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Chengcheng Hao
 doctoral thesis 
Explicit Influence Analysis in Crossover Models
Abstract
This dissertation develops influence diagnostics for crossover models. Mixed linear models and generalised mixed linear models are utilised to investigate continuous and count data from crossover studies, respectively.
For both types of models, changes in the maximum likelihood estimates of parameters, particularly in the estimated treatment effect, due to minor perturbations of the observed data, are assessed. The novelty of this dissertation lies in the analytical derivation of influence diagnostics using decompositions of the perturbed mixed models. Consequently, the suggested influence diagnostics, referred to as the deltabeta and varianceratio influences, provide new findings about how the constructed residuals affect the estimation in terms of different parameters of interest.
The deltabeta and varianceratio influence in three different crossover models are studied in Chapters 56, respectively. Chapter 5 analyses the influence of subjects in a twoperiod continuous crossover model. Possible problems with observationlevel perturbations in crossover models are discussed. Chapter 6 extends the approach to higherorder crossover models. Furthermore, not only the individual deltabeta and varianceratio influences of a subject are derived, but also the joint influences of two subjects from different sequences. Chapters 56 show that the deltabeta and varianceratio influences of a particular parameter are decided by the special linear combination of the constructed residuals. In Chapter 7, explicit deltabeta influence on the estimated treatment effect in the twoperiod count crossover model is derived. The influence is related to the Pearson residuals of the subject. Graphical tools are developed to visualise information of influence concerning crossover models for both continuous and count data. Illustrative examples are provided in each chapter.
Keywords: explicit maximum likelihood estimate, generalised mixed linear model, influential observation, perturbation scheme, statistical diagnostics
ISBN 9789176490068
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