Statistical Analysis of Dose-Response Experiments by Maximum Likelihood Analysis and Iteratively Reweighted Nonlinear Least Squares Regression Techniques

Dose-response studies often form integral parts of pharmacological investigations of drug activity and efficacy and of toxicological investigations of drug and chemical safety. Standardized dose-response study protocols, statistical models, model fitting techniques, and computer programs are widely available for such applications. Many studies however, require nonstandard models and model fitting procedures to adequately describe the resulting data. Maximum likelihood analysis can accommodate a wide variety of model structures in a unified manner. This presentation illustrates how general purpose nonlinear regression analysis routines, such as those that are available in SAS or in BMDP, can be used to obtain maximum likelihood model solutions and associated error analyses for nonstandard model fitting situations. This reduces the need for special purpose computer programs for individual modeling applications. Methodological considerations in the application of nonlinear regression modeling procedures to maximum likelihood estimation are discussed. The methodology is illustrated with several modeling situations.