Usage of hypothesis testing methods for the equivalence of covariance matrices in dementia outcome analysis
OA Version
Citation
Abstract
Dementia and its most common form Alzheimer's disease (AD) are urgent yet complicated problems to decipher and as such predictive modeling for AD outcomes attracted researchers' attention for years. Numerous works in literature have identified categories of predictors that are linked to AD such as inflammatory cerebrospinal fluid (CSF) biomarkers and brain MRI measurements. A major contribution of the thesis is introducing covariance structures as a tool to signify AD. In clinical settings, it is often imperative to account for demographic covariates as potential confounding factors. We explore two ways to account for these covariates: one by removing their effects via partial covariance and the other by calculating the covariance matrices for given values of covariates via function covariance matrix estimators. For both covariance estimating methods we use hypothesis testing methods to determine if the covariance estimates are significantly different between AD outcome groups. These methods are the parametric Tracy-Widom, the semi-parametric Forkman's test, and the nonparametric Permutation method. We evaluate the utility of the covariance estimation as well as the hypothesis testing methods via extensive simulation studies. Additionally, we apply these methods to real world data studies such as the FHS and the ADNI. Moreover, we explore the scenario where the cases are rare compared to the controls in a binary outcome (\textit{aka} rare event), as often the case in bio-medical application such as AD data. The imbalance between the outcomes has been shown to introduce bias in the estimation of the model parameters, which in turn affects the predictive probabilities. The problem becomes more severe as the imbalance becomes starker, therefore methods that adjust for the imbalance could be beneficial in such situations. As part of the thesis, we explore the adequacy of logistic regression model which is known to suffer from the problem of bias in rare event cases. Additionally, we evaluate derivative methods that aim to compensate for rare event cases such as prior correction, weighting, Firth’s logistic regression, FLIC, and FLAC using the ADNI data set. Our investigation into the performances of the various methods show that the weighting method provides a significant improvement in the predictive utility of the regression model.
Description
2024
License
Attribution-NoDerivatives 4.0 International