Pleiotropy refers to the shared effects of a gene or genes on multiple phenotypes, a major reason for genetic correlation between phenotypes. For example, for osteoporosis, bone mineral densities at different skeletal sites may share common genetic factors; thus, examining the shared effects of genes may enable more effective fracture treatments. To date, methods are not available for estimating and testing the pleiotropic effects of single nucleotide polymorphisms (SNPs) in genetic association studies. In this dissertation, we explore two types of methods to evaluate the SNP-specific pleiotropic effect based on multivariate techniques. First, we propose two approaches based on variance components (VC) analysis for family-based studies, which quantify and test the pleiotropic effect by examining the contribution of specific genetic marker(s) to polygenic correlation or covariance of traits. Second, we propose a multivariate linear regression approach for population-based studies with samples of families or unrelated subjects. This method partitions the specific effect of the marker(s) from phenotypic covariance. We evaluate the performance of our proposed methods in simulation studies, compare them to existing multivariate analysis methods and illustrate their application using real data to assess candidate SNPs for osteoporosis-related phenotypes in the Framingham Osteoporosis Study. In contrast to existing methods, our newly proposed approaches allow the quantification of pleiotropic effects. The bootstrap resampling percentile method is used to construct confidence intervals for statistical hypothesis testing. Simulation results suggest that the VC-based approaches are affected by the polygenic correlation level. The covariance analysis approach outperforms the VC-based approaches, with unbiased estimates and better power, which remain consistent regardless of the polygenic correlation. In addition, the covariance analysis approach is simple to implement and can be applied to both family data and genetically unrelated data. Using simulation, we also show that existing methods, such as MANOVA, can have high rejection rates when a SNP has a large effect on a single trait, which prevent us from using them for pleiotropic effect analysis. In summary, this dissertation introduces promising new approaches in multiple phenotypic models for SNP-specific pleiotropic effect.

Die biotechnologischen Entwicklungen der letzten Jahre ermöglichen eine immer detailliertere Untersuchung von genetischen und molekularen Markern mit multiplen komplexen Traits. Allerdings liefern vorhandene statistische Methoden für diese komplexen Analysen oft keine valide Inferenz. Das erste Ziel der vorliegenden Arbeit ist, zwei neue statistische Methoden für Assoziationsstudien von genetischen Markern mit multiplen Phänotypen zu entwickeln, effizient und robust zu implementieren, und im Vergleich zu existierenden statistischen Methoden zu evaluieren. Der erste Ansatz, C-JAMP (Copula-based Joint Analysis of Multiple Phenotypes), ermöglicht die Assoziation von genetischen Varianten mit multiplen Traits in einem gemeinsamen Copula Modell zu untersuchen. Der zweite Ansatz, CIEE (Causal Inference using Estimating Equations), ermöglicht direkte genetische Effekte zu schätzen und testen. C-JAMP wird in dieser Arbeit für Assoziationsstudien von seltenen genetischen Varianten mit quantitativen Traits evaluiert, und CIEE für Assoziationsstudien von häufigen genetischen Varianten mit quantitativen Traits und Ereigniszeiten. Die Ergebnisse von umfangreichen Simulationsstudien zeigen, dass beide Methoden unverzerrte und effiziente Parameterschätzer liefern und die statistische Power von Assoziationstests im Vergleich zu existierenden Methoden erhöhen können - welche ihrerseits oft keine valide Inferenz liefern. Für das zweite Ziel dieser Arbeit, neue genetische und transkriptomische Marker für kardiometabolische Traits zu identifizieren, werden zwei Studien mit genom- und transkriptomweiten Daten mit C-JAMP und CIEE analysiert. In den Analysen werden mehrere neue Kandidatenmarker und -gene für Blutdruck und Adipositas identifiziert. Dies unterstreicht den Wert, neue statistische Methoden zu entwickeln, evaluieren, und implementieren. Für beide entwickelten Methoden sind R Pakete verfügbar, die ihre Anwendung in zukünftigen Studien ermöglichen. / In recent years, the biotechnological advancements have allowed to investigate associations of genetic and molecular markers with multiple complex phenotypes in much greater depth. However, for the analysis of such complex datasets, available statistical methods often don’t yield valid inference. The first aim of this thesis is to develop two novel statistical methods for association analyses of genetic markers with multiple phenotypes, to implement them in a computationally efficient and robust manner so that they can be used for large-scale analyses, and evaluate them in comparison to existing statistical approaches under realistic scenarios. The first approach, called the copula-based joint analysis of multiple phenotypes (C-JAMP) method, allows investigating genetic associations with multiple traits in a joint copula model and is evaluated for genetic association analyses of rare genetic variants with quantitative traits. The second approach, called the causal inference using estimating equations (CIEE) method, allows estimating and testing direct genetic effects in directed acyclic graphs, and is evaluated for association analyses of common genetic variants with quantitative and time-to-event traits. The results of extensive simulation studies show that both approaches yield unbiased and efficient parameter estimators and can improve the power of association tests in comparison to existing approaches, which yield invalid inference in many scenarios. For the second goal of this thesis, to identify novel genetic and transcriptomic markers associated with cardiometabolic traits, C-JAMP and CIEE are applied in two large-scale studies including genome- and transcriptome-wide data. In the analyses, several novel candidate markers and genes are identified, which highlights the merit of developing, evaluating, and implementing novel statistical approaches. R packages are available for both methods and enable their application in future studies.