Optimization of error spending and power spending in sequentially planned statistical experiments

Optimal sequentially planned statistical experiments are flexible designs where groups of variable sizes are sampled sequentially, and the size of each groups is chosen in an optimal way, based on the already obtained data. Such a flexibility allows to design cost-effective statistical experiments that achieve the same accuracy as the classical, commonly used procedures, but at a lower expected cost. On the other hand, due to its generality and complexity, derivation of the best sequentially planned design is feasible only in a few sufficiently simple situations, because otherwise such computation involves minimization of the cost function over a large and unstructured set of all possible sequentially plans. This dissertation focuses on the development of constructive algorithms that result in cost-efficient sequentially planned statistical experiments. As the main technique, it follows the error spending approach developed that was developed by Slud and Wei (1982) and Lan and DeMets (1983) to provide convenient flexibility of group sizes in group sequential clinical trials. According to a suitably chosen error spending function, a sequential design can be chosen that partitions the overall significance level and the overall power between the interim points of the trial in an optimal way. This dissertation focuses on the construction of optimal error spending and power spending functions for a wide range of sequential tests, aiming to minimize the expected information level, and therefore, the expected sample size and cost, under the given significance level and power. Two different principles of unconditional and conditional boundaries, combined with the idea of binary segmentation of sampled groups in sequential designs lead to the development of two main techniques. Based on the obtained error and power spending functions, the resulting sequentially planned designs achieve the corresponding optimality and result in cost efficiency superior to the commonly used Pocock and O'Brien-Fleming group sequential tests.;Keywords: Error spending; Group sequential methods; Power; Sequential planning; Stopping boundaries.