Genetic association studies have successfully identified many genetic markers associated with complex human diseases and related quantitative traits. However, for most complex diseases and quantitative traits, all associated genetic markers identified to date only explain a small proportion of heritability. Thus, exploring the unexplained heritability in these traits will help us discover novel genetic determinants for these traits and better understand disease etiology and pathophysiology. Due to limited sample size, a single cohort study may not have sufficient power to identify novel genetic association with a small effect size, and meta-analysis approaches have been proposed and applied to combine results from multiple cohorts in large consortia, increasing the sample size and statistical power. Rare genetic variants and gene by environment interaction may both play a role in genetic association studies. In this dissertation, we develop statistical methods in meta-analysis, rare genetic variants analysis and gene by environment interaction analysis, conduct extensive simulation studies, and apply these methods in real data examples. First, we develop a method of moments estimator for the between-study covariance matrix in random effects model multivariate meta-analysis. Our estimator is the first such estimator in matrix form, and holds the invariance property to linear transformations. It has similar performance with existing methods in simulation studies and real data analysis. Next, we extend the Sequence Kernel Association Test (SKAT), a rare genetic variants analysis approach for unrelated individuals, to be applicable in family samples for quantitative traits. The extension is necessary, as the original test has inflated type I error when directly applied to related individuals, and selecting an unrelated subset from family samples reduces the sample size and power. Finally, we derive methods for rare genetic variants analysis in detecting gene by environment interaction on quantitative traits, in the context of univariate test on the interaction term parameter. We develop statistical tests in the settings of both burden test and SKAT, for both unrelated and related individuals. Our methods are relevant to genetic association studies, and we hope that they can facilitate research in this field and beyond.

Obsessive-compulsive disorder (OCD) and the spectrum of associated conditions, affect 2-4% of the population worldwide. Although heritability studies in OCD have shown a 3 - 12 times increased risk for first degree relatives, the identification of the underlying risk-conferring genetic variation using classic genetic association studies has proven to be difficult. The possibility of a larger contribution of rare genetic variants to the risk of psychiatric disorder has been suggested by several successful studies. We expect that a spectrum of risk allele frequencies exists, which includes not only common variation but also a substantial amount of rare genetic variants that contribute to OCD. This thesis is aimed at identifying and functionally characterizing rare genetic variation in the OCD spectrum. Identified statistically significant variants were scrutinized for changes related to synaptic function using high content screening and subsequent functional analyses. Identifying the genetic profile of rare variants found in the OCD spectrum cohort combined with the functional impact that these variants have has provided insight into the etiology of the OCD spectrum. With these approaches a foundation can be laid for the development of a predictive model of the OCD spectrum.

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.