UBC Theses and Dissertations
The design of quantal response experiments and the modelling of quantal response experiments over time Sitter, Randy Rudolf
The problem of designing a quantal response experiment when estimation of the median effective dose (ED50) is of main interest is examined. The asymptotic variances of the maximum likelihood estimators of the ED50 for various 3 and 5 point designs, using the logit model, are compared to the minimum possible which is achieved with an inadvisable 1 point design (Cher-noff). Alternate criteria for choosing a design that attempt to incorporate goodness-of-fit of the model are then examined. The modelling of quantal response experiments observed over time is also considered. A growth-curve approach to this problem was suggested by Carter and Hubert, and applied to a data set. The feasibility of this approach is discussed, and a simpler, more direct approach is proposed. The two models are applied to the presented data set, and the resulting fits are compared. The model proposed here appears to fit the data better. Inference about the ED50 using the two models is also compared.