variable, Y, may depend on its mean, as in the following power model (Finney, 1976; Karpinski, 1990; Hedayat et al, 1997):

In cell-based assay studies, the response variable is a cell count and is often assumed to follow a Poisson distribution. Under this assumption, ...