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Abstract
Because treatments can be compared on the same subject and fewer subjects are needed to obtain the same number of observations as in a parallel trial, crossover designs have been applied extensively in various fields. With the development and application of crossover designs, researchers realized that one serious potential problem involved in their use is the presence of carryover effects. In this dissertation, in order to capture the variabilities due to different direct and carryover treatments, we propose a model that includes interactions of subject by treatment and subject by carryover effects. We assume subject effects to be random, and therefore take these interaction terms to be random too. We study the identifiability properties of the corresponding variance components and the conditions under which the parameters of the model are identifiable. The REML estimation method for those variance components and other model parameters is also considered. Some special cases and practical applications of this model are studied as well. A second objective of this dissertation is to investigate appropriate ways to handle baseline measurements in crossover studies in different situations. Four different methods are considered to incorporate the baseline measurements in the 2x2 crossover design for both single measurements and repeated measurements. Analytical expressions of variances of the estimators of the treatment contrast from those methods are derived and compared under different scenarios. Simulation studies are conducted to evaluate the performance of each method when the variance components are unknown. For the case of repeated measurements, graphical methods are discussed to study the change in treatment effect over time; different types of baselines and different assumptions for the random error terms are also considered. The methods are applied to real data analysis. Designs with more than two treatments are discussed briefly.