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Topics in Regression Splines: Dynamic Network Construction and Optimal Treatment Selection


This thesis is concerned with spline techniques for nonparametric and semiparametric regression.

First, we study the relationships between phenotypes across taxa under different environmental conditions. The correlation/network structure of taxa can be affected by the disease-associated environmental conditions. Besides, taxa abundance is differentiated under conditions. Therefore, knowing how the correlation or relative abundance changes with these factors would be of great interest to researchers. We develop a nonparametric regularized regression method to construct dynamic taxa association networks under different clinical conditions. We also use a varying coefficient model to estimate taxa abundance to see how it changes across different environmental conditions. Moreover, for conducting inference, we propose a bootstrap method to construct the simultaneous confidence bands for inferring the nonparametric functions. We perform simulations to check the performance of the proposed method in identifying the dynamic network structures, and the results are generally better than other existing graphical method. As such, the proposed method has potential applications for researchers to construct differential networks and to identify taxa.

The second part of the thesis considers how to select optimal treatment for patients using a large number of baseline covariates. Based on causal inference framework, we develop a new semiparametric model representing the heterogeneous treatment effect. We use this model to estimate the covariate-specific treatment effect curve and the corresponding simultaneous confidence bands to make individualized treatment decision rule. In particular, we use the B-spline approximation to obtain point estimators and construct the bands via spline-backfitted kernel smoothing. We provide asymptotic theory and simulation studies demonstrating the performance of our proposed selection procedure. We also illustrate the application of the proposed method in a clinical trial on migraine treatment.

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