Antagonism and synergism detection in multidimensional quantal response surfaces

• Main Author: Parks, Thomas P
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-1998
• Subjects: Biostatistics; Statistics; Toxicology
• ISBN: 0599048751; 9780599048751

In this dissertation methods described in the literature to model and test for antagonism, synergism and independence (ASI) are reviewed. Stochastic approximation techniques applied to a radial design are investigated for determining ASI by estimating a contour of constant probability. Monte Carlo error estimates are calculated to determine regions where ASI can be determined. This work appears to be the first successful application of stochastic approximation to this problem. A review and comparison of stochastic approximation techniques is presented. Additionally, two new stochastic approximation techniques are introduced along with some variants. One of these, the Gamma method, was second in performance only to Kesten's method when Kesten used a sample size of one. When the larger sample size used by the Gamma method was applied to Kesten's technique, the Gamma method outperformed it. Surface estimation was also studied in the presence of ASI. Parameter estimates, error estimates and bias are calculated using Monte Carlo simulations. With small samples at each set of stimuli levels, a need for bias correction was observed. Hypothesis tests of model form for a particular experiment are described. Model comparisons were made using maximum likelihood estimates of several model forms calculated for a single simulated data set. Generalized likelihood ratio statistics were calculated to perform these comparisons. In this dissertation, the response probability model is multiplicative whereas much of the literature focuses on additive models. A Farlie-Gumbel-Morgenstern (FGM) distribution was used in the probability model. The results indicate that use of the FGM family is limited and only slightly effective. Other models should be considered for future work. Lastly, it was observed that calculating numerical maximum likelihood estimates is difficult in this application. The surface complexities often caused failure of the SAS/IML optimization routines.