Stepwise hypothesis testing with applications in pharmaceutical responses

by 1973- Gauvin, Jennifer Lynn

GAUVIN, JENNIFER LYNN SHANNON. Stepwise Hypothesis Testing with Applications in Pharmaceutical Responses. (Advisor: Dr. Roger L. Berger) In some studies researchers seek to identify conditions under which a mean response exceeds a specified threshold. This work examines the case in which such conditions are defined in terms of two quantitative independent variables. For example, a pharmaceutical researcher might want to identify what values of dose and post-dose time yield an average blood concentration above a certain threshold. New methods of specifying a rectangular set of (time, dose) values for which the researcher can assert that the mean response exceeds the threshold are described. By using intersection-union tests applied in a stepwise fashion, the methods maintain a specified high probability that the rectangular set contains no (time, dose) values for which the mean response is lower than the threshold. The observations at each (time, dose) value must be independent, but neither method requires independent observations at different (time, dose) values. For example, concentrations measured on a subject at different time points may be correlated. Exact calculations and simulation studies are used to assess the error rates and performance properties of the new methods.