Graphical models are a family of models commonly used to represent the conditional independence structure among the variables of interest. Directed acyclic graphs (DAGs) provide a representation of the causal relationships and can be helpful for research in Epidemiology and other public health areas. When modeling causal relationships, issues such as effect measure modification and potential unmeasured confounders need to be considered. Recent advances in biomedical research and technology have made more data available, such as multi-omics data, biomarker profiles as well as biological pathway information. Therefore, we developed three graphical models for DAGs to better leverage these versatile data while accounting for effect measure modification and potential unmeasured confounders. First, we generalized a Bayesian graphical regression by Ni et al. (2018). We used a Gaussian copula to connect a latent variable with the multiple types of observed data. The proposed method allows for multiple data types while estimating the graph structure that depends on potential effect measure modification. Simulation studies showed that this proposed method outperforms the method by Ni et al. (2018) when there are multiple data types. Second, we extended the structural factor equation model by Zhou et al. (2021) and proposed an information-aided graphical model. The proposed method can incorporate the group information via the group Lasso penalty while accounting for the potential unmeasured confounders. Simulations demonstrated that the proposed method performs better than the original method that does not incorporate group information. Third, we additionally imposed the within-group sparsity constraint on our second method, yielding both the sparsity of groups and within-group variables while incorporating the group information. The proposed method is shown to be robust against the proportion of variables without effect in a group. We illustrated our proposed methods with data from the Framingham Heart Study to explore the relationships between metabolic syndromes, important inflammation biomarkers, and individual demographic characteristics. We also explored the gene regulatory networks of genes that are related to inflammation and adipose tissue. The findings may offer helpful insights into the mechanisms of metabolic syndrome and patient-specific health management strategies. / 2025-01-23T00:00:00Z

Dimensional rating scale-based scores such as the Beck anxiety inventory (BAI) in general populations often take on right-skewed integer values with many zeros, approximately semi-continuous data. As research outcomes, variables with a large proportion of zeros have been analyzed either ignoring the zeros or categorizing the total scores as binary outcomes. This can result in a loss of information. Two-part regression models typically have been used for analyzing semi-continuous data, with a logistic (or probit) model for the probability of being nonzero and a separate model for the magnitude of nonzero values. There is limited research about statistical model performance on semi-continuous data in integer form. To fill some gaps in statistical knowledge, we addressed model performance in this research. First, we evaluated the effects of rounding in simulation studies on model estimation of the two-part gamma model. We demonstrated that the two-part gamma model has good estimation characteristics when used to analyze semi-continuous outcome data in integer form for scores that include many zeros. Second, we conducted simulation studies to examine the statistical power and type I error rate of two-part gamma model for testing the difference in outcome between two groups; we compared the two-part gamma versus generalized linear models (gamma or log-normal) that add a constant of 1 to values of the outcome variable. The two-part gamma model performed better than the generalized linear model in most settings we considered. Further, we extend the work on type I error rate and power by varying the levels of skewness and introducing log-normal distribution data. With highly skewed data, two-part models performed differently depending upon unequal zero percentage or unequal mean of nonzero values between groups. Similar patterns were observed for simulated log-normal data. Through simulation studies, our research suggests that two-part gamma models may perform better than generalized linear models in analyzing semi-continuous positive-integer data that contain excess zeros.

Alzheimer's disease, and other related dementia diseases, are a worsening issue with an acceleration in today's aging population. Longitudinal cognitive assessment of those suffering from dementia offers vital insight into disease progression and allows for assessment of possible disease interventions. Difficulty in modeling such data arises as there are often non-linear and heterogenous patterns of decline from patient to patient. We propose the use of state space models (SSM), specifically a Local Linear Trend (LLT) model, as an alternative to the commonly used linear mixed effect models (LMEM) for longitudinal assessments. The proposed model includes the estimation of interpretable population linear effects on the outcome, while also allowing for subject-specific non-linearities in cognitive trajectories. To fit the LLT model, we utilize the traditional full likelihood estimation using the Kalman Filter and Kalman Smoother. We also compare the use of a partitioned LLT and a Bayesian LLT for computational efficiency. In two separate simulation analyses, we show the advantages of the LLT models over the predominant techniques. We go on to show that of the LLT methods, the Bayesian LLT excels. The LLT models are then used to estimate the effect of the APOE e4 allele on cognitive trajectory. Running the LLT on a single outcome provides accurate estimation of linear effects, but multiple tests are often offered for better understanding of different cognitive domains. To gain a more thorough understanding of cognition and how it relates to Alzheimer's disease we propose the use of a multivariate local linear trend model (MLLT), which simultaneously models linear effects for multiple tests, while also measuring inter-correlation of the underlying cognitive state between tests. Lastly, we propose a factor MLLT (FMLLT) to clarify underlying factors of cognition. The FMLLT can be utilized in both a structured and unstructured approach. These tools are shown to provide a flexible and accurate framework for analyzing longitudinal neuropsychological data.

Our ultimate goal is to better understand the biological mechanisms that lead to disease pathogenesis, by investigating the regulatory and mediating processes across multiple layers of biological processes. Recent advances in high-throughput technologies have generated an unprecedented amount of multi-omics data. Multi-omics measurements, including genomics data such as genotype and copy number variation (CNV), transcriptomics data such as messenger ribonucleic acid (mRNA) and microRNA expression, as well as epigenomics data such as deoxyribonucleic acid (DNA) methylation, have been traditionally analyzed separately. Multi-omics measurements profiled on different layers of biological processes are interconnected and the biological features identified on different layers influence clinical outcomes at different levels. Integrative analysis borrows strength across multiple levels of omics data by incorporating the regulatory relationship. This could substantially increase the power to reveal the underlying biology of the associations. This dissertation includes 3 projects on multi-omic data integration. In project 1, we propose a novel approach for clustering gene expression with the information from gene regulators that are measured on different but overlapping samples. This allows integration of multiple types of omics data from different but overlapping samples. Genes with similar expression patterns under various conditions may imply co-regulation or relation in functional pathways. In project 2, we study the causal relationships between omics layers and complex traits using association summary statistics as data in multivariable Mendelian randomization (MVMR) and extend the Mendelian Randomization Pleiotropy RESidual Sum and Outlier (MR-PRESSO) method to detect horizontal pleiotropy in the MVMR setting. In project 3, we further optimize the MVMR-PRESSO method so that it yields higher power to detect horizontal pleiotropy under situations of directional pleiotropy – when effects of pleiotropic genetic variants on the outcome are distributed with a non-zero mean. All of these approaches will facilitate the integration of multi-omics data and lead to a better understanding of biological mechanisms underlying complex diseases.

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