Sample size reduction approach in experimental designs: Basket design

In this thesis, minimum and maximum sample size were investigated in the sample size results obtained from Bayesci Basket Design (BST) methods, which started to direct the drug development process with the development of personalized medicine with Simon's Optimal Two Stage Design (SOT), which is frequently used in the early stage clinical studies of drug development research. In the study, 9 scenarios belonging to SOT were defined using the minimum probability of success required for active acceptance of the drug (p1), maximum probability of failure required for accepting the drug useless (p0) and error rates of type-I and type-II. For BST, 27 scenarios were created using p0, p1, the number of baskets (K), the probability of the baskets to be fully correlated (λ) and the preliminary probability (γ) of drug activation in any basket. In MCT, 1000 MCMCs were repeated for each scenario. The maximum sample size for both designs is limited to 100. The scenarios giving the smallest and largest sample size in each scenario are specified in the tables. It was observed that the sample size decreased when p1-p0 difference increased in SOT, and the sample size were lowest when (λ = 0.1; γ = 0.1) and (λ = 0.8; γ = 0.8) in BST. When both designs were compared (λ = 0.5; γ = 0.5), it was determined that SOT calculated the sample size lower than BST, otherwise BST should be used. In this study, it was concluded that using the SOT method may be more useful in cases where the sample size per basket in the BST method is less than the SOT method, but the a priori information is moderate.