Experimental Designs Based on Weighted Differential Entropies in Clinical Trials

The problem of finding "the best" among a number of alternatives is one of the main in Statistics. In clinical trials this can be stated in the form of the question: which arm is the most efficacious for a certain disease treatment? Clinical trials is a procedure that allows to answer this question with a certain degree of confidence. Consider a set of p alternative arms {A1,...,Ap}, and n patients {x1,...,xn} (experimental sample). Experimental design in clinical trials is an algorithm that governs allocation of an arm from the set {A1,...,Ap} to each patient {x1,...,xn}. Performance of experimental design is measured by a set of criteria which depends on the Phase of clinical trials and other details of the experiment. In this thesis, based on the ideas of recent researches, author derives a number of new experimental designs which utilize information gain principle. The proposed designs are compared to currently widespread alternatives in a comprehensive simulation study.