Bayesian sequential methods in clinical trials

Abstract

Bayesian techniques allow the design of flexible and adaptive trials. This flexibility is given by accepting the Likelihood principle, which is presented in the first chapter, that shows equivalence to the Conditionality principle. The second chapter introduces the Bayesian foundations and finishes with an introduction into hierarchical Bayesian modeling. Latter permits inference about the efficiency of treatments on rare diseases with many subgroups and/or by including patients from multiple clinics into the study. Additionally, a coherent combination of multiple studies is possible in this framework. The third chapter covers decision theory and the intrinsically linked Bayesian hypothesis testing. It further shows some modeling tools available to the statisticians. The fourth chapter presents Bayesian sequential decision theory. Backward induction a method to find an optimal procedure is used to deduce the widely known sequential probability ratio test. This chapter concludes with the introduction of predictive probabilities and the corresponding clinical trial design. The temporal classification is used in the fifth chapter to introduce the reader into clinical trials. The work completes with exemplary clinical studies. A decision theoretical design optimize the simultaneous run of many phase \RM{2} studies in one center is presented in detail. Furthermore, a lung cancer trial designed with predictive probabilities is described. Lastly, accrual of patients for trials on the treatment of rare diseases like sarcomas is challenging. A design that uses hierarchical Bayes to analyze a treatment for twelve different sarcomas is shown.