One approach to estimating the number of cells with high growth potent
ial in a cancer patient is the assessment of tumor cell colony formati
on in semisolid medium. A potential indicator of the clinical response
to a specific drug is the capacity of the drug to reduce the formatio
n of cell colonies. Often, a Poisson log-linear model provides an adeq
uate representation of the dose-response curve. This model is then sum
marized by the dose required to reduce the number of colonies to a pre
determined percentage of the maximum growth. But more general models a
re needed to account for the overdispersion and the resistant subpopul
ations often present in these assays. This article explores alternativ
e methods for selecting the dose levels to obtain precise estimates of
the parameters of interest. Optimal dose allocations for a single pat
ient or a group of patients are derived. Methods to incorporate the in
formation from pilot studies are discussed. A study of drug sensitivit
y with leukemia patients provides the framework and motivation for the
problem.