Efficient Designs for Cyclic Data Generated by Multivariate Harmonic Mixed Models

dc.contributor.advisorRoy, Anindya
dc.contributor.authorYe, Aijun
dc.contributor.departmentMathematics and Statistics
dc.description.abstractThe primary focus of this dissertations is to design efficient data collection schemes (including pooling bio-specimens, subsampling and combining laboratory and monitor data) for longitudinal studies, particularly in medical fields where repeated cyclical patterns over time are expected in the model response. Motivation of the work comes from the need for efficient designs in the expensive medical studies where collection of data at regular frequency may not be feasible due to budget constraints. Throughout the dissertations we use multivariate mixed-effects exponential harmonic models to mimic the cyclical evolution of biomarkers and individual varia-tion. We propose to optimize objective criteria related to efficiency of parameter estimation, such as D-optimality, with respect to pooling and sampling design. Due to analytical intractability, we mostly rely on numerical optimization to devise sensible schemes for finding effective study designs. We apply the optimal design to the BioCycle data. We propose a combined model to use both monitor and laboratory data to improve the efficiency of the design. The laboratory measurements are more accurate than the monitor ones. Because the accuracy of the laboratory measurements is higher than that of the monitor measurements, when we combine the monitor and laboratory measurements, the efficiency is improved compared to using just monitor data. The efficiency of optimal design based on combined measurements close to that of designs with similar cost and using only laboratory measurements, and much higher than those using equally spaced laboratory measurements. We apply the combined design to the EAGeR study. The combined design improves the efficiency compared to using only laboratory measurements for the luteinizing hormone (LH). For designs using pooled bio-specimens, we add a novel aspect by incorporating a fatigue model to the data preparation process. We explicitly model the heteroscedasticity of the error of the pooling volume under pooling design using Hill type models. We study the efficiency for small and large pooling procedures. We investigate the evolution of the relative efficiency over pooling size and discuss the relative gain from pooling in terms of cost. We apply our approach to the EAGeR data. The results indicate definitive improvement that are obtained from pooling designs for longitudinal studies with cyclical mean response.
dc.relation.isAvailableAtThe University of Maryland, Baltimore County (UMBC)
dc.relation.ispartofUMBC Mathematics and Statistics Department Collection
dc.relation.ispartofUMBC Theses and Dissertations Collection
dc.relation.ispartofUMBC Graduate School Collection
dc.relation.ispartofUMBC Student Collection
dc.sourceOriginal File Name: Ye_umbc_0434D_11905.pdf
dc.titleEfficient Designs for Cyclic Data Generated by Multivariate Harmonic Mixed Models
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