Statistical Methods for Temporal Biomedical Data

Abstract

Temporal biomedical data provide critical insights for disease identification, prevention, and treatment by capturing how biological and clinical variables evolve over time. Understanding temporal patterns in patient health records, biomarker fluctuations, and disease progression enables early detection of emerging conditions, informs timely medical interventions, and supports personalized treatment strategies. However, existing statistical methods face challenges in effectively analyzing these complex datasets. This dissertation addresses three key challenges in temporal biomedical data analysis: (1) identifying dynamic, time-dependent effects of risk factors on the outcome while avoiding aggregation that can potentially obscure biologically relevant associations, (2) modeling temporal trends in the presence of excessive zeros, particularly in sparse datasets like single-cell RNA sequencing (scRNA-seq), and (3) detecting and summarizing clinically meaningful temporal patterns. The first project introduces TIDE, a novel method for individual-level scRNA-seq analysis that enhances the accuracy and resolution of dynamic differentially expressed (DE) regions along cell pseudotime. Unlike traditional approaches that focus on global DE gene identification, TIDE provides a more granular view of gene expression changes within regions of pseudotime, making it particularly valuable for studying cellular differentiation, disease progression, and treatment responses. The method employs gene-specific functional principal component regression (FPCR) to model gene expression in relation to the outcome, followed by a permutation test on the estimated coefficient function to obtain time-specific p-values. TIDE demonstrates well-controlled type I error and decent statistical power across different sample sizes and group imbalances. Additionally, TIDE’s flexibility allows for branch-specific analysis within pseudotime structures and the incorporation of individual-level covariates, making it adaptable to diverse experimental designs. While our implementation uses TSCAN-derived pseudotime, TIDE can integrate trajectories from other methods, further enhancing its applicability across single-cell studies. The second project presents a novel statistical method ZISS to handle zero inflation and over-dispersion in scRNA-seq datasets. ZISS consists of two parts: a time-dependent function that models the probability of excessive zeros and another that estimates the mean of the zero-inflated Poisson distribution. To address the challenge of irregularly observed temporal data in existing methods, ZISS employs smoothing spline ANOVA for mean function estimation. B-spline basis functions are used to adaptively model the dynamic zero probabilities over time. ZISS outperforms traditional models in challenging conditions, achieving the lowest mean square error of 0.169 and the smallest standard deviation of 0.009. It excels in high zero-inflation data analysis, and adaptively differentiates between true zeros and technical zeros in scRNA-seq data in simulation studies. Additionally, ZISS maintains consistent accuracy across varying levels of over-dispersion and is versatile enough for applications in other domains involving temporal or spatial data with excessive zeros. The third project applies a cluster-based method to analyze temporal medical data, i.e., corrected QT (QTc) variability, to evaluate disease severity subtypes that complement the severity defined by the traditional metric in patients with obstructive sleep apnea (OSA). We identify a high-risk OSA subtype that more precisely distinguishes cardiovascular disease (CVD)-related mortality risk. Unlike previous metric based on apnea-hypopnea index (AHI) that failed to differentiate mortality risks between moderate and severe OSA, our clustering approach reveals a distinct severe subtype (pattern 2) associated with significantly higher CVD-related mortality compared to other OSA subtypes, including those with mild OSA, no OSA, and those categorized under cluster pattern 1. Furthermore, the severity subtypes detected from temporal records of QTc variability moderate the relationship between the mean QTc and CVD-related mortality, after adjusting for age and gender. This framework provides a more comprehensive understanding of QT variability across different OSA severity levels, offering a novel framework to explore the relationship between QT dynamics and OSA severity.