| Author: | Feng, Anyin |
| Title: | Nonparametric and semiparametric inference for panel count data and distributed regression for brain images |
| Advisors: | Zhao, Xingqiu (AMA) He, Daihai (AMA) Li, Ting (AMA) |
| Degree: | Ph.D. |
| Year: | 2025 |
| Department: | Department of Applied Mathematics |
| Pages: | xiii, 161 pages : color illustrations |
| Language: | English |
| Abstract: | Recent advances in biomedical data analysis demand innovative statistical approaches to handle complex datasets. Researchers face significant challenges in addressing these complexities. This thesis focuses on two types of data: panel count data and brain image data, and provide the framework of statistical analysis for each data respectively. The proportional mean model is the most commonly used approach for modeling the conditional mean function of recurrent events in panel count data. However, violation of the proportional mean assumption may lead to biased estimation and poor predictive performance. Furthermore, existing diagnostic methods for the proportional mean assumption primarily rely on graphical assessments and lack rigorous theoretical justification. In this thesis, we propose a deep extended mean model as a flexible alternative for the analysis of panel count data. The proposed model integrates the proportional mean and accelerated mean models into a unified framework and employs deep neural networks (DNNs) to capture complex nonlinear covariate effects and interactions. We establish theoretical guarantees for the proposed estimator, including nonasymptotic error bounds and asymptotic normality. In addition, we develop a formal hypothesis testing method to evaluate the adequacy of proportional mean model, providing a practical tool for structural assumption testing in clinical and epidemiological studies. Extensive simulation studies and an application to data from a skin cancer chemoprevention trial demonstrate the superior performance of the proposed method. The second part investigates a partially linear additive reversed mean model for panel count data with an informative terminal event. By anchoring at the terminal event, the proposed model focuses on capturing the characteristics of recurrent events prior to the occurrence of the terminal event. The partially linear additive form provides a flexible framework for modeling the covariate effects. We use the B-spline functions to approximate the baseline reversed mean function and the link function. To simplify the optimization of loss function, we treat the distribution function of the terminal event as a nuisance functional parameter and propose a two-stage estimation procedure. We establish the asymptotic properties of the proposed estimator, including the consistency, convergence rate, and asymptotic distribution. Our simulation studies show that the proposed estimator performs well in finite-sample settings. Finally, we illustrate our method with an application to the Chinese Longitudinal Healthy Longevity Survey (CLHLS) study. The last part we consider brain image data and aim to understand how brain regions react to cognitive demands. We introduce distributed tensor regression via fused structure. This method effectively reduces the computational load through distributed computing, while preserving the intrinsic piecewise smoothness structure in the analysis of neuroimaging data. A novel objective function and communication strategy between distributed machines are constructed to ensure that local smoothness in voxel coefficients is maintained in distributed computing. Our data analysis consistently identifies the role of area in the occipital pole and temporal lobe in three touch screen cognitive tasks, duration to complete numeric path and numeric memory on the application of UK Biobank study. It is the first time such results have been identified using MRI with a large sample size. |
| Rights: | All rights reserved |
| Access: | open access |
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