Inference and Design Strategies for a Hierarchical Logistic Regression Model

Inference and Design Strategiesfor a Hierarchical Logistic Regression Mo delMerlise ClydePeter MullerandGiovanni ParmigianiInstitute of Statistics and Decision SciencesDuke University Durham NC AbstractThis chapter fo cuses on Bayesian inference and design in binary regression exp eriments As a casestudywe consider heart debrillator exp eriments in which the numb er of observations that can b etaken is limited and it is imp ortant to incorp orate all available prior information In particular bymo deling the individualtoindi vi dual variation in the appropriate debrillation setting we can useinformation on past patients in formulating a sensible prior distribution for designing exp erimentsfor current patients The rst part illustrates the use of hierarchical mo dels to obtain such priordistributionsThe second part of the chapter considers design strategiesAn imp ortantadvantage of aBayesian technique is that it is conceptually easy to adapt to information that accrues sequentially This is particularly desirable when early stopping of the exp erimentation is of interest Ingeneral analytic expressions for optimal sequential solutions are not available and a combinationof approximation techniques and numerical computation must b e used Here we fo cus on ndingoptima within restricted sets of strategies We compare an adaptive strategy based on xed p ercentage changes in the energy levels and variable sample size with a strategy in which all levelsare chosen optimally but the sample size is xed