Mismeasurements or imprecise measurements have been a concern in various disciplines. The consequence of mismeasurement is degradation of the quality of inference, and mismeasurement itself should be avoided whenever possible. However, in practice, these features are sometimes inevitable. For example, due to the inevitable substantial noises involved with imaging and modeling, there is measurement error associated with the obtained binding potential values used in brain imaging analysis. Motivated by such issues, this dissertation aims to develop better ways to incorporate measurement error into statistical methods. Specifically, this involves three methodology developments on existing and widely used statistical tools: 1) incorporate variable-specific measurement error as weights into the construction of correlation coefficient; 2) explore approaches based on Monte Carlo Simulation to correct for measurement error; 3) generate ROC and its corresponding confidence band using measurement error correction model.
In Chapter 1, we introduce different measurement error models to describe the relationships between the observed error-prone variable and the true but unobservable variable. Due to the generation scheme of the brain imaging data, the specific measurement error models for brain imaging values are specified as the classical additive error model with heteroscedastic variances. In Chapter 2, I define two generalized weighted correlation coefficients with different weights using their measurement error. In Chapter 3, I develop two Monte Carlo simulation-based measurement error correction methods and methods on how to construct the corresponding ROC confidence regions. Extensive simulation studies were conducted to compare performances among different methods under various scenarios. Real data analysis was also performed to illustrate the usage of the proposed methods in practice. In addition, I hope to raise the importance of using a confidence band along with a single ROC curve when presenting it as a visual illustration of the classification ability of biomarkers. With these proposed methods, I hope to provide better understanding on how to incorporate measurement error in analyzing brain imaging data, and to increase the precision of discoveries in brain imaging studies.
|Commitee:||DeLorenzo, Christine, Wu, Song, Zhu, Wei|
|School:||State University of New York at Stony Brook|
|Department:||Applied Mathematics and Statistics|
|School Location:||United States -- New York|
|Source:||DAI-B 80/08(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Statistics|
|Keywords:||Brain imaging data, Measurement error correction|
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