Research On Statistical Problems In Four-period Crossover Trials

Crossover design trial is commonly used in clinical research.Statistical analyses of crossover clinical trials have mainly focused on assessing the treatment effect,carry-over effect,and period effect.When a treatment-by-period interaction is plausible,it is important to test such interaction first before making inferences on differences among in-dividual treatments.Considerably less attention has been paid to the treatment-by-period interaction,which has historically been aliased with the carryover effect in two-period or three-period designs.In this dissertation,from the data of a brand new four-period crossover design,we propose a statistical method to compare the effects of two active drugs with respect to multiple responses.We study estimation and hypothesis testing considering the treatment-by-period interaction.Constrained least squares is exploited to estimate the treatment effect,period effect,and treatment-by-period interaction.For hypothesis testing,we extend a general multivariate method for analyzing the crossover design with multiple responses.Results from simulation studies have shown that this method performs very well.In addition,the proposed method is applied to the real data of crossover trials for hypertension drugs conducted by Fuwai hospital to compare the effects of two active drugs.The linear mixed effects model is commonly used in longitudinal data analysis.In high-dimensional cases,it is particularly important to select effective fixed effects and random effects.Shrinkage methods are often used to select fixed effects and random ef-fects by frequentists,however,the choice of penalty parameters is more complicated.On the other hand,there is less research on the simultaneous selection of fixed effects and random effects by Bayesians in the literature.In this dissertation,a Bayesian hierarchi-cal model is established to select fixed effects and random effects simultaneously in the linear mixed effects model.Modified Cholesky decomposition is used to reparametrize the linear mixed effects model and the model is transformed into a linear form of the un-known parameters of covariance matrix for random effects.Using the idea of spike and slab prior,we assign mixture of normal priors and the mixture of truncated normal priors to fixed effects and random effects corresponding parameters respectively to select active variables.In order to ensure the consistency of the selection,the choice of the prior dis-tribution parameters is related to the sample size,and the selection consistency of fixed effects is proved under certain conditions for the model.We conduct Monte Carlo sim-ulation to evaluate the proposed selection method.We also apply the selection method to the real data of clinical trials for hypertension drugs conducted by Fuwai hospital and select the active explanatory variables.The main contributions made by this dissertation are as follows:·For a brand new four-period crossover design,we proposed a unified,effective and robust test procedure for both cases of single response and multiple responses,taking into account the treatment-by-period interaction;·From the Bayesian perspective,we proposed a Bayesian variable selection method for simultaneous selection of fixed and random effects in mixed effects models;·We used the modified Cholesky decomposition to reparametrize the mixed model so that the model could be expressed as a linear form of the covariance parameters for random effects,which was convenient for the posterior calculation using the MCMC method.